-FHm2pQmiSM.txt

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the following content is provided under

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the following content is provided under
 

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the following content is provided under
a Creative Commons license your support

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a Creative Commons license your support
 

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a Creative Commons license your support
will help MIT open courseware continue

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will help MIT open courseware continue
 

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will help MIT open courseware continue
to offer highquality educational

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to offer highquality educational
 

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to offer highquality educational
resources for free to make a donation or

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resources for free to make a donation or
 

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resources for free to make a donation or
view additional materials from hundreds

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view additional materials from hundreds
 

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view additional materials from hundreds
of MIT courses visit mitop courseware at

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ocw.mit.edu everybody would like to

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ocw.mit.edu everybody would like to
 

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ocw.mit.edu everybody would like to
believe that they just simply sort of

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believe that they just simply sort of
 

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believe that they just simply sort of
think about the subject a little bit and

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think about the subject a little bit and
 

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think about the subject a little bit and
it'll come to them it's kind of like the

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it'll come to them it's kind of like the
 

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it'll come to them it's kind of like the
osmosis theory of learning but in fact

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osmosis theory of learning but in fact
 

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osmosis theory of learning but in fact
the way you get good at something is

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the way you get good at something is
 

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the way you get good at something is
practicing it's the same for music it's

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practicing it's the same for music it's
 

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practicing it's the same for music it's
the same for sports it's the same for

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the same for sports it's the same for
 

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the same for sports it's the same for
academics so the way you get good in

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academics so the way you get good in
 

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academics so the way you get good in
this subject is to work on the homework

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this subject is to work on the homework
 

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this subject is to work on the homework
we'll give two kinds of

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we'll give two kinds of
 

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we'll give two kinds of
homework there will be conventional

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homework there will be conventional
 

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homework there will be conventional
kinds of problems followed by

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kinds of problems followed by
 

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kinds of problems followed by
engineering design

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engineering design
 

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engineering design
problems the conventional kinds of

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problems the conventional kinds of
 

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problems the conventional kinds of
problems are intended to be the kinds of

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problems are intended to be the kinds of
 

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problems are intended to be the kinds of
problems

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problems
 

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problems
that have simple

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that have simple
 

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that have simple
unambiguous easily checkable

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unambiguous easily checkable
 

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unambiguous easily checkable
answers so well-defined problem single

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answers so well-defined problem single
 

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answers so well-defined problem single
unambiguous

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unambiguous
 

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unambiguous
answer uh the kinds of problems that you

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answer uh the kinds of problems that you
 

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answer uh the kinds of problems that you
might be expecting to see on an exam for

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might be expecting to see on an exam for
 

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might be expecting to see on an exam for
example but then we'll also have uh

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example but then we'll also have uh
 

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example but then we'll also have uh
engineering design problems engineering

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engineering design problems engineering
 

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engineering design problems engineering
design problems are intended to

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design problems are intended to
 

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design problems are intended to
be a little more ambitious a little more

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be a little more ambitious a little more
 

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be a little more ambitious a little more
fun a little harder

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fun a little harder
 

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fun a little harder
Perhaps Perhaps not completely well

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Perhaps Perhaps not completely well
 

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Perhaps Perhaps not completely well
specified sort of more like the kind of

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specified sort of more like the kind of
 

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specified sort of more like the kind of
a problem that your boss might give you

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a problem that your boss might give you
 

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a problem that your boss might give you
after you've

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after you've
 

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after you've
graduated so part of the exercise will

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graduated so part of the exercise will
 

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graduated so part of the exercise will
be figuring out exactly how to convince

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be figuring out exactly how to convince
 

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be figuring out exactly how to convince
somebody that you got the right answer

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somebody that you got the right answer
 

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somebody that you got the right answer
so those kinds of problems are often the

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so those kinds of problems are often the
 

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so those kinds of problems are often the
it will often be the case that numerics

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it will often be the case that numerics
 

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it will often be the case that numerics
will help you in making an

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will help you in making an
 

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will help you in making an
argument so it's often will be the case

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argument so it's often will be the case
 

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argument so it's often will be the case
that we'll ask you to plot something or

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that we'll ask you to plot something or
 

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that we'll ask you to plot something or
maybe you just decide that a plot is the

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maybe you just decide that a plot is the
 

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maybe you just decide that a plot is the
most effective way to communicate your

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most effective way to communicate your
 

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most effective way to communicate your
result we are completely Ambi ambivalent

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result we are completely Ambi ambivalent
 

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result we are completely Ambi ambivalent
about what programming language we that

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about what programming language we that
 

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about what programming language we that
you use since uh 601 and 602 are

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you use since uh 601 and 602 are
 

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you use since uh 601 and 602 are
prerequisites we assume you all know

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prerequisites we assume you all know
 

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prerequisites we assume you all know
python so all the examples that I give

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python so all the examples that I give
 

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python so all the examples that I give
in lecture handouts or in homework

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in lecture handouts or in homework
 

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in lecture handouts or in homework
solutions will be in Python but if you'd

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solutions will be in Python but if you'd
 

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solutions will be in Python but if you'd
rather use mat lab I just don't care

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rather use mat lab I just don't care
 

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rather use mat lab I just don't care
okay we're completely ambivalent about

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okay we're completely ambivalent about
 

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okay we're completely ambivalent about
what programming language you use but it

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what programming language you use but it
 

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what programming language you use but it
will be important that in some of the

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will be important that in some of the
 

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will be important that in some of the
problems you'll find that useful to be

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problems you'll find that useful to be
 

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problems you'll find that useful to be
able to to um generate a numerical kind

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able to to um generate a numerical kind
 

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able to to um generate a numerical kind
of

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of
 

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of
solution these are very different kinds

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solution these are very different kinds
 

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solution these are very different kinds
of problems and to help you with both of

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of problems and to help you with both of
 

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of problems and to help you with both of
them we have a different idea about

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them we have a different idea about
 

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them we have a different idea about
each so to help you with the

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each so to help you with the
 

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each so to help you with the
conventional problems the kind that have

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conventional problems the kind that have
 

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conventional problems the kind that have
precise

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precise
 

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precise
easy to Che answers we've developed for

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easy to Che answers we've developed for
 

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easy to Che answers we've developed for
the first time ever over the summer a

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the first time ever over the summer a
 

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the first time ever over the summer a
tutor type environment for

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tutor type environment for
 

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tutor type environment for
63 so this was intended to be like the

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63 so this was intended to be like the
 

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63 so this was intended to be like the
tutor environment that we use in 601

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tutor environment that we use in 601
 

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tutor environment that we use in 601
it's one of the more popular aspects of

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it's one of the more popular aspects of
 

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it's one of the more popular aspects of
61 the fact that you can put in an

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61 the fact that you can put in an
 

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61 the fact that you can put in an
answer and hit the button that says

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answer and hit the button that says
 

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answer and hit the button that says
check okay so we're going to have one of

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check okay so we're going to have one of
 

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check okay so we're going to have one of
those so the idea is going to be that in

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those so the idea is going to be that in
 

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those so the idea is going to be that in
the case that we ask you a simple

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the case that we ask you a simple
 

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the case that we ask you a simple
question that has a pre precise answer

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question that has a pre precise answer
 

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question that has a pre precise answer
we'll use a tutor environment to let you

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we'll use a tutor environment to let you
 

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we'll use a tutor environment to let you
check your answer to see if you got the

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check your answer to see if you got the
 

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check your answer to see if you got the
right answer in the case of the

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right answer in the case of the
 

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right answer in the case of the
engineering design problems that won't

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engineering design problems that won't
 

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engineering design problems that won't
be the case it will not be the case that

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be the case it will not be the case that
 

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be the case it will not be the case that
it's very easy at all to think about a

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it's very easy at all to think about a
 

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it's very easy at all to think about a
computer program that would check

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computer program that would check
 

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computer program that would check
you so the alternative is going to be

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you so the alternative is going to be
 

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you so the alternative is going to be
that we will have extended office

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that we will have extended office
 

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that we will have extended office
hours so we're going to have something

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hours so we're going to have something
 

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hours so we're going to have something
that I think of as open or Block office

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that I think of as open or Block office
 

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that I think of as open or Block office
hours Monday and Tuesday afternoon and

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hours Monday and Tuesday afternoon and
 

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hours Monday and Tuesday afternoon and
early evening we've reserved the

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early evening we've reserved the
 

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early evening we've reserved the
basement of sta

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basement of sta
 

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basement of sta
32044 for use of this class the idea

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32044 for use of this class the idea
 

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32044 for use of this class the idea
being that that's a nice space you can

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being that that's a nice space you can
 

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being that that's a nice space you can
just come there to work anytime you want

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just come there to work anytime you want
 

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just come there to work anytime you want
to hopefully because it's

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to hopefully because it's
 

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to hopefully because it's
nice and hopefully because you all know

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nice and hopefully because you all know
 

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nice and hopefully because you all know
that there will be other 63 people there

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that there will be other 63 people there
 

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that there will be other 63 people there
you'll just decide that's a good place

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you'll just decide that's a good place
 

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you'll just decide that's a good place
to work and that's convenient because in

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to work and that's convenient because in
 

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to work and that's convenient because in
these engineering design problems if you

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these engineering design problems if you
 

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these engineering design problems if you
run into something that's unclear to you

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run into something that's unclear to you
 

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run into something that's unclear to you
we don't really want you to spend an

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we don't really want you to spend an
 

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we don't really want you to spend an
hour pondering what was being

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hour pondering what was being
 

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hour pondering what was being
asked so we want to make it easy for you

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asked so we want to make it easy for you
 

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asked so we want to make it easy for you
to get

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to get
 

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to get
help and you can get help from peers

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help and you can get help from peers
 

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help and you can get help from peers
from other students who are there but

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from other students who are there but
 

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from other students who are there but
we'll also make sure that there's at

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we'll also make sure that there's at
 

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we'll also make sure that there's at
least one six3 staff member there all

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least one six3 staff member there all
 

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least one six3 staff member there all
the

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the
 

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the
time okay so the homeworks will be due

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time okay so the homeworks will be due
 

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time okay so the homeworks will be due
on Wednesday that's the Strategic value

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on Wednesday that's the Strategic value
 

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on Wednesday that's the Strategic value
of Mondays and Tuesdays so that you can

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of Mondays and Tuesdays so that you can
 

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of Mondays and Tuesdays so that you can
uh use that time to get ready for

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uh use that time to get ready for
 

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uh use that time to get ready for
turning in the homework on Wednesday

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turning in the homework on Wednesday
 

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turning in the homework on Wednesday
questions or

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comments okay we're required to say

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comments okay we're required to say
 

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comments okay we're required to say
something about what we mean by a

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something about what we mean by a
 

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something about what we mean by a
collaboration policy so in this course

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collaboration policy so in this course
 

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collaboration policy so in this course
we would like you to talk to each other

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we would like you to talk to each other
 

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we would like you to talk to each other
and help each other figure out what's

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and help each other figure out what's
 

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and help each other figure out what's
going

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on at the same time we'd like to reward

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on at the same time we'd like to reward
 

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on at the same time we'd like to reward
you for being on the honest Side by

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you for being on the honest Side by
 

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you for being on the honest Side by
which I'm going to mean if you sign your

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which I'm going to mean if you sign your
 

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which I'm going to mean if you sign your
name to something you actually did it

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so we'd like to believe that the

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so we'd like to believe that the
 

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so we'd like to believe that the
homework that you turn in under your

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homework that you turn in under your
 

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homework that you turn in under your
name you

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name you
 

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name you
did you're perfectly welcome to talk to

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did you're perfectly welcome to talk to
 

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did you're perfectly welcome to talk to
each other to talk to the staff to talk

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each other to talk to the staff to talk
 

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each other to talk to the staff to talk
to friends who took this course

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to friends who took this course
 

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to friends who took this course
previously get all the help you like in

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previously get all the help you like in
 

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previously get all the help you like in
trying to understand the concepts but

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trying to understand the concepts but
 

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trying to understand the concepts but
when it comes down to writing up your

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when it comes down to writing up your
 

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when it comes down to writing up your
homework and turning it in we expect

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homework and turning it in we expect
 

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homework and turning it in we expect
that what you signed your name to is

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that what you signed your name to is
 

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that what you signed your name to is
something you did if you got especially

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something you did if you got especially
 

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something you did if you got especially
large amount of help at the conceptual

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large amount of help at the conceptual
 

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large amount of help at the conceptual
level we we'd like you to acknowledge

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level we we'd like you to acknowledge
 

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level we we'd like you to acknowledge
that you don't need to acknowledge that

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that you don't need to acknowledge that
 

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that you don't need to acknowledge that
the ta's helped you we expect that but

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the ta's helped you we expect that but
 

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the ta's helped you we expect that but
if you collaborated with somebody to

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if you collaborated with somebody to
 

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if you collaborated with somebody to
understand what the problem was we'd

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understand what the problem was we'd
 

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understand what the problem was we'd
like you to tell us that just right at

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like you to tell us that just right at
 

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like you to tell us that just right at
the top collaborated on figuring out the

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the top collaborated on figuring out the
 

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the top collaborated on figuring out the
concept with so and

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concept with so and
 

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concept with so and
so but we'd like you to have written

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so but we'd like you to have written
 

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so but we'd like you to have written
your homework so for example we would

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your homework so for example we would
 

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your homework so for example we would
like you not to say I copied so and so's

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like you not to say I copied so and so's
 

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like you not to say I copied so and so's
homework word for word even though

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homework word for word even though
 

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homework word for word even though
that's an honest statement that's not

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that's an honest statement that's not
 

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that's an honest statement that's not
something that we're actually looking

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something that we're actually looking
 

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something that we're actually looking
for okay is that is that clear we want

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for okay is that is that clear we want
 

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for okay is that is that clear we want
you to work together but we would like

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you to work together but we would like
 

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you to work together but we would like
you to write up your own

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Solutions okay there's a dead we have

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Solutions okay there's a dead we have
 

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Solutions okay there's a dead we have
firm

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firm
 

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firm
deadlines uh the homeworks will always

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deadlines uh the homeworks will always
 

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deadlines uh the homeworks will always
be do on

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be do on
 

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be do on
Wednesday you'll be able to slip on one

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Wednesday you'll be able to slip on one
 

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Wednesday you'll be able to slip on one
without

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without
 

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without
penalty so if you turn in one late it

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penalty so if you turn in one late it
 

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penalty so if you turn in one late it
won't change it won't have any effect on

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won't change it won't have any effect on
 

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won't change it won't have any effect on
your grade whatever if you do twice that

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your grade whatever if you do twice that
 

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your grade whatever if you do twice that
could have an effect unless you're

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could have an effect unless you're
 

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could have an effect unless you're
excused by a Dean or an instructor or a

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excused by a Dean or an instructor or a
 

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excused by a Dean or an instructor or a
medical

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medical
 

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medical
person uh that submission will count

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person uh that submission will count
 

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person uh that submission will count
half what it would normally

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half what it would normally
 

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half what it would normally
count I should have mentioned when I was

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count I should have mentioned when I was
 

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count I should have mentioned when I was
talking about homework homework one is

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talking about homework homework one is
 

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talking about homework homework one is
already posted it will be due next

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Wednesday uh the online submission part

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Wednesday uh the online submission part
 

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Wednesday uh the online submission part
is almost ready to be posted and will be

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is almost ready to be posted and will be
 

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is almost ready to be posted and will be
posted later this afternoon so right now

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posted later this afternoon so right now
 

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posted later this afternoon so right now
you can see all the problems but the

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you can see all the problems but the
 

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you can see all the problems but the
online will become available this

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afternoon okay here's uh3 at a

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afternoon okay here's uh3 at a
 

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afternoon okay here's uh3 at a
glance it's not too unlike what you

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glance it's not too unlike what you
 

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glance it's not too unlike what you
might have expected just a couple things

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might have expected just a couple things
 

 align:start position:0%
might have expected just a couple things
to point out the order of coverage is

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to point out the order of coverage is
 

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to point out the order of coverage is
not the same as the order of coverage in

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not the same as the order of coverage in
 

 align:start position:0%
not the same as the order of coverage in
oppenheim and

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oppenheim and
 

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oppenheim and
wiski the reason for doing that is that

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wiski the reason for doing that is that
 

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wiski the reason for doing that is that
having taught this class for 15 years

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having taught this class for 15 years
 

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having taught this class for 15 years
years I just think there's some subjects

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years I just think there's some subjects
 

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years I just think there's some subjects
that are easier starting

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that are easier starting
 

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that are easier starting
points than

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points than
 

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points than
others so I'm doing what I think is the

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others so I'm doing what I think is the
 

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others so I'm doing what I think is the
easiest entry to this

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easiest entry to this
 

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easiest entry to this
material with the idea that after you've

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material with the idea that after you've
 

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material with the idea that after you've
got the easy stuff under your belt it's

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got the easy stuff under your belt it's
 

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got the easy stuff under your belt it's
easier to move on to the more difficult

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easier to move on to the more difficult
 

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easier to move on to the more difficult
material so the order is not precisely

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material so the order is not precisely
 

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material so the order is not precisely
the same as that in oppenheim and wilski

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the same as that in oppenheim and wilski
 

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the same as that in oppenheim and wilski
but there is a map on the website that

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but there is a map on the website that
 

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but there is a map on the website that
gives you a week-by-week

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gives you a week-by-week
 

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gives you a week-by-week
breakdown of what part of oppenheim and

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breakdown of what part of oppenheim and
 

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breakdown of what part of oppenheim and
wil are we working on right

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wil are we working on right
 

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wil are we working on right
now so Oppenheimer wiski is the

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now so Oppenheimer wiski is the
 

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now so Oppenheimer wiski is the
recommended text but it's not quite in

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recommended text but it's not quite in
 

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recommended text but it's not quite in
the regular order of oppenheim and

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the regular order of oppenheim and
 

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the regular order of oppenheim and
wilsky we will eventually cover exactly

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wilsky we will eventually cover exactly
 

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wilsky we will eventually cover exactly
the same material that is in that

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the same material that is in that
 

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the same material that is in that
oppenheim and wilsky was written for

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oppenheim and wilsky was written for
 

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oppenheim and wilsky was written for
this class we'll cover the same material

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this class we'll cover the same material
 

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this class we'll cover the same material
just not quite in the same

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order another thing to notice is exams

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order another thing to notice is exams
 

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order another thing to notice is exams
we'll have three midterm

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we'll have three midterm
 

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we'll have three midterm
exams and a final the midterm term exams

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exams and a final the midterm term exams
 

 align:start position:0%
exams and a final the midterm term exams
are all evening exams 7:30 to 9:30 on

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are all evening exams 7:30 to 9:30 on
 

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are all evening exams 7:30 to 9:30 on
Wednesday

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evening the idea is that there's

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evening the idea is that there's
 

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evening the idea is that there's
intended to be a gentle ramp through the

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intended to be a gentle ramp through the
 

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intended to be a gentle ramp through the
exams exam one is worth 10% exam two is

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exams exam one is worth 10% exam two is
 

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exams exam one is worth 10% exam two is
worth 15% exam three is worth 20% the

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worth 15% exam three is worth 20% the
 

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worth 15% exam three is worth 20% the
final exam is worth

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final exam is worth
 

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final exam is worth
40% so the idea is that if you have a

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40% so the idea is that if you have a
 

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40% so the idea is that if you have a
mismatch on the way if you don't quite

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mismatch on the way if you don't quite
 

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mismatch on the way if you don't quite
understand the way we're going to be

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understand the way we're going to be
 

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understand the way we're going to be
asking questions and so forth there's

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asking questions and so forth there's
 

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asking questions and so forth there's
not a big penalty for screwing up the

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not a big penalty for screwing up the
 

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not a big penalty for screwing up the
first exam that's the idea so there's a

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first exam that's the idea so there's a
 

 align:start position:0%
first exam that's the idea so there's a
intended to be a gentle ramp um in how

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intended to be a gentle ramp um in how
 

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intended to be a gentle ramp um in how
much the exams

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count okay and finally I'd like feedback

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count okay and finally I'd like feedback
 

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count okay and finally I'd like feedback
on what you think is happening so I

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on what you think is happening so I
 

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on what you think is happening so I
would like to ask for a few volunteers

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would like to ask for a few volunteers
 

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would like to ask for a few volunteers
few is four or

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fewer who would be interested to meet

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fewer who would be interested to meet
 

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fewer who would be interested to meet
with me once a week just to tell me what

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with me once a week just to tell me what
 

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with me once a week just to tell me what
you think

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you think
 

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you think
think ideally those people would be kind

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think ideally those people would be kind
 

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think ideally those people would be kind
of outgoing and tell me things that

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of outgoing and tell me things that
 

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of outgoing and tell me things that
other people think too but if you're

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other people think too but if you're
 

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other people think too but if you're
completely introverted and want to only

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completely introverted and want to only
 

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completely introverted and want to only
tell me what you think that's fine

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tell me what you think that's fine
 

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tell me what you think that's fine
too so uh this is an opportunity for you

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too so uh this is an opportunity for you
 

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too so uh this is an opportunity for you
to tell the staff to give us feedback on

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to tell the staff to give us feedback on
 

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to tell the staff to give us feedback on
how things are going we're going too

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how things are going we're going too
 

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how things are going we're going too
slow we're going too fast we're going

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slow we're going too fast we're going
 

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slow we're going too fast we're going
too boring we're intensely too

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too boring we're intensely too
 

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too boring we're intensely too
interesting that kind of stuff

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interesting that kind of stuff
 

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interesting that kind of stuff
um uh

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um uh
 

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um uh
and it's a it's an opportunity for you

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and it's a it's an opportunity for you
 

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and it's a it's an opportunity for you
to understand our perspective like well

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to understand our perspective like well
 

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to understand our perspective like well
the reason we did that was blah and then

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the reason we did that was blah and then
 

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the reason we did that was blah and then
you can tell us we but that's not

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you can tell us we but that's not
 

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you can tell us we but that's not
important so it's an opportunity for um

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important so it's an opportunity for um
 

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important so it's an opportunity for um
you to convey to

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you to convey to
 

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you to convey to
us how you think things are going and

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us how you think things are going and
 

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us how you think things are going and
how you think things should be different

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how you think things should be different
 

 align:start position:0%
how you think things should be different
it's also an opportunity for you to

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it's also an opportunity for you to
 

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it's also an opportunity for you to
learn about teaching so if you think

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learn about teaching so if you think
 

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learn about teaching so if you think
about teaching as a career it's a good

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about teaching as a career it's a good
 

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about teaching as a career it's a good
thing to do completely voluntary has

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thing to do completely voluntary has
 

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thing to do completely voluntary has
absolutely absolutely no effect on your

 align:start position:0%
absolutely absolutely no effect on your
 

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absolutely absolutely no effect on your
grade uh if you think you might be

 align:start position:0%
grade uh if you think you might be
 

 align:start position:0%
grade uh if you think you might be
interested it's probably going to meet

 align:start position:0%
interested it's probably going to meet
 

 align:start position:0%
interested it's probably going to meet
on we'll probably meet on Thursday

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on we'll probably meet on Thursday
 

 align:start position:0%
on we'll probably meet on Thursday
afternoon but that's negotiable since

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afternoon but that's negotiable since
 

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afternoon but that's negotiable since
it's only four people and if you are

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it's only four people and if you are
 

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it's only four people and if you are
interested please send me an email and

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interested please send me an email and
 

 align:start position:0%
interested please send me an email and
the first four people who ask they're

 align:start position:0%
the first four people who ask they're
 

 align:start position:0%
the first four people who ask they're
there

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okay that's it on

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 align:start position:0%
 
Administration are there things you'd

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Administration are there things you'd
 

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Administration are there things you'd
like to know about course Administration

 align:start position:0%
like to know about course Administration
 

 align:start position:0%
like to know about course Administration
before we go on to technical

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things wonderful okay this course is

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things wonderful okay this course is
 

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things wonderful okay this course is
about

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systems this is not the first course

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systems this is not the first course
 

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systems this is not the first course
you've had about

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you've had about
 

 align:start position:0%
you've had about
systems you've had lots of courses in

 align:start position:0%
systems you've had lots of courses in
 

 align:start position:0%
systems you've had lots of courses in
systems every Physics course you've ever

 align:start position:0%
systems every Physics course you've ever
 

 align:start position:0%
systems every Physics course you've ever
taken is about

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systems what's different about this

 align:start position:0%
systems what's different about this
 

 align:start position:0%
systems what's different about this
course is the way we think about systems

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course is the way we think about systems
 

 align:start position:0%
course is the way we think about systems
we think about systems in a particular

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we think about systems in a particular
 

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we think about systems in a particular
way that turns out to be extraordinarily

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way that turns out to be extraordinarily
 

 align:start position:0%
way that turns out to be extraordinarily
powerful useful shows up all the time

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powerful useful shows up all the time
 

 align:start position:0%
powerful useful shows up all the time
and that's what the focus of this course

 align:start position:0%
and that's what the focus of this course
 

 align:start position:0%
and that's what the focus of this course
is the the abstraction that we're going

 align:start position:0%
is the the abstraction that we're going
 

 align:start position:0%
is the the abstraction that we're going
to use is we think about a system as a

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to use is we think about a system as a
 

 align:start position:0%
to use is we think about a system as a
thing that has an input and an

 align:start position:0%
thing that has an input and an
 

 align:start position:0%
thing that has an input and an
output given the input and the system

 align:start position:0%
output given the input and the system
 

 align:start position:0%
output given the input and the system
you can compute the

 align:start position:0%
you can compute the
 

 align:start position:0%
you can compute the
output systems have one input and one

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output systems have one input and one
 

 align:start position:0%
output systems have one input and one
output it's a very special

 align:start position:0%
output it's a very special
 

 align:start position:0%
output it's a very special
way of thinking about a

 align:start position:0%
way of thinking about a
 

 align:start position:0%
way of thinking about a
system that turns out to be surprisingly

 align:start position:0%
system that turns out to be surprisingly
 

 align:start position:0%
system that turns out to be surprisingly
powerful it's so powerful that that's

 align:start position:0%
powerful it's so powerful that that's
 

 align:start position:0%
powerful it's so powerful that that's
really the thing that we will focus on

 align:start position:0%
really the thing that we will focus on
 

 align:start position:0%
really the thing that we will focus on
in this class so it's the thing that I

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in this class so it's the thing that I
 

 align:start position:0%
in this class so it's the thing that I
will call

 align:start position:0%
will call
 

 align:start position:0%
will call
the

 align:start position:0%
the
 

 align:start position:0%
the

 align:start position:0%
 
 

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abstraction that's going to be the theme

 align:start position:0%
abstraction that's going to be the theme
 

 align:start position:0%
abstraction that's going to be the theme
in everything we do that represents

 align:start position:0%
in everything we do that represents
 

 align:start position:0%
in everything we do that represents
entation and the best way to get across

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entation and the best way to get across
 

 align:start position:0%
entation and the best way to get across
I think how that's different from other

 align:start position:0%
I think how that's different from other
 

 align:start position:0%
I think how that's different from other
representations that you're already

 align:start position:0%
representations that you're already
 

 align:start position:0%
representations that you're already
quite familiar with is to just look at

 align:start position:0%
quite familiar with is to just look at
 

 align:start position:0%
quite familiar with is to just look at
an example so here's a system that I'm

 align:start position:0%
an example so here's a system that I'm
 

 align:start position:0%
an example so here's a system that I'm
sure you all know all about right this

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sure you all know all about right this
 

 align:start position:0%
sure you all know all about right this
is not the first time you've seen this

 align:start position:0%
is not the first time you've seen this
 

 align:start position:0%
is not the first time you've seen this
kind of a

 align:start position:0%
kind of a
 

 align:start position:0%
kind of a
system so you all know how to do this

 align:start position:0%
system so you all know how to do this
 

 align:start position:0%
system so you all know how to do this
free body diagrams f equals ma there's

 align:start position:0%
free body diagrams f equals ma there's
 

 align:start position:0%
free body diagrams f equals ma there's
an enormous number of ways that you can

 align:start position:0%
an enormous number of ways that you can
 

 align:start position:0%
an enormous number of ways that you can
analyze such a system we're going to

 align:start position:0%
analyze such a system we're going to
 

 align:start position:0%
analyze such a system we're going to
take a very special approach where we

 align:start position:0%
take a very special approach where we
 

 align:start position:0%
take a very special approach where we
think about the

 align:start position:0%
think about the
 

 align:start position:0%
think about the
system as having an input and an

 align:start position:0%
 
 

 align:start position:0%
 
output okay that's a little bit

 align:start position:0%
output okay that's a little bit
 

 align:start position:0%
output okay that's a little bit
arbitrary we'll say a little more in a

 align:start position:0%
arbitrary we'll say a little more in a
 

 align:start position:0%
arbitrary we'll say a little more in a
minute about how arbitrary it is but the

 align:start position:0%
minute about how arbitrary it is but the
 

 align:start position:0%
minute about how arbitrary it is but the
idea is going to be that this system the

 align:start position:0%
idea is going to be that this system the
 

 align:start position:0%
idea is going to be that this system the
mass spring system the Anvil with a

 align:start position:0%
mass spring system the Anvil with a
 

 align:start position:0%
mass spring system the Anvil with a
spring there's an

 align:start position:0%
spring there's an
 

 align:start position:0%
spring there's an
input and there's an output so for

 align:start position:0%
input and there's an output so for
 

 align:start position:0%
input and there's an output so for
example for some particular purpose I

 align:start position:0%
example for some particular purpose I
 

 align:start position:0%
example for some particular purpose I
might want to think that the

 align:start position:0%
might want to think that the
 

 align:start position:0%
might want to think that the
input is the position of my

 align:start position:0%
input is the position of my
 

 align:start position:0%
input is the position of my
hand one reason I might want to think

 align:start position:0%
hand one reason I might want to think
 

 align:start position:0%
hand one reason I might want to think
about that is it is under my control so

 align:start position:0%
about that is it is under my control so
 

 align:start position:0%
about that is it is under my control so
it might be reasonable to think about my

 align:start position:0%
it might be reasonable to think about my
 

 align:start position:0%
it might be reasonable to think about my
hand being the input so for example my

 align:start position:0%
hand being the input so for example my
 

 align:start position:0%
hand being the input so for example my
hand can do

 align:start position:0%
hand can do
 

 align:start position:0%
hand can do
this right so I might think about the

 align:start position:0%
this right so I might think about the
 

 align:start position:0%
this right so I might think about the
position of my hand being the

 align:start position:0%
position of my hand being the
 

 align:start position:0%
position of my hand being the
input so if I did that then what I could

 align:start position:0%
input so if I did that then what I could
 

 align:start position:0%
input so if I did that then what I could
do is characterize the input by some

 align:start position:0%
do is characterize the input by some
 

 align:start position:0%
do is characterize the input by some
waveform a

 align:start position:0%
 
 

 align:start position:0%
 
signal in order to use the abstraction I

 align:start position:0%
signal in order to use the abstraction I
 

 align:start position:0%
signal in order to use the abstraction I
also have to say what the output is I

 align:start position:0%
also have to say what the output is I
 

 align:start position:0%
also have to say what the output is I
might be interested for example in

 align:start position:0%
might be interested for example in
 

 align:start position:0%
might be interested for example in
knowing the position of the

 align:start position:0%
knowing the position of the
 

 align:start position:0%
knowing the position of the
mass then the output would be the

 align:start position:0%
mass then the output would be the
 

 align:start position:0%
mass then the output would be the
displacement of the

 align:start position:0%
displacement of the
 

 align:start position:0%
displacement of the
mass that assignment of input and output

 align:start position:0%
mass that assignment of input and output
 

 align:start position:0%
mass that assignment of input and output
is somewhat

 align:start position:0%
 
 

 align:start position:0%
 
arbitrary I get to choose that to make

 align:start position:0%
arbitrary I get to choose that to make
 

 align:start position:0%
arbitrary I get to choose that to make
the problem that I'm interested it in as

 align:start position:0%
the problem that I'm interested it in as
 

 align:start position:0%
the problem that I'm interested it in as
easy as

 align:start position:0%
easy as
 

 align:start position:0%
easy as
possible so for example if I'm thinking

 align:start position:0%
possible so for example if I'm thinking
 

 align:start position:0%
possible so for example if I'm thinking
about this uh mass and spring system

 align:start position:0%
about this uh mass and spring system
 

 align:start position:0%
about this uh mass and spring system
here at using my hand as the input that

 align:start position:0%
here at using my hand as the input that
 

 align:start position:0%
here at using my hand as the input that
seems kind of natural because that's the

 align:start position:0%
seems kind of natural because that's the
 

 align:start position:0%
seems kind of natural because that's the
thing I control thinking about the

 align:start position:0%
thing I control thinking about the
 

 align:start position:0%
thing I control thinking about the
position of the mass as the output that

 align:start position:0%
position of the mass as the output that
 

 align:start position:0%
position of the mass as the output that
seems reasonable because that's the PCT

 align:start position:0%
seems reasonable because that's the PCT
 

 align:start position:0%
seems reasonable because that's the PCT
that's the thing you could take a

 align:start position:0%
that's the thing you could take a
 

 align:start position:0%
that's the thing you could take a
picture of it's the thing you can

 align:start position:0%
picture of it's the thing you can
 

 align:start position:0%
picture of it's the thing you can
observe from where you are now but it's

 align:start position:0%
observe from where you are now but it's
 

 align:start position:0%
observe from where you are now but it's
not unique I might have wanted to think

 align:start position:0%
not unique I might have wanted to think
 

 align:start position:0%
not unique I might have wanted to think
about the force that I'm putting into it

 align:start position:0%
about the force that I'm putting into it
 

 align:start position:0%
about the force that I'm putting into it
as the

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as the
 

 align:start position:0%
as the
input I might have wanted to think about

 align:start position:0%
input I might have wanted to think about
 

 align:start position:0%
input I might have wanted to think about
the output being the acceleration of the

 align:start position:0%
the output being the acceleration of the
 

 align:start position:0%
the output being the acceleration of the
mass maybe maybe there's some limit to

 align:start position:0%
mass maybe maybe there's some limit to
 

 align:start position:0%
mass maybe maybe there's some limit to
how much acceleration some Mass can can

 align:start position:0%
how much acceleration some Mass can can
 

 align:start position:0%
how much acceleration some Mass can can
take so you get to choose the input and

 align:start position:0%
take so you get to choose the input and
 

 align:start position:0%
take so you get to choose the input and
the

 align:start position:0%
the
 

 align:start position:0%
the
output but you have to choose an input

 align:start position:0%
output but you have to choose an input
 

 align:start position:0%
output but you have to choose an input
and an output that's part of the

 align:start position:0%
and an output that's part of the
 

 align:start position:0%
and an output that's part of the
abstraction and that's part of the power

 align:start position:0%
abstraction and that's part of the power
 

 align:start position:0%
abstraction and that's part of the power
we'll see later that part of the power

 align:start position:0%
we'll see later that part of the power
 

 align:start position:0%
we'll see later that part of the power
of doing it this way is that you draw

 align:start position:0%
of doing it this way is that you draw
 

 align:start position:0%
of doing it this way is that you draw
attention to the things things of

 align:start position:0%
attention to the things things of
 

 align:start position:0%
attention to the things things of
interest and push into the background

 align:start position:0%
interest and push into the background
 

 align:start position:0%
interest and push into the background
the parts that are not of interest at

 align:start position:0%
the parts that are not of interest at
 

 align:start position:0%
the parts that are not of interest at
least not

 align:start position:0%
 
 

 align:start position:0%
 
now this kind of an abstraction is

 align:start position:0%
now this kind of an abstraction is
 

 align:start position:0%
now this kind of an abstraction is
extremely

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extremely
 

 align:start position:0%
extremely
versatile here's a completely different

 align:start position:0%
versatile here's a completely different
 

 align:start position:0%
versatile here's a completely different
kind of

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kind of
 

 align:start position:0%
kind of
problem imagine water flowing into a

 align:start position:0%
problem imagine water flowing into a
 

 align:start position:0%
problem imagine water flowing into a
tank the Tank's leaky so it flows

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tank the Tank's leaky so it flows
 

 align:start position:0%
tank the Tank's leaky so it flows
out there's a second tank okay what on

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out there's a second tank okay what on
 

 align:start position:0%
out there's a second tank okay what on
Earth could this be this could be maybe

 align:start position:0%
Earth could this be this could be maybe
 

 align:start position:0%
Earth could this be this could be maybe
this is the it's appropriate to today

 align:start position:0%
this is the it's appropriate to today
 

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this is the it's appropriate to today
right it's raining or it was raining uh

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right it's raining or it was raining uh
 

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right it's raining or it was raining uh
so it was pouring when I came in it was

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so it was pouring when I came in it was
 

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so it was pouring when I came in it was
pouring uh maybe this

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pouring uh maybe this
 

 align:start position:0%
pouring uh maybe this
is nature delivering

 align:start position:0%
is nature delivering
 

 align:start position:0%
is nature delivering
rain this is the wuber

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rain this is the wuber
 

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rain this is the wuber
reservoir from which we get water in

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reservoir from which we get water in
 

 align:start position:0%
reservoir from which we get water in
Boston maybe this is the Fresh Pond

 align:start position:0%
Boston maybe this is the Fresh Pond
 

 align:start position:0%
Boston maybe this is the Fresh Pond
Reservoir from which we get water in

 align:start position:0%
Reservoir from which we get water in
 

 align:start position:0%
Reservoir from which we get water in
Cambridge maybe this is is the rate at

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Cambridge maybe this is is the rate at
 

 align:start position:0%
Cambridge maybe this is is the rate at
which water goes from wubber

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which water goes from wubber
 

 align:start position:0%
which water goes from wubber
to Fresh

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to Fresh
 

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to Fresh
Pond maybe this is the rate at which

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Pond maybe this is the rate at which
 

 align:start position:0%
Pond maybe this is the rate at which
water leaves Fresh Pond and goes into

 align:start position:0%
water leaves Fresh Pond and goes into
 

 align:start position:0%
water leaves Fresh Pond and goes into
consumers

 align:start position:0%
consumers
 

 align:start position:0%
consumers
houses the point is that there's some

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houses the point is that there's some
 

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houses the point is that there's some
abstraction there's there's some

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abstraction there's there's some
 

 align:start position:0%
abstraction there's there's some
physical I didn't say that right there's

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physical I didn't say that right there's
 

 align:start position:0%
physical I didn't say that right there's
a physical

 align:start position:0%
a physical
 

 align:start position:0%
a physical
thing rain wuber Wu Reservoir um Fresh

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thing rain wuber Wu Reservoir um Fresh
 

 align:start position:0%
thing rain wuber Wu Reservoir um Fresh
Pond Reservoir consumer houses there

 align:start position:0%
Pond Reservoir consumer houses there
 

 align:start position:0%
Pond Reservoir consumer houses there
some physical thing there's some laws of

 align:start position:0%
some physical thing there's some laws of
 

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some physical thing there's some laws of
physics that dictate things but we

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physics that dictate things but we
 

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physics that dictate things but we
ignore or ignore is not quite the right

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ignore or ignore is not quite the right
 

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ignore or ignore is not quite the right
way to think about it we think about

 align:start position:0%
way to think about it we think about
 

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way to think about it we think about
those rules of physics as rules that

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those rules of physics as rules that
 

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those rules of physics as rules that
govern the input output relationship so

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govern the input output relationship so
 

 align:start position:0%
govern the input output relationship so
we think about then the entire system

 align:start position:0%
we think about then the entire system
 

 align:start position:0%
we think about then the entire system
rather than thinking about it as

 align:start position:0%
rather than thinking about it as
 

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rather than thinking about it as
reservoirs and rain and water and flow

 align:start position:0%
reservoirs and rain and water and flow
 

 align:start position:0%
reservoirs and rain and water and flow
and all that sort of thing we think

 align:start position:0%
and all that sort of thing we think
 

 align:start position:0%
and all that sort of thing we think
about it as there's a signal

 align:start position:0%
about it as there's a signal
 

 align:start position:0%
about it as there's a signal
in rain

 align:start position:0%
in rain
 

 align:start position:0%
in rain
and there's a signal out water

 align:start position:0%
and there's a signal out water
 

 align:start position:0%
and there's a signal out water
usage and we take all the details of the

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usage and we take all the details of the
 

 align:start position:0%
usage and we take all the details of the
system and bury it in this box it's an

 align:start position:0%
system and bury it in this box it's an
 

 align:start position:0%
system and bury it in this box it's an
abstraction it's a way to suppress some

 align:start position:0%
abstraction it's a way to suppress some
 

 align:start position:0%
abstraction it's a way to suppress some
details to highlight

 align:start position:0%
 
 

 align:start position:0%
 
others okay it's and we use this in huge

 align:start position:0%
others okay it's and we use this in huge
 

 align:start position:0%
others okay it's and we use this in huge
variety of situations we can think about

 align:start position:0%
variety of situations we can think about
 

 align:start position:0%
variety of situations we can think about
a third example here a cell phone cell

 align:start position:0%
a third example here a cell phone cell
 

 align:start position:0%
a third example here a cell phone cell
phone is enormously complicated system

 align:start position:0%
phone is enormously complicated system
 

 align:start position:0%
phone is enormously complicated system
but for the purpose of understanding the

 align:start position:0%
but for the purpose of understanding the
 

 align:start position:0%
but for the purpose of understanding the
input output

 align:start position:0%
input output
 

 align:start position:0%
input output
characteristics if what I really want to

 align:start position:0%
characteristics if what I really want to
 

 align:start position:0%
characteristics if what I really want to
know is how good is the quality of the

 align:start position:0%
know is how good is the quality of the
 

 align:start position:0%
know is how good is the quality of the
audio not that that's even a little bit

 align:start position:0%
audio not that that's even a little bit
 

 align:start position:0%
audio not that that's even a little bit
important for cell phones right cell

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important for cell phones right cell
 

 align:start position:0%
important for cell phones right cell
phones are important for texting and

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phones are important for texting and
 

 align:start position:0%
phones are important for texting and
taking pictures and have nothing to do

 align:start position:0%
taking pictures and have nothing to do
 

 align:start position:0%
taking pictures and have nothing to do
with voice but in the old days cell

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with voice but in the old days cell
 

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with voice but in the old days cell
phones had to do with voice and I made

 align:start position:0%
phones had to do with voice and I made
 

 align:start position:0%
phones had to do with voice and I made
this slide back when that was still true

 align:start position:0%
this slide back when that was still true
 

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this slide back when that was still true
so I apologize it's out of date um so

 align:start position:0%
so I apologize it's out of date um so
 

 align:start position:0%
so I apologize it's out of date um so
here the important thing of the cell

 align:start position:0%
here the important thing of the cell
 

 align:start position:0%
here the important thing of the cell
phone system was the sound in and the

 align:start position:0%
phone system was the sound in and the
 

 align:start position:0%
phone system was the sound in and the
sound out

 align:start position:0%
sound out
 

 align:start position:0%
sound out
and the idea was to represent the cell

 align:start position:0%
and the idea was to represent the cell
 

 align:start position:0%
and the idea was to represent the cell
phone system by the

 align:start position:0%
phone system by the
 

 align:start position:0%
phone system by the
transformation between how the sound

 align:start position:0%
transformation between how the sound
 

 align:start position:0%
transformation between how the sound
comes in and how the sound comes

 align:start position:0%
comes in and how the sound comes
 

 align:start position:0%
comes in and how the sound comes
out okay so we do this for an enormous

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out okay so we do this for an enormous
 

 align:start position:0%
out okay so we do this for an enormous
number of reasons one is that it's

 align:start position:0%
number of reasons one is that it's
 

 align:start position:0%
number of reasons one is that it's
widely applicable you can do this kind

 align:start position:0%
widely applicable you can do this kind
 

 align:start position:0%
widely applicable you can do this kind
of a characterization for systems from

 align:start position:0%
of a characterization for systems from
 

 align:start position:0%
of a characterization for systems from
uh electrical systems mechanical systems

 align:start position:0%
uh electrical systems mechanical systems
 

 align:start position:0%
uh electrical systems mechanical systems
Optical systems acoustic systems

 align:start position:0%
Optical systems acoustic systems
 

 align:start position:0%
Optical systems acoustic systems
biological systems Financial systems all

 align:start position:0%
biological systems Financial systems all
 

 align:start position:0%
biological systems Financial systems all
over the

 align:start position:0%
over the
 

 align:start position:0%
over the
place

 align:start position:0%
place
 

 align:start position:0%
place
that means that this kind of an approach

 align:start position:0%
that means that this kind of an approach
 

 align:start position:0%
that means that this kind of an approach
is very powerful because it's so widely

 align:start position:0%
is very powerful because it's so widely
 

 align:start position:0%
is very powerful because it's so widely
applicable it also means that for

 align:start position:0%
applicable it also means that for
 

 align:start position:0%
applicable it also means that for
example every engineering discipline

 align:start position:0%
example every engineering discipline
 

 align:start position:0%
example every engineering discipline
everywhere has some course like this

 align:start position:0%
everywhere has some course like this
 

 align:start position:0%
everywhere has some course like this
it's just too powerful not to do

 align:start position:0%
it's just too powerful not to do
 

 align:start position:0%
it's just too powerful not to do
it so what regardless of what department

 align:start position:0%
it so what regardless of what department
 

 align:start position:0%
it so what regardless of what department
you were in in the School of Engineering

 align:start position:0%
you were in in the School of Engineering
 

 align:start position:0%
you were in in the School of Engineering
for example there is something like

 align:start position:0%
 
 

 align:start position:0%
 
this another reason this is interesting

 align:start position:0%
this another reason this is interesting
 

 align:start position:0%
this another reason this is interesting
is that it provides a layer of

 align:start position:0%
is that it provides a layer of
 

 align:start position:0%
is that it provides a layer of
abstraction that lets you focus on

 align:start position:0%
abstraction that lets you focus on
 

 align:start position:0%
abstraction that lets you focus on
certain things so for example let's

 align:start position:0%
certain things so for example let's
 

 align:start position:0%
certain things so for example let's
expand on the cell phone network imagine

 align:start position:0%
expand on the cell phone network imagine
 

 align:start position:0%
expand on the cell phone network imagine
that sound comes into a cell phone well

 align:start position:0%
that sound comes into a cell phone well
 

 align:start position:0%
that sound comes into a cell phone well
the job of the phone is to communicate

 align:start position:0%
the job of the phone is to communicate
 

 align:start position:0%
the job of the phone is to communicate
to a

 align:start position:0%
to a
 

 align:start position:0%
to a
tower and that communication is via some

 align:start position:0%
tower and that communication is via some
 

 align:start position:0%
tower and that communication is via some
electromag magnetic

 align:start position:0%
electromag magnetic
 

 align:start position:0%
electromag magnetic
signal then the job of the tower is to

 align:start position:0%
signal then the job of the tower is to
 

 align:start position:0%
signal then the job of the tower is to
communicate with another

 align:start position:0%
communicate with another
 

 align:start position:0%
communicate with another
tower that happens in all kinds of ways

 align:start position:0%
tower that happens in all kinds of ways
 

 align:start position:0%
tower that happens in all kinds of ways
it could be if optic link it could be a

 align:start position:0%
it could be if optic link it could be a
 

 align:start position:0%
it could be if optic link it could be a
satellite link it could be

 align:start position:0%
satellite link it could be
 

 align:start position:0%
satellite link it could be
electromagnetism it could be lots of

 align:start position:0%
electromagnetism it could be lots of
 

 align:start position:0%
electromagnetism it could be lots of
different things there's a lot of

 align:start position:0%
different things there's a lot of
 

 align:start position:0%
different things there's a lot of
different Technologies for getting

 align:start position:0%
different Technologies for getting
 

 align:start position:0%
different Technologies for getting
Towers to talk to Towers then Towers

 align:start position:0%
Towers to talk to Towers then Towers
 

 align:start position:0%
Towers to talk to Towers then Towers
talk back to cell phones via

 align:start position:0%
talk back to cell phones via
 

 align:start position:0%
talk back to cell phones via
electromagnetic signals just like these

 align:start position:0%
electromagnetic signals just like these
 

 align:start position:0%
electromagnetic signals just like these
and gener and the cell phone eventually

 align:start position:0%
and gener and the cell phone eventually
 

 align:start position:0%
and gener and the cell phone eventually
generates an acoustical

 align:start position:0%
generates an acoustical
 

 align:start position:0%
generates an acoustical
output the idea is that by thinking

 align:start position:0%
output the idea is that by thinking
 

 align:start position:0%
output the idea is that by thinking
about the signals and systems approach

 align:start position:0%
about the signals and systems approach
 

 align:start position:0%
about the signals and systems approach
we have um abstracted away everything

 align:start position:0%
we have um abstracted away everything
 

 align:start position:0%
we have um abstracted away everything
other than the flow of information

 align:start position:0%
other than the flow of information
 

 align:start position:0%
other than the flow of information
it makes it easy to

 align:start position:0%
it makes it easy to
 

 align:start position:0%
it makes it easy to
concentrate to follow the flow of

 align:start position:0%
concentrate to follow the flow of
 

 align:start position:0%
concentrate to follow the flow of
information through a complex

 align:start position:0%
information through a complex
 

 align:start position:0%
information through a complex
system because we have pushed every

 align:start position:0%
system because we have pushed every
 

 align:start position:0%
system because we have pushed every
element into the same framework every

 align:start position:0%
element into the same framework every
 

 align:start position:0%
element into the same framework every
element has an input and

 align:start position:0%
element has an input and
 

 align:start position:0%
element has an input and
output regardless of the underlying

 align:start position:0%
output regardless of the underlying
 

 align:start position:0%
output regardless of the underlying
substrate the analysis is

 align:start position:0%
substrate the analysis is
 

 align:start position:0%
substrate the analysis is
similar that means that components who

 align:start position:0%
similar that means that components who
 

 align:start position:0%
similar that means that components who
that are characterized using the

 align:start position:0%
that are characterized using the
 

 align:start position:0%
that are characterized using the
substraction are easily

 align:start position:0%
substraction are easily
 

 align:start position:0%
substraction are easily
combined so we refer to this as we say

 align:start position:0%
combined so we refer to this as we say
 

 align:start position:0%
combined so we refer to this as we say
that these systems are

 align:start position:0%
that these systems are
 

 align:start position:0%
that these systems are
combinational they're combinational in

 align:start position:0%
combinational they're combinational in
 

 align:start position:0%
combinational they're combinational in
the same sense that python was

 align:start position:0%
the same sense that python was
 

 align:start position:0%
the same sense that python was
combinational in

 align:start position:0%
combinational in
 

 align:start position:0%
combinational in
601 if you represent things by python

 align:start position:0%
601 if you represent things by python
 

 align:start position:0%
601 if you represent things by python
functions it's very easy to combine the

 align:start position:0%
functions it's very easy to combine the
 

 align:start position:0%
functions it's very easy to combine the
functions to have a bigger

 align:start position:0%
functions to have a bigger
 

 align:start position:0%
functions to have a bigger
function whose purpose and details can

 align:start position:0%
function whose purpose and details can
 

 align:start position:0%
function whose purpose and details can
be understood without knowing what was

 align:start position:0%
be understood without knowing what was
 

 align:start position:0%
be understood without knowing what was
was inside every individual

 align:start position:0%
was inside every individual
 

 align:start position:0%
was inside every individual
function similarly here by knowing the

 align:start position:0%
function similarly here by knowing the
 

 align:start position:0%
function similarly here by knowing the
input Behavior the input output behavior

 align:start position:0%
input Behavior the input output behavior
 

 align:start position:0%
input Behavior the input output behavior
of the cell phone the input output

 align:start position:0%
of the cell phone the input output
 

 align:start position:0%
of the cell phone the input output
behavior of the tower the input output

 align:start position:0%
behavior of the tower the input output
 

 align:start position:0%
behavior of the tower the input output
behavior of this Tower is easy to

 align:start position:0%
behavior of this Tower is easy to
 

 align:start position:0%
behavior of this Tower is easy to
compose them and in fact we will spend a

 align:start position:0%
compose them and in fact we will spend a
 

 align:start position:0%
compose them and in fact we will spend a
fair amount of time thinking through the

 align:start position:0%
fair amount of time thinking through the
 

 align:start position:0%
fair amount of time thinking through the
rules of

 align:start position:0%
 
 

 align:start position:0%
 
combination um so that's kind of an

 align:start position:0%
combination um so that's kind of an
 

 align:start position:0%
combination um so that's kind of an
overview of the most important thing

 align:start position:0%
overview of the most important thing
 

 align:start position:0%
overview of the most important thing
we're going to talk about in this class

 align:start position:0%
we're going to talk about in this class
 

 align:start position:0%
we're going to talk about in this class
which is the 63 abstraction the idea of

 align:start position:0%
which is the 63 abstraction the idea of
 

 align:start position:0%
which is the 63 abstraction the idea of
representing a

 align:start position:0%
representing a
 

 align:start position:0%
representing a
system by the way it transforms an input

 align:start position:0%
system by the way it transforms an input
 

 align:start position:0%
system by the way it transforms an input
into an

 align:start position:0%
into an
 

 align:start position:0%
into an
output so with that kind of overview

 align:start position:0%
output so with that kind of overview
 

 align:start position:0%
output so with that kind of overview
what I want to do next is say a little

 align:start position:0%
what I want to do next is say a little
 

 align:start position:0%
what I want to do next is say a little
more about what are signals and what are

 align:start position:0%
more about what are signals and what are
 

 align:start position:0%
more about what are signals and what are
systems it's the signals and systems

 align:start position:0%
systems it's the signals and systems
 

 align:start position:0%
systems it's the signals and systems
abstraction we're going to need to know

 align:start position:0%
abstraction we're going to need to know
 

 align:start position:0%
abstraction we're going to need to know
some more details about what is a

 align:start position:0%
some more details about what is a
 

 align:start position:0%
some more details about what is a
signal and what is a

 align:start position:0%
signal and what is a
 

 align:start position:0%
signal and what is a
system so basically a signal is just a

 align:start position:0%
system so basically a signal is just a
 

 align:start position:0%
system so basically a signal is just a
mathematical function in all the

 align:start position:0%
mathematical function in all the
 

 align:start position:0%
mathematical function in all the
examples I talked about so

 align:start position:0%
examples I talked about so
 

 align:start position:0%
examples I talked about so
far and in many of the examples that

 align:start position:0%
far and in many of the examples that
 

 align:start position:0%
far and in many of the examples that
we'll talk about throughout the

 align:start position:0%
we'll talk about throughout the
 

 align:start position:0%
we'll talk about throughout the
term the function is a function of

 align:start position:0%
term the function is a function of
 

 align:start position:0%
term the function is a function of
time and the signal can have many

 align:start position:0%
time and the signal can have many
 

 align:start position:0%
time and the signal can have many
different dimensions so for example the

 align:start position:0%
different dimensions so for example the
 

 align:start position:0%
different dimensions so for example the
mass spring system uh evolved as a

 align:start position:0%
mass spring system uh evolved as a
 

 align:start position:0%
mass spring system uh evolved as a
function of time the tank system The

 align:start position:0%
function of time the tank system The
 

 align:start position:0%
function of time the tank system The
Leaky tank system evolved as a function

 align:start position:0%
Leaky tank system evolved as a function
 

 align:start position:0%
Leaky tank system evolved as a function
of time the cell phone system had

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of time the cell phone system had
 

 align:start position:0%
of time the cell phone system had
acoustic signals that were functions of

 align:start position:0%
acoustic signals that were functions of
 

 align:start position:0%
acoustic signals that were functions of
time time was the same in each case but

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time time was the same in each case but
 

 align:start position:0%
time time was the same in each case but
the dependent variable can be a a

 align:start position:0%
the dependent variable can be a a
 

 align:start position:0%
the dependent variable can be a a
variety of things here it was

 align:start position:0%
variety of things here it was
 

 align:start position:0%
variety of things here it was
position so here it was flow rates meter

 align:start position:0%
position so here it was flow rates meter
 

 align:start position:0%
position so here it was flow rates meter
cubed per second of

 align:start position:0%
cubed per second of
 

 align:start position:0%
cubed per second of
water uh here it was uh perhaps Pascal's

 align:start position:0%
water uh here it was uh perhaps Pascal's
 

 align:start position:0%
water uh here it was uh perhaps Pascal's
some unit of pressure to characterize

 align:start position:0%
some unit of pressure to characterize
 

 align:start position:0%
some unit of pressure to characterize
the acoustic waveform

 align:start position:0%
the acoustic waveform
 

 align:start position:0%
the acoustic waveform
so the point is that signals are

 align:start position:0%
so the point is that signals are
 

 align:start position:0%
so the point is that signals are
generally

 align:start position:0%
generally
 

 align:start position:0%
generally
functions we'll see that just like

 align:start position:0%
functions we'll see that just like
 

 align:start position:0%
functions we'll see that just like
functions in

 align:start position:0%
functions in
 

 align:start position:0%
functions in
mathematics there's a lot more to

 align:start position:0%
mathematics there's a lot more to
 

 align:start position:0%
mathematics there's a lot more to
functions than dependent variables and

 align:start position:0%
functions than dependent variables and
 

 align:start position:0%
functions than dependent variables and
independent variables and in fact that's

 align:start position:0%
independent variables and in fact that's
 

 align:start position:0%
independent variables and in fact that's
going to be a key feature of our

 align:start position:0%
going to be a key feature of our
 

 align:start position:0%
going to be a key feature of our
analysis of signals but that's to come

 align:start position:0%
analysis of signals but that's to come
 

 align:start position:0%
analysis of signals but that's to come
so for the time being the simplest and

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so for the time being the simplest and
 

 align:start position:0%
so for the time being the simplest and
complete model for what a signal is is

 align:start position:0%
complete model for what a signal is is
 

 align:start position:0%
complete model for what a signal is is
it's just a function the function

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it's just a function the function
 

 align:start position:0%
it's just a function the function
doesn't have to be a onedimensional

 align:start position:0%
doesn't have to be a onedimensional
 

 align:start position:0%
doesn't have to be a onedimensional
function in fact a lot of the

 align:start position:0%
function in fact a lot of the
 

 align:start position:0%
function in fact a lot of the
interesting um applications of signals

 align:start position:0%
interesting um applications of signals
 

 align:start position:0%
interesting um applications of signals
and systems is to look at

 align:start position:0%
and systems is to look at
 

 align:start position:0%
and systems is to look at
multi-dimensional functions so for

 align:start position:0%
multi-dimensional functions so for
 

 align:start position:0%
multi-dimensional functions so for
example my research is in

 align:start position:0%
example my research is in
 

 align:start position:0%
example my research is in
hearing I'm interested to

 align:start position:0%
hearing I'm interested to
 

 align:start position:0%
hearing I'm interested to
study how do the cells respond to sound

 align:start position:0%
study how do the cells respond to sound
 

 align:start position:0%
study how do the cells respond to sound
so that we can understand how broken

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so that we can understand how broken
 

 align:start position:0%
so that we can understand how broken
ears work

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ears work
 

 align:start position:0%
ears work
differently when you have a when you

 align:start position:0%
differently when you have a when you
 

 align:start position:0%
differently when you have a when you
have a hearing deficit like I do when

 align:start position:0%
have a hearing deficit like I do when
 

 align:start position:0%
have a hearing deficit like I do when
you have a hearing deficit how it what

 align:start position:0%
you have a hearing deficit how it what
 

 align:start position:0%
you have a hearing deficit how it what
is the manifestation of that at a signal

 align:start position:0%
is the manifestation of that at a signal
 

 align:start position:0%
is the manifestation of that at a signal
processing level how do the cells

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processing level how do the cells
 

 align:start position:0%
processing level how do the cells
respond differently to people who have

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respond differently to people who have
 

 align:start position:0%
respond differently to people who have
impaired hearing from people who have

 align:start position:0%
impaired hearing from people who have
 

 align:start position:0%
impaired hearing from people who have
normal

 align:start position:0%
normal
 

 align:start position:0%
normal
hearing uh in order to study that

 align:start position:0%
hearing uh in order to study that
 

 align:start position:0%
hearing uh in order to study that
problem we take video

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problem we take video
 

 align:start position:0%
problem we take video
pictures of the cells at large

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pictures of the cells at large
 

 align:start position:0%
pictures of the cells at large
magnifications and watch them wiggle

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magnifications and watch them wiggle
 

 align:start position:0%
magnifications and watch them wiggle
when sounds hit

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when sounds hit
 

 align:start position:0%
when sounds hit
them so that's a picture processing

 align:start position:0%
them so that's a picture processing
 

 align:start position:0%
them so that's a picture processing
example so the signals are not the

 align:start position:0%
example so the signals are not the
 

 align:start position:0%
example so the signals are not the
independent variable is not just time

 align:start position:0%
independent variable is not just time
 

 align:start position:0%
independent variable is not just time
it's a picture so it might have X and

 align:start position:0%
it's a picture so it might have X and
 

 align:start position:0%
it's a picture so it might have X and
Y in fact the pictures we take are three

 align:start position:0%
Y in fact the pictures we take are three
 

 align:start position:0%
Y in fact the pictures we take are three
dimensional so it has X Y and Z and in

 align:start position:0%
dimensional so it has X Y and Z and in
 

 align:start position:0%
dimensional so it has X Y and Z and in
fact they're four dimensional because

 align:start position:0%
fact they're four dimensional because
 

 align:start position:0%
fact they're four dimensional because
they change with

 align:start position:0%
they change with
 

 align:start position:0%
they change with
time so we do we apply this kind of a

 align:start position:0%
time so we do we apply this kind of a
 

 align:start position:0%
time so we do we apply this kind of a
technique on 4D signals X YZ time but

 align:start position:0%
technique on 4D signals X YZ time but
 

 align:start position:0%
technique on 4D signals X YZ time but
it's still the the property it still has

 align:start position:0%
it's still the the property it still has
 

 align:start position:0%
it's still the the property it still has
a property that the signals of Interest

 align:start position:0%
a property that the signals of Interest
 

 align:start position:0%
a property that the signals of Interest
are

 align:start position:0%
are
 

 align:start position:0%
are
functions

 align:start position:0%
functions
 

 align:start position:0%
functions
we will have an we will be especially

 align:start position:0%
we will have an we will be especially
 

 align:start position:0%
we will have an we will be especially
interested in this

 align:start position:0%
interested in this
 

 align:start position:0%
interested in this
class in two distinct representations of

 align:start position:0%
class in two distinct representations of
 

 align:start position:0%
class in two distinct representations of
signals we will call them CT signals and

 align:start position:0%
signals we will call them CT signals and
 

 align:start position:0%
signals we will call them CT signals and
DT signals CT is continuous time DT is

 align:start position:0%
DT signals CT is continuous time DT is
 

 align:start position:0%
DT signals CT is continuous time DT is
discreet time we're very interested in

 align:start position:0%
discreet time we're very interested in
 

 align:start position:0%
discreet time we're very interested in
that because we're

 align:start position:0%
 
 

 align:start position:0%
 
Engineers a lot of

 align:start position:0%
Engineers a lot of
 

 align:start position:0%
Engineers a lot of
physics lives in continuous

 align:start position:0%
physics lives in continuous
 

 align:start position:0%
physics lives in continuous
time okay the m spring dashbot system

 align:start position:0%
time okay the m spring dashbot system
 

 align:start position:0%
time okay the m spring dashbot system
the signals were functions of

 align:start position:0%
the signals were functions of
 

 align:start position:0%
the signals were functions of
time time was a continuously varying uh

 align:start position:0%
time time was a continuously varying uh
 

 align:start position:0%
time time was a continuously varying uh
independent

 align:start position:0%
independent
 

 align:start position:0%
independent
variable so uh so the Leaky tank the

 align:start position:0%
variable so uh so the Leaky tank the
 

 align:start position:0%
variable so uh so the Leaky tank the
cell phones those were all systems whose

 align:start position:0%
cell phones those were all systems whose
 

 align:start position:0%
cell phones those were all systems whose
signals evolve in time uh so they're all

 align:start position:0%
signals evolve in time uh so they're all
 

 align:start position:0%
signals evolve in time uh so they're all
continuous you can you can start with a

 align:start position:0%
continuous you can you can start with a
 

 align:start position:0%
continuous you can you can start with a
second and break it in half and get a

 align:start position:0%
second and break it in half and get a
 

 align:start position:0%
second and break it in half and get a
half a second and a half and a half and

 align:start position:0%
half a second and a half and a half and
 

 align:start position:0%
half a second and a half and a half and
a half and there's no limit to how many

 align:start position:0%
a half and there's no limit to how many
 

 align:start position:0%
a half and there's no limit to how many
halves you can take

 align:start position:0%
halves you can take
 

 align:start position:0%
halves you can take
by contrast a lot of the a lot of the

 align:start position:0%
by contrast a lot of the a lot of the
 

 align:start position:0%
by contrast a lot of the a lot of the
systems that we will look at are things

 align:start position:0%
systems that we will look at are things
 

 align:start position:0%
systems that we will look at are things
that are um that evolve in discrete time

 align:start position:0%
that are um that evolve in discrete time
 

 align:start position:0%
that are um that evolve in discrete time
what's your bank account well it only

 align:start position:0%
what's your bank account well it only
 

 align:start position:0%
what's your bank account well it only
gets computed once a

 align:start position:0%
gets computed once a
 

 align:start position:0%
gets computed once a
day so it doesn't make sense to talk

 align:start position:0%
day so it doesn't make sense to talk
 

 align:start position:0%
day so it doesn't make sense to talk
about your bank account at 9:00 am and

 align:start position:0%
about your bank account at 9:00 am and
 

 align:start position:0%
about your bank account at 9:00 am and
and and 2 p.m right the bank account

 align:start position:0%
and and 2 p.m right the bank account
 

 align:start position:0%
and and 2 p.m right the bank account
updates your account the the bank

 align:start position:0%
updates your account the the bank
 

 align:start position:0%
updates your account the the bank
updates your account once a day so it's

 align:start position:0%
updates your account once a day so it's
 

 align:start position:0%
updates your account once a day so it's
something that happens in discret time

 align:start position:0%
something that happens in discret time
 

 align:start position:0%
something that happens in discret time
it's something that happens in all

 align:start position:0%
it's something that happens in all
 

 align:start position:0%
it's something that happens in all
computational

 align:start position:0%
computational
 

 align:start position:0%
computational
systems so computational systems

 align:start position:0%
systems so computational systems
 

 align:start position:0%
systems so computational systems
generally operate on signals that uh

 align:start position:0%
generally operate on signals that uh
 

 align:start position:0%
generally operate on signals that uh
that are functions of discret

 align:start position:0%
that are functions of discret
 

 align:start position:0%
that are functions of discret
time what was the state at Time Zero

 align:start position:0%
time what was the state at Time Zero
 

 align:start position:0%
time what was the state at Time Zero
what was the state at time one what was

 align:start position:0%
what was the state at time one what was
 

 align:start position:0%
what was the state at time one what was
the state at time

 align:start position:0%
the state at time
 

 align:start position:0%
the state at time
two so the system is something that eats

 align:start position:0%
two so the system is something that eats
 

 align:start position:0%
two so the system is something that eats
a discrete time signal and generates a

 align:start position:0%
a discrete time signal and generates a
 

 align:start position:0%
a discrete time signal and generates a
discrete time

 align:start position:0%
discrete time
 

 align:start position:0%
discrete time
output

 align:start position:0%
output
 

 align:start position:0%
output
signal and a unique part of this class

 align:start position:0%
signal and a unique part of this class
 

 align:start position:0%
signal and a unique part of this class
will be converting between the two

 align:start position:0%
will be converting between the two
 

 align:start position:0%
will be converting between the two
representations because as Engineers we

 align:start position:0%
representations because as Engineers we
 

 align:start position:0%
representations because as Engineers we
often want to take build something that

 align:start position:0%
often want to take build something that
 

 align:start position:0%
often want to take build something that
operates in the physical world masses

 align:start position:0%
operates in the physical world masses
 

 align:start position:0%
operates in the physical world masses
and springs and reservoirs and that kind

 align:start position:0%
and springs and reservoirs and that kind
 

 align:start position:0%
and springs and reservoirs and that kind
of

 align:start position:0%
of
 

 align:start position:0%
of
stuff and do the processing

 align:start position:0%
stuff and do the processing
 

 align:start position:0%
stuff and do the processing
computationally ever since the Advent of

 align:start position:0%
computationally ever since the Advent of
 

 align:start position:0%
computationally ever since the Advent of
digital electronics it's just much

 align:start position:0%
digital electronics it's just much
 

 align:start position:0%
digital electronics it's just much
easier digital one it's just much easier

 align:start position:0%
easier digital one it's just much easier
 

 align:start position:0%
easier digital one it's just much easier
to process signals in the in the digital

 align:start position:0%
to process signals in the in the digital
 

 align:start position:0%
to process signals in the in the digital
domain so we will often be interested in

 align:start position:0%
domain so we will often be interested in
 

 align:start position:0%
domain so we will often be interested in
how do you

 align:start position:0%
how do you
 

 align:start position:0%
how do you
represent a signal who naturally lives

 align:start position:0%
represent a signal who naturally lives
 

 align:start position:0%
represent a signal who naturally lives
in the physical world and is therefore

 align:start position:0%
in the physical world and is therefore
 

 align:start position:0%
in the physical world and is therefore
part at whose signals are continuous in

 align:start position:0%
part at whose signals are continuous in
 

 align:start position:0%
part at whose signals are continuous in
nature continuous time how do you

 align:start position:0%
nature continuous time how do you
 

 align:start position:0%
nature continuous time how do you
convert it into a discrete

 align:start position:0%
convert it into a discrete
 

 align:start position:0%
convert it into a discrete
representation so you can crunch it on a

 align:start position:0%
representation so you can crunch it on a
 

 align:start position:0%
representation so you can crunch it on a
computer and in fact how do you go back

 align:start position:0%
computer and in fact how do you go back
 

 align:start position:0%
computer and in fact how do you go back
so for

 align:start position:0%
so for
 

 align:start position:0%
so for
example if we were thinking about

 align:start position:0%
example if we were thinking about
 

 align:start position:0%
example if we were thinking about
processing audio signals we might want

 align:start position:0%
processing audio signals we might want
 

 align:start position:0%
processing audio signals we might want
to think about how we would take a

 align:start position:0%
to think about how we would take a
 

 align:start position:0%
to think about how we would take a
signal of continuous time and turn it

 align:start position:0%
signal of continuous time and turn it
 

 align:start position:0%
signal of continuous time and turn it
into a discrete time

 align:start position:0%
into a discrete time
 

 align:start position:0%
into a discrete time
representation that's precisely what we

 align:start position:0%
representation that's precisely what we
 

 align:start position:0%
representation that's precisely what we
do when we want to record something in

 align:start position:0%
do when we want to record something in
 

 align:start position:0%
do when we want to record something in
mp3 mp3 represents a sound a sound is

 align:start position:0%
mp3 mp3 represents a sound a sound is
 

 align:start position:0%
mp3 mp3 represents a sound a sound is
something that I think of as a signal in

 align:start position:0%
something that I think of as a signal in
 

 align:start position:0%
something that I think of as a signal in
continuous time it's pascals as a

 align:start position:0%
continuous time it's pascals as a
 

 align:start position:0%
continuous time it's pascals as a
function of

 align:start position:0%
function of
 

 align:start position:0%
function of
seconds but we want to represent it by a

 align:start position:0%
seconds but we want to represent it by a
 

 align:start position:0%
seconds but we want to represent it by a
sequence of numbers because it's a

 align:start position:0%
sequence of numbers because it's a
 

 align:start position:0%
sequence of numbers because it's a
sequence of numbers that's easy to store

 align:start position:0%
sequence of numbers that's easy to store
 

 align:start position:0%
sequence of numbers that's easy to store
to communicate

 align:start position:0%
to communicate
 

 align:start position:0%
to communicate
Etc we do the same sort of thing with

 align:start position:0%
Etc we do the same sort of thing with
 

 align:start position:0%
Etc we do the same sort of thing with
images the images of the ear that I

 align:start position:0%
images the images of the ear that I
 

 align:start position:0%
images the images of the ear that I
talked about in my research are things

 align:start position:0%
talked about in my research are things
 

 align:start position:0%
talked about in my research are things
that I think about happening at

 align:start position:0%
that I think about happening at
 

 align:start position:0%
that I think about happening at
continuous

 align:start position:0%
continuous
 

 align:start position:0%
continuous
space every time we look at a smaller

 align:start position:0%
space every time we look at a smaller
 

 align:start position:0%
space every time we look at a smaller
and smaller Dimension we get a different

 align:start position:0%
and smaller Dimension we get a different
 

 align:start position:0%
and smaller Dimension we get a different
answer because the the image has no

 align:start position:0%
answer because the the image has no
 

 align:start position:0%
answer because the the image has no
quantization in

 align:start position:0%
quantization in
 

 align:start position:0%
quantization in
space but when I crunch it I don't want

 align:start position:0%
space but when I crunch it I don't want
 

 align:start position:0%
space but when I crunch it I don't want
to work in something in continuous space

 align:start position:0%
to work in something in continuous space
 

 align:start position:0%
to work in something in continuous space
I want to work in a in a sampled version

 align:start position:0%
I want to work in a in a sampled version
 

 align:start position:0%
I want to work in a in a sampled version
like a JPEG

 align:start position:0%
like a JPEG
 

 align:start position:0%
like a JPEG
version similarly we want to convert

 align:start position:0%
version similarly we want to convert
 

 align:start position:0%
version similarly we want to convert
back I mean it would be useless for the

 align:start position:0%
back I mean it would be useless for the
 

 align:start position:0%
back I mean it would be useless for the
case of the cell phone to convert it

 align:start position:0%
case of the cell phone to convert it
 

 align:start position:0%
case of the cell phone to convert it
into a discrete representation and then

 align:start position:0%
into a discrete representation and then
 

 align:start position:0%
into a discrete representation and then
not be able to hear

 align:start position:0%
not be able to hear
 

 align:start position:0%
not be able to hear
it so we'll think about the inverse

 align:start position:0%
it so we'll think about the inverse
 

 align:start position:0%
it so we'll think about the inverse
process which is reconstruction if you

 align:start position:0%
process which is reconstruction if you
 

 align:start position:0%
process which is reconstruction if you
had a discrete representation of a

 align:start position:0%
had a discrete representation of a
 

 align:start position:0%
had a discrete representation of a
signal how would you turn it

 align:start position:0%
signal how would you turn it
 

 align:start position:0%
signal how would you turn it
into a continuous representation and

 align:start position:0%
into a continuous representation and
 

 align:start position:0%
into a continuous representation and
there's lots of ways people do that

 align:start position:0%
there's lots of ways people do that
 

 align:start position:0%
there's lots of ways people do that
here's a way that we call zero order

 align:start position:0%
here's a way that we call zero order
 

 align:start position:0%
here's a way that we call zero order
hold where you convert every sample into

 align:start position:0%
hold where you convert every sample into
 

 align:start position:0%
hold where you convert every sample into
a corresponding

 align:start position:0%
a corresponding
 

 align:start position:0%
a corresponding
voltage and just hold that voltage until

 align:start position:0%
voltage and just hold that voltage until
 

 align:start position:0%
voltage and just hold that voltage until
the next sample comes along this is the

 align:start position:0%
the next sample comes along this is the
 

 align:start position:0%
the next sample comes along this is the
representation that is most commonly

 align:start position:0%
representation that is most commonly
 

 align:start position:0%
representation that is most commonly
used in things like

 align:start position:0%
 
 

 align:start position:0%
 
mp3 by contrast we might do something

 align:start position:0%
mp3 by contrast we might do something
 

 align:start position:0%
mp3 by contrast we might do something
cleverer we might linearly extrapolate

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cleverer we might linearly extrapolate
 

 align:start position:0%
cleverer we might linearly extrapolate
between

 align:start position:0%
between
 

 align:start position:0%
between
samples that is commonly done in picture

 align:start position:0%
samples that is commonly done in picture
 

 align:start position:0%
samples that is commonly done in picture
processing the reason we use the two

 align:start position:0%
processing the reason we use the two
 

 align:start position:0%
processing the reason we use the two
different schemes is that

 align:start position:0%
different schemes is that
 

 align:start position:0%
different schemes is that
psychophysically the things that are

 align:start position:0%
psychophysically the things that are
 

 align:start position:0%
psychophysically the things that are
important to your eyes and the things

 align:start position:0%
important to your eyes and the things
 

 align:start position:0%
important to your eyes and the things
that are important to your ears are

 align:start position:0%
that are important to your ears are
 

 align:start position:0%
that are important to your ears are
different so you would hear the errors

 align:start position:0%
different so you would hear the errors
 

 align:start position:0%
different so you would hear the errors
more if you did the linear interpolation

 align:start position:0%
more if you did the linear interpolation
 

 align:start position:0%
more if you did the linear interpolation
and you would see the errors

 align:start position:0%
and you would see the errors
 

 align:start position:0%
and you would see the errors
more if you did the other interpolation

 align:start position:0%
more if you did the other interpolation
 

 align:start position:0%
more if you did the other interpolation
and we'll do lots of examples later on

 align:start position:0%
and we'll do lots of examples later on
 

 align:start position:0%
and we'll do lots of examples later on
in the course so you see why that's

 align:start position:0%
 
 

 align:start position:0%
 
true okay too much talking not enough

 align:start position:0%
true okay too much talking not enough
 

 align:start position:0%
true okay too much talking not enough
thinking so I've told you a lot about

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thinking so I've told you a lot about
 

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thinking so I've told you a lot about
signals now I'd like you to think about

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signals now I'd like you to think about
 

 align:start position:0%
signals now I'd like you to think about
some

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some
 

 align:start position:0%
some
signals and so a common thing I'm going

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signals and so a common thing I'm going
 

 align:start position:0%
signals and so a common thing I'm going
to do in this class is ask you to think

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to do in this class is ask you to think
 

 align:start position:0%
to do in this class is ask you to think
about a question talk to your neighbor

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about a question talk to your neighbor
 

 align:start position:0%
about a question talk to your neighbor
come to a consensus and then vote so

 align:start position:0%
come to a consensus and then vote so
 

 align:start position:0%
come to a consensus and then vote so
that's what we're going to do here I'm

 align:start position:0%
that's what we're going to do here I'm
 

 align:start position:0%
that's what we're going to do here I'm
going to play some sounds you're going

 align:start position:0%
going to play some sounds you're going
 

 align:start position:0%
going to play some sounds you're going
to try to figure out what signals were

 align:start position:0%
to try to figure out what signals were
 

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to try to figure out what signals were
represented by those sounds but I would

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represented by those sounds but I would
 

 align:start position:0%
represented by those sounds but I would
like you to have an opinion before we we

 align:start position:0%
like you to have an opinion before we we
 

 align:start position:0%
like you to have an opinion before we we
communicate the answer because you can

 align:start position:0%
communicate the answer because you can
 

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communicate the answer because you can
prove that people get more out of it

 align:start position:0%
prove that people get more out of it
 

 align:start position:0%
prove that people get more out of it
when there's something at stake so I

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when there's something at stake so I
 

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when there's something at stake so I
would like you to work with a partner so

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would like you to work with a partner so
 

 align:start position:0%
would like you to work with a partner so
in order to work with a partner

 align:start position:0%
in order to work with a partner
 

 align:start position:0%
in order to work with a partner
everybody stand up introduce yourself to

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everybody stand up introduce yourself to
 

 align:start position:0%
everybody stand up introduce yourself to
your neighbor figure out a good partner

 align:start position:0%
your neighbor figure out a good partner
 

 align:start position:0%
your neighbor figure out a good partner
figure out where they

 align:start position:0%
 
 

 align:start position:0%
 
live

 align:start position:0%
 
 

 align:start position:0%
 
okay so what I'm I'm going to do

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okay so what I'm I'm going to do
 

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okay so what I'm I'm going to do
now is play a computer generated sound

 align:start position:0%
now is play a computer generated sound
 

 align:start position:0%
now is play a computer generated sound
this is a computerated computer

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this is a computerated computer
 

 align:start position:0%
this is a computerated computer
generated speech sound made by Bob

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generated speech sound made by Bob
 

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generated speech sound made by Bob
Donovan who did his PhD thesis figuring

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Donovan who did his PhD thesis figuring
 

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Donovan who did his PhD thesis figuring
out how to do computer generated

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out how to do computer generated
 

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out how to do computer generated
speech and then I'm going to play Four

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speech and then I'm going to play Four
 

 align:start position:0%
speech and then I'm going to play Four
transformations of that

 align:start position:0%
transformations of that
 

 align:start position:0%
transformations of that
sound and the your task is to identify

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sound and the your task is to identify
 

 align:start position:0%
sound and the your task is to identify
what's the mathematical representation

 align:start position:0%
what's the mathematical representation
 

 align:start position:0%
what's the mathematical representation
of the Transformations that I'm telling

 align:start position:0%
of the Transformations that I'm telling
 

 align:start position:0%
of the Transformations that I'm telling
you okay so first the original

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you okay so first the original
 

 align:start position:0%
you okay so first the original
first is the signal that Bob Donovan

 align:start position:0%
 
 

 align:start position:0%
 
MaDee and now I'm going to play a

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MaDee and now I'm going to play a
 

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MaDee and now I'm going to play a
sequence of four

 align:start position:0%
sequence of four
 

 align:start position:0%
sequence of four
Transformations 1 2 3 four and the

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Transformations 1 2 3 four and the
 

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Transformations 1 2 3 four and the
question is going to be is this the ma

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question is going to be is this the ma
 

 align:start position:0%
question is going to be is this the ma
the correct mathematical representation

 align:start position:0%
the correct mathematical representation
 

 align:start position:0%
the correct mathematical representation
for this sound the sound you just heard

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for this sound the sound you just heard
 

 align:start position:0%
for this sound the sound you just heard
was F of t

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was F of t
 

 align:start position:0%
was F of t
is the following sound which by

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is the following sound which by
 

 align:start position:0%
is the following sound which by
definition is

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definition is
 

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definition is
F1 the same as F of

 align:start position:0%
 
 

 align:start position:0%
 
[Music]

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2T you're allowed to

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 align:start position:0%
 
talk

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 align:start position:0%
 
e

 align:start position:0%
 
 

 align:start position:0%
 
okay remember that answer now is the

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okay remember that answer now is the
 

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okay remember that answer now is the
following sound minus F

 align:start position:0%
 
 

 align:start position:0%
 
[Music]

 align:start position:0%
 
 

 align:start position:0%
 
of

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 align:start position:0%
 
okay remember that answer is the

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okay remember that answer is the
 

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okay remember that answer is the
following sound F of

 align:start position:0%
 
 

 align:start position:0%
 
2T

 align:start position:0%
 
 

 align:start position:0%
 
and

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and
 

 align:start position:0%
and
finally is the following signal oneir of

 align:start position:0%
finally is the following signal oneir of
 

 align:start position:0%
finally is the following signal oneir of
f of

 align:start position:0%
 
 

 align:start position:0%
 
te okay conver confer with your

 align:start position:0%
te okay conver confer with your
 

 align:start position:0%
te okay conver confer with your
partner figure out how many are true

 align:start position:0%
partner figure out how many are true
 

 align:start position:0%
partner figure out how many are true
because in 30 seconds I'm going to ask

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because in 30 seconds I'm going to ask
 

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because in 30 seconds I'm going to ask
you to raise your

 align:start position:0%
 
 

 align:start position:0%
 
hand

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 align:start position:0%
 
question

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question
 

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question
or fft was the original

 align:start position:0%
 
 

 align:start position:0%
 
signal uh

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signal uh
 

 align:start position:0%
signal uh
pressure pressure in the acoustic

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pressure pressure in the acoustic
 

 align:start position:0%
pressure pressure in the acoustic
waveform

 align:start position:0%
 
 

 align:start position:0%
 
that's

 align:start position:0%
 
 

 align:start position:0%
 
true okay how many of those statements

 align:start position:0%
true okay how many of those statements
 

 align:start position:0%
true okay how many of those statements
are true raise your hand with some

 align:start position:0%
are true raise your hand with some
 

 align:start position:0%
are true raise your hand with some
number of fingers keeping in mind that

 align:start position:0%
number of fingers keeping in mind that
 

 align:start position:0%
number of fingers keeping in mind that
you're voting having collaborated with

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you're voting having collaborated with
 

 align:start position:0%
you're voting having collaborated with
your partner so it's not your fault you

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your partner so it's not your fault you
 

 align:start position:0%
your partner so it's not your fault you
have a right anyway okay so how many so

 align:start position:0%
have a right anyway okay so how many so
 

 align:start position:0%
have a right anyway okay so how many so
everybody raise your hands I want to

 align:start position:0%
 
 

 align:start position:0%
 
see okay it's about 90% no less than

 align:start position:0%
see okay it's about 90% no less than
 

 align:start position:0%
see okay it's about 90% no less than
that about 85% correct okay uh so first

 align:start position:0%
that about 85% correct okay uh so first
 

 align:start position:0%
that about 85% correct okay uh so first
one was that F of

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one was that F of
 

 align:start position:0%
one was that F of
2T why do you think that everybody seems

 align:start position:0%
2T why do you think that everybody seems
 

 align:start position:0%
2T why do you think that everybody seems
to be saying

 align:start position:0%
to be saying
 

 align:start position:0%
to be saying
yes it was fast it sounded faster so

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yes it was fast it sounded faster so
 

 align:start position:0%
yes it was fast it sounded faster so
what's faster mean from a signal point

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what's faster mean from a signal point
 

 align:start position:0%
what's faster mean from a signal point
of

 align:start position:0%
 
 

 align:start position:0%
 
view change the time scales that's a

 align:start position:0%
view change the time scales that's a
 

 align:start position:0%
view change the time scales that's a
very good way of thinking about it so if

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very good way of thinking about it so if
 

 align:start position:0%
very good way of thinking about it so if
we thought about if we made a simple

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we thought about if we made a simple
 

 align:start position:0%
we thought about if we made a simple
representation for

 align:start position:0%
representation for
 

 align:start position:0%
representation for
f ignore what it really is let's say

 align:start position:0%
f ignore what it really is let's say
 

 align:start position:0%
f ignore what it really is let's say
it's

 align:start position:0%
it's
 

 align:start position:0%
it's
that what would F1 look like in order to

 align:start position:0%
that what would F1 look like in order to
 

 align:start position:0%
that what would F1 look like in order to
make it sound

 align:start position:0%
 
 

 align:start position:0%
 
faster okay we have people doing this

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faster okay we have people doing this
 

 align:start position:0%
faster okay we have people doing this
and we have people doing this and I'm

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and we have people doing this and I'm
 

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and we have people doing this and I'm
not quite sure what that means so could

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not quite sure what that means so could
 

 align:start position:0%
not quite sure what that means so could
somebody be a little more

 align:start position:0%
somebody be a little more
 

 align:start position:0%
somebody be a little more
descriptive hand gestures are fine yes

 align:start position:0%
descriptive hand gestures are fine yes
 

 align:start position:0%
descriptive hand gestures are fine yes
squished squished exactly right so what

 align:start position:0%
squished squished exactly right so what
 

 align:start position:0%
squished squished exactly right so what
we want to have happen

 align:start position:0%
we want to have happen
 

 align:start position:0%
we want to have happen
in order to sound faster we want to have

 align:start position:0%
in order to sound faster we want to have
 

 align:start position:0%
in order to sound faster we want to have
it come out faster so we would like that

 align:start position:0%
it come out faster so we would like that
 

 align:start position:0%
it come out faster so we would like that
to happen to it so it's all over in one

 align:start position:0%
to happen to it so it's all over in one
 

 align:start position:0%
to happen to it so it's all over in one
second if the original was all over in

 align:start position:0%
second if the original was all over in
 

 align:start position:0%
second if the original was all over in
two seconds right that's what faster

 align:start position:0%
two seconds right that's what faster
 

 align:start position:0%
two seconds right that's what faster
means so we would like that to be true

 align:start position:0%
means so we would like that to be true
 

 align:start position:0%
means so we would like that to be true
is that what's going on in that

 align:start position:0%
is that what's going on in that
 

 align:start position:0%
is that what's going on in that
function

 align:start position:0%
function
 

 align:start position:0%
function
yeah okay so that's right second

 align:start position:0%
yeah okay so that's right second
 

 align:start position:0%
yeah okay so that's right second
one

 align:start position:0%
one
 

 align:start position:0%
one
yes

 align:start position:0%
yes
 

 align:start position:0%
yes
and that also makes it higher pitched in

 align:start position:0%
and that also makes it higher pitched in
 

 align:start position:0%
and that also makes it higher pitched in
fact we will talk a lot about this later

 align:start position:0%
fact we will talk a lot about this later
 

 align:start position:0%
fact we will talk a lot about this later
but pitch has to do with a related kind

 align:start position:0%
but pitch has to do with a related kind
 

 align:start position:0%
but pitch has to do with a related kind
of waveform if I thought about a

 align:start position:0%
of waveform if I thought about a
 

 align:start position:0%
of waveform if I thought about a
waveform that was a single

 align:start position:0%
waveform that was a single
 

 align:start position:0%
waveform that was a single
tone that might look like

 align:start position:0%
tone that might look like
 

 align:start position:0%
tone that might look like
this so if you were to play an

 align:start position:0%
this so if you were to play an
 

 align:start position:0%
this so if you were to play an
OBO and play Just A C constantly you get

 align:start position:0%
OBO and play Just A C constantly you get
 

 align:start position:0%
OBO and play Just A C constantly you get
some periodic

 align:start position:0%
some periodic
 

 align:start position:0%
some periodic
waveform if I did the same

 align:start position:0%
waveform if I did the same
 

 align:start position:0%
waveform if I did the same
transformation on that periodic wave

 align:start position:0%
transformation on that periodic wave
 

 align:start position:0%
transformation on that periodic wave
form what would happen to that waveform

 align:start position:0%
form what would happen to that waveform
 

 align:start position:0%
form what would happen to that waveform
what would happen to this if I did

 align:start position:0%
what would happen to this if I did
 

 align:start position:0%
what would happen to this if I did
transformation

 align:start position:0%
transformation
 

 align:start position:0%
transformation
one squish what's squish

 align:start position:0%
one squish what's squish
 

 align:start position:0%
one squish what's squish
being more High higher frequency more

 align:start position:0%
being more High higher frequency more
 

 align:start position:0%
being more High higher frequency more
cycles per second yeah so how you make

 align:start position:0%
cycles per second yeah so how you make
 

 align:start position:0%
cycles per second yeah so how you make
the same go as fast have the same that's

 align:start position:0%
the same go as fast have the same that's
 

 align:start position:0%
the same go as fast have the same that's
very hard in fact I worked on that as a

 align:start position:0%
very hard in fact I worked on that as a
 

 align:start position:0%
very hard in fact I worked on that as a
research project um so one of the

 align:start position:0%
research project um so one of the
 

 align:start position:0%
research project um so one of the
techniques that we use to try to fix

 align:start position:0%
techniques that we use to try to fix
 

 align:start position:0%
techniques that we use to try to fix
people's

 align:start position:0%
people's
 

 align:start position:0%
people's
ears uh it turns out that people who

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ears uh it turns out that people who
 

 align:start position:0%
ears uh it turns out that people who
have hearing disorders like

 align:start position:0%
have hearing disorders like
 

 align:start position:0%
have hearing disorders like
mine can more easily understand male

 align:start position:0%
mine can more easily understand male
 

 align:start position:0%
mine can more easily understand male
speech than female speech just because

 align:start position:0%
speech than female speech just because
 

 align:start position:0%
speech than female speech just because
of the shift in frequencies male speech

 align:start position:0%
of the shift in frequencies male speech
 

 align:start position:0%
of the shift in frequencies male speech
is primarily about an octave lower on

 align:start position:0%
is primarily about an octave lower on
 

 align:start position:0%
is primarily about an octave lower on
average than female speech so we tried

 align:start position:0%
average than female speech so we tried
 

 align:start position:0%
average than female speech so we tried
to convert every female into a male

 align:start position:0%
to convert every female into a male
 

 align:start position:0%
to convert every female into a male
speaker and every male into the Jolly

 align:start position:0%
speaker and every male into the Jolly
 

 align:start position:0%
speaker and every male into the Jolly
Green

 align:start position:0%
Green
 

 align:start position:0%
Green
Giant and it worked males sounded like

 align:start position:0%
Giant and it worked males sounded like
 

 align:start position:0%
Giant and it worked males sounded like
the Jolly Green Giant and females

 align:start position:0%
the Jolly Green Giant and females
 

 align:start position:0%
the Jolly Green Giant and females
sounded like males and it didn't help

 align:start position:0%
sounded like males and it didn't help
 

 align:start position:0%
sounded like males and it didn't help
hearing at all and that's primarily

 align:start position:0%
hearing at all and that's primarily
 

 align:start position:0%
hearing at all and that's primarily
because it's a hard problem so but we

 align:start position:0%
because it's a hard problem so but we
 

 align:start position:0%
because it's a hard problem so but we
will say more about that as we go on

 align:start position:0%
will say more about that as we go on
 

 align:start position:0%
will say more about that as we go on
through the course but is a hard

 align:start position:0%
through the course but is a hard
 

 align:start position:0%
through the course but is a hard
problem because you end up having to do

 align:start position:0%
problem because you end up having to do
 

 align:start position:0%
problem because you end up having to do
other than just

 align:start position:0%
other than just
 

 align:start position:0%
other than just
squish

 align:start position:0%
squish
 

 align:start position:0%
squish
okay second one is this the right

 align:start position:0%
okay second one is this the right
 

 align:start position:0%
okay second one is this the right
transformation no why

 align:start position:0%
transformation no why
 

 align:start position:0%
transformation no why
not

 align:start position:0%
 
 

 align:start position:0%
 
yeah if you flipped over the

 align:start position:0%
yeah if you flipped over the
 

 align:start position:0%
yeah if you flipped over the
amplitude so what it's so flip over the

 align:start position:0%
amplitude so what it's so flip over the
 

 align:start position:0%
amplitude so what it's so flip over the
amplitude you're saying that didn't do

 align:start position:0%
amplitude you're saying that didn't do
 

 align:start position:0%
amplitude you're saying that didn't do
it what what was the transformation if

 align:start position:0%
it what what was the transformation if
 

 align:start position:0%
it what what was the transformation if
it wasn't flip over the amplitude what

 align:start position:0%
it wasn't flip over the amplitude what
 

 align:start position:0%
it wasn't flip over the amplitude what
is it

 align:start position:0%
is it
 

 align:start position:0%
is it
yeah F of minus t it was flipped this

 align:start position:0%
yeah F of minus t it was flipped this
 

 align:start position:0%
yeah F of minus t it was flipped this
way right flipping this way is largely

 align:start position:0%
way right flipping this way is largely
 

 align:start position:0%
way right flipping this way is largely
inaudible if you had a pressure wave

 align:start position:0%
inaudible if you had a pressure wave
 

 align:start position:0%
inaudible if you had a pressure wave
form versus a rare faction waveform

 align:start position:0%
form versus a rare faction waveform
 

 align:start position:0%
form versus a rare faction waveform
positive pressures versus negative

 align:start position:0%
positive pressures versus negative
 

 align:start position:0%
positive pressures versus negative
pressures this is very hard to tell not

 align:start position:0%
pressures this is very hard to tell not
 

 align:start position:0%
pressures this is very hard to tell not
impossible if you're one of those audio

 align:start position:0%
impossible if you're one of those audio
 

 align:start position:0%
impossible if you're one of those audio
types like me you can probably hear the

 align:start position:0%
types like me you can probably hear the
 

 align:start position:0%
types like me you can probably hear the
difference but it's very hard hearing

 align:start position:0%
difference but it's very hard hearing
 

 align:start position:0%
difference but it's very hard hearing
this not

 align:start position:0%
this not
 

 align:start position:0%
this not
hard okay uh how about this

 align:start position:0%
 
 

 align:start position:0%
 
one obviously wrong because this one was

 align:start position:0%
one obviously wrong because this one was
 

 align:start position:0%
one obviously wrong because this one was
right okay how about this

 align:start position:0%
right okay how about this
 

 align:start position:0%
right okay how about this
one yeah so the idea was that um there

 align:start position:0%
one yeah so the idea was that um there
 

 align:start position:0%
one yeah so the idea was that um there
were two that were correct so the 85% of

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were two that were correct so the 85% of
 

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were two that were correct so the 85% of
you or so who got two presumably you got

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you or so who got two presumably you got
 

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you or so who got two presumably you got
the right two right the bet I won't ask

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the right two right the bet I won't ask
 

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the right two right the bet I won't ask
um okay here's a here's a an image

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um okay here's a here's a an image
 

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um okay here's a here's a an image
processing

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processing
 

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processing
question think about this picture of

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question think about this picture of
 

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question think about this picture of
sta I know it's hard to think about

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sta I know it's hard to think about
 

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sta I know it's hard to think about
pictures of sta that's

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pictures of sta that's
 

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pictures of sta that's
okay think about this picture of sta

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okay think about this picture of sta
 

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okay think about this picture of sta
I've indexed XM Y and I've written that

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I've indexed XM Y and I've written that
 

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I've indexed XM Y and I've written that
as f a signal that depends on two

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as f a signal that depends on two
 

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as f a signal that depends on two
independent variables XM

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independent variables XM
 

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independent variables XM
Y and I've got three Transformations the

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Y and I've got three Transformations the
 

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Y and I've got three Transformations the
F1 transformation the F2 and the

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F3 the question is is this the right

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F3 the question is is this the right
 

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F3 the question is is this the right
mathematical

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mathematical
 

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mathematical
representation for transforming that

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representation for transforming that
 

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representation for transforming that
picture into this

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picture into this
 

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picture into this
one is this the one for that one and is

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one is this the one for that one and is
 

 align:start position:0%
one is this the one for that one and is
is this a representation for this one is

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is this a representation for this one is
 

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is this a representation for this one is
this a representation for that one take

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this a representation for that one take
 

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this a representation for that one take
30 seconds talk to your partner and and

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30 seconds talk to your partner and and
 

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30 seconds talk to your partner and and
figure out how many of those

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figure out how many of those
 

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figure out how many of those
Transformations are

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correct

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e

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okay so how many of the Transformations

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okay so how many of the Transformations
 

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okay so how many of the Transformations
are correct raise your

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are correct raise your
 

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are correct raise your
hand everybody raise your

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hand everybody raise your
 

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hand everybody raise your
hand oh

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hand oh
 

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hand oh
uh it's a zero or three okay just

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uh it's a zero or three okay just
 

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uh it's a zero or three okay just
checking okay about 85% correct again

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checking okay about 85% correct again
 

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checking okay about 85% correct again
okay probably a different 85% um so how

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okay probably a different 85% um so how
 

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okay probably a different 85% um so how
do you think about this problem so

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do you think about this problem so
 

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do you think about this problem so
there's a variety of ways you could

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there's a variety of ways you could
 

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there's a variety of ways you could
think about

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think about
 

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think about
it let me show you a way that focuses on

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it let me show you a way that focuses on
 

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it let me show you a way that focuses on
an idea called mapping because I think

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an idea called mapping because I think
 

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an idea called mapping because I think
is a very powerful way so if you think

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is a very powerful way so if you think
 

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is a very powerful way so if you think
about a map how does the how does the T

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about a map how does the how does the T
 

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about a map how does the how does the T
variable in the first problem map to the

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variable in the first problem map to the
 

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variable in the first problem map to the
T variable in the second

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T variable in the second
 

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T variable in the second
problem so a way you can think about

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problem so a way you can think about
 

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problem so a way you can think about
this is if this is true for um all X and

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this is if this is true for um all X and
 

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this is if this is true for um all X and
Y it's true for particular X so let's

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Y it's true for particular X so let's
 

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Y it's true for particular X so let's
ask is it true for x equals

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ask is it true for x equals
 

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ask is it true for x equals
z so how does the point x equals 0 map

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z so how does the point x equals 0 map
 

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z so how does the point x equals 0 map
from one image to another so if you

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from one image to another so if you
 

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from one image to another so if you
substitute at x equals 0 then F1 of0 so

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substitute at x equals 0 then F1 of0 so
 

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substitute at x equals 0 then F1 of0 so
if you look at uh this

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if you look at uh this
 

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if you look at uh this
transformation the claim would be that

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transformation the claim would be that
 

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transformation the claim would be that
fub1 of0 is the same as F of

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fub1 of0 is the same as F of
 

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fub1 of0 is the same as F of
zero is that

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true so F1 of

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true so F1 of
 

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true so F1 of
zero bcts

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sta F of Z bisects

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sta F of Z bisects
 

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sta F of Z bisects
Theta so yeah that's the right thing

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Theta so yeah that's the right thing
 

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Theta so yeah that's the right thing
everybody see

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everybody see
 

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everybody see
that is the statement true for xal

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that is the statement true for xal
 

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that is the statement true for xal
250 well F1 of

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250 well F1 of
 

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250 well F1 of
250 so F1 of

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250 so F1 of
 

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250 so F1 of
250 is

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250 is
 

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250 is
through uh the right hand side of

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through uh the right hand side of
 

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through uh the right hand side of
sta sort of where the steel and the

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sta sort of where the steel and the
 

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sta sort of where the steel and the
bricks come

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bricks come
 

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bricks come
together is that the same as

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together is that the same as
 

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together is that the same as
substituting in here if x is 250 then F

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substituting in here if x is 250 then F
 

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substituting in here if x is 250 then F
of 500

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of 500
 

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of 500
F of 500 is off the screen so is that

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F of 500 is off the screen so is that
 

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F of 500 is off the screen so is that
transformation hold at the point xal 250

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transformation hold at the point xal 250
 

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transformation hold at the point xal 250
no okay it can't be right okay one one

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no okay it can't be right okay one one
 

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no okay it can't be right okay one one
bad sample proves that it can't be the

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bad sample proves that it can't be the
 

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bad sample proves that it can't be the
general

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general
 

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general
transformation okay everybody see

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transformation okay everybody see
 

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transformation okay everybody see
that similarly for the second

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that similarly for the second
 

 align:start position:0%
that similarly for the second
transformation let's just try some

 align:start position:0%
transformation let's just try some
 

 align:start position:0%
transformation let's just try some
points if we try the point xal

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points if we try the point xal
 

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points if we try the point xal
0 this says that F2 at location Z should

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0 this says that F2 at location Z should
 

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0 this says that F2 at location Z should
be F at location minus

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be F at location minus
 

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be F at location minus
250 is that

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correct so F of zero well that's the

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correct so F of zero well that's the
 

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correct so F of zero well that's the
left hand side of

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left hand side of
 

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left hand side of
theta and so F2 of Zer that's the left

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theta and so F2 of Zer that's the left
 

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theta and so F2 of Zer that's the left
hand side of theta F of 2 *

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hand side of theta F of 2 *
 

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hand side of theta F of 2 *
0 minus 250 IS F of 250 minus 250 that's

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0 minus 250 IS F of 250 minus 250 that's
 

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0 minus 250 IS F of 250 minus 250 that's
also the left of sta

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also the left of sta
 

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also the left of sta
okay so by using that reasoning you can

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okay so by using that reasoning you can
 

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okay so by using that reasoning you can
go through and see if certain points map

 align:start position:0%
go through and see if certain points map
 

 align:start position:0%
go through and see if certain points map
to the corresponding place where they

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to the corresponding place where they
 

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to the corresponding place where they
were supposed to go that's the idea of

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were supposed to go that's the idea of
 

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were supposed to go that's the idea of
mapping and in this particular case if

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mapping and in this particular case if
 

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mapping and in this particular case if
we Trace two

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we Trace two
 

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we Trace two
points and the map 2x - 250 is a linear

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points and the map 2x - 250 is a linear
 

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points and the map 2x - 250 is a linear
function of

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function of
 

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function of
X so two points determine a straight

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X so two points determine a straight
 

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X so two points determine a straight
line so after you've determined two two

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line so after you've determined two two
 

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line so after you've determined two two
points you're

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points you're
 

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points you're
done seem seem

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done seem seem
 

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done seem seem
right so similarly you can figure out

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right so similarly you can figure out
 

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right so similarly you can figure out
that the particular points didn't work

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that the particular points didn't work
 

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that the particular points didn't work
here and so the answer is that only one

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here and so the answer is that only one
 

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here and so the answer is that only one
of those Transformations was

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right okay so I spent a fair amount of

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right okay so I spent a fair amount of
 

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right okay so I spent a fair amount of
time on S signals in the last minute oh

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time on S signals in the last minute oh
 

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time on S signals in the last minute oh
minute no I'm not going to do that am I

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minute no I'm not going to do that am I
 

 align:start position:0%
minute no I'm not going to do that am I
okay I spent a fair amount of time

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okay I spent a fair amount of time
 

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okay I spent a fair amount of time
talking about signals next

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talking about signals next
 

 align:start position:0%
talking about signals next
time we'll talk about

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time we'll talk about
 

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time we'll talk about
similar ways of thinking about simple

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similar ways of thinking about simple
 

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similar ways of thinking about simple
systems so have a good

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weekend