text stringlengths 81 47k | source stringlengths 59 147 |
|---|---|
Question: <p>I am reading a book on Laplace transform, and in the section on the convergence of Laplace transform for various signals the following theorem is stated, without any proof :</p>
<p><em>If a signal's Fourier transform be zero in some frequencies, or have discontinuities, it will not have Laplace transform ... | https://dsp.stackexchange.com/questions/20075/do-signals-with-a-fourier-transform-with-discontinuities-or-zero-amplitude-in-s |
Question: <p>Assume I have a discrete random signal, $f(t)$ for which I want to calculate the laplace transform. </p>
<p>How can I do it in matlab without using <code>sym</code> variables, for example consider I have this discrete signal <code>f(t)</code>:</p>
<pre><code>>> t=linspace(0,1000, 10000);
>> f... | https://dsp.stackexchange.com/questions/45030/how-to-compute-the-laplace-transform-of-a-discrete-signal |
Question: <p>I don't study electrical engineering or something related but I was assigned a problem on transfer functions, impulse responses, and in general, everything related to <a href="https://dsp.stackexchange.com/questions/536/what-is-meant-by-a-systems-impulse-response-and-frequency-response">this post</a>. (Spe... | https://dsp.stackexchange.com/questions/26775/can-i-use-fourier-transforms-instead-of-laplace-transforms-analyzing-rc-circuit |
Question: <p>I do not understand how the last equality is derived from the previous.
Apparently the first term in the integral (involving $\mathrm{cos}$) is equivalent to the second (involving $\mathrm{sin}$)!! How so??</p>
<p>I DO understand how the integral range is halved (since $F(s)^*=F(s^*)$; where $F(s)$ is the... | https://dsp.stackexchange.com/questions/41525/how-is-the-simplified-version-of-the-bromwich-inverse-laplace-transform-integral |
Question: <p>I've read that <strong>Laplace Transform</strong> is more versatile and can cover a broad range of signals compared to <strong>Continuous Time Fourier Transform</strong>. Then why are we still using <strong>Continuous Time Fourier Transform</strong> ?</p>
Answer: | https://dsp.stackexchange.com/questions/36709/why-are-we-still-using-continuous-time-fourier-transform-when-we-have-laplace-tr |
Question: <p>I am trying to understand the connection between Laplace transform ($s$-plane), and frequency domain calculation.</p>
<p>Let's take the Fourier transform of $\cos(\omega_0t)$, which equals to $\pi[\delta(\omega - \omega_0) + \delta(\omega + \omega_0)]$. So clearly the frequency domain has only two non-zer... | https://dsp.stackexchange.com/questions/37265/laplace-transform-of-cosine-poles-and-mapping-to-frequency-domain |
Question: <ul>
<li><p>Is there an easy way to explain the motivation behind the use of Laplace transform instead of Fourier transform?</p></li>
<li><p>Isn't that any periodic function can be represented by sines and cosines? - Why to introduce exponential idea? </p></li>
<li>Why not using differential equations with Fo... | https://dsp.stackexchange.com/questions/32357/why-fourier-transform-is-not-sufficient-and-we-have-to-use-laplace-transform |
Question: <p>(Please note that I'm aware there are already several questions asking about the difference between the two transforms. However, none of them that I could find touch on this specific issue of the affect of singularities.)</p>
<p>I was reading <a href="https://dsp.stackexchange.com/a/15356/56502">this answ... | https://dsp.stackexchange.com/questions/91712/why-do-singularities-on-the-imaginary-axis-affect-the-fourier-transform-differen |
Question: <p>Always had a thought about why Laplace transform reveals the transient properties of the system?
My doubt is based on the following fact,
Fourier transform is given as </p>
<p><span class="math-container">\begin{equation}
\mathscr{F}\left\lbrace f(t)\right\rbrace = \int_{-\infty}^\infty f(t) e^{ -j \omega... | https://dsp.stackexchange.com/questions/64624/is-the-laplace-transform-a-special-case-of-fourier-transform-not-the-other-way |
Question: <p>For $a > 0$, is there any known representation of the Laplace transform of $f(t+a)$ in terms of the Laplace Transform of $f(t) $</p>
<p>Note: In my application, $f(t)$ is not a periodic function and the functional form of $f(t)$ is not actually known a-priori, because I have to couple it to another set... | https://dsp.stackexchange.com/questions/41211/laplace-transform-of-fta-a0-where-ft-is-not-periodic |
Question: <p>Suppose that for a system <span class="math-container">$S$</span> if we have <span class="math-container">$t_{2} = t_{1}+t_{0}\rightarrow h(t,t_{2}) =h(t,t_{1})+h(t,t_{0}) $</span> .Then if we take the double Laplace transform to<span class="math-container">$t,t_{2}$</span> we will get:</p>
<p><span class=... | https://dsp.stackexchange.com/questions/87456/linear-linearly-time-varying-systems-laplace-transform |
Question: <p>I was going through an Electrical Engineering textbook for understanding the Laplace transform and came across the following proof for one of the properties of the Unilateral Laplace transform.</p>
<p>Integration property of the unilateral Laplace transform:
<a href="https://i.sstatic.net/sjRS6.png" rel="n... | https://dsp.stackexchange.com/questions/72903/how-can-we-prove-the-correctness-of-the-integration-property-of-the-laplace-tran |
Question: <p>Consider the following signal:
<span class="math-container">$$ x(t) = e^{-2t}[u(t) - u(t-5)] $$</span></p>
<p>This signal exists only from 0 to 5 time units. Elsewhere, it is zero.</p>
<p>Now, let's find the laplace transform of this signal using Linearity and Time shift properties.</p>
<p><span class="... | https://dsp.stackexchange.com/questions/59694/laplace-transform-of-a-finite-duration-signal |
Question: <p>I have two sets of one second voltage data sampled with 4000Hz and I can plot all the voltage points vs time points in MATLAB. So it means I have a data matrix with with length of 4000 one column for the time in seconds the other for the voltage. </p>
<p>Now I have simultaneously sampled two data matrix i... | https://dsp.stackexchange.com/questions/45287/laplace-transform-of-a-time-domain-sampled-data-matlab |
Question: <p>While studying the Laplace transform using <a href="http://www.dspguide.com/pdfbook.htm" rel="nofollow noreferrer">Steven W. Smith Book</a> I found something uncomprehending. In the 32th chapter - The Laplace Transform, page 590, last paragraph describes the cancelling phenomena when an impulse response i... | https://dsp.stackexchange.com/questions/80628/the-laplace-transform-steven-w-smith-book-impulse-response-cancellation-met |
Question: <p>Let <span class="math-container">$L_t\{f(x, t)\}$</span> denotes the Laplace transform (two-sided) of <span class="math-container">$f(x,t)$</span> with respect to <span class="math-container">$t$</span>. That is,</p>
<p><span class="math-container">$L_t\{f(x, t)\}(s)=\int_{-∞}^{+∞}f(x, t) e^{-st} dt$</span... | https://dsp.stackexchange.com/questions/95963/is-it-possible-to-take-fractional-fourier-transform-of-laplace-transform |
Question: <p>I have a basic understanding of Laplace and Fourier but having trouble making a connection. Every time I attempt to look at reasons these are connected I'm told about the s-plane and regions of convergence which confuse me quite a lot trying to wrap my head around. What I would like to know is whether my u... | https://dsp.stackexchange.com/questions/78924/connection-from-fourier-to-laplace-transform |
Question: <p>I know that <span class="math-container">$$X_L(s) \Big|_{s=j\omega}=X_F(\omega)$$</span> if <span class="math-container">$x(t)$</span> is one sided and absolutely integrable and hence the imaginary axis of the Laplace transform is the Fourier transform.</p>
<p>But Fourier transform also has imaginary and ... | https://dsp.stackexchange.com/questions/28100/relation-between-laplace-and-fourier-transforms |
Question: <p>I'm reading 'Discrete Time Control Systems' book by Ogata and came across a few statements (specifically, (3-1) and (3-2)) which I have not been able to understand.</p>
<p>It is said that any continuous signal can be sampled and the output represented as
$$y(t) = \sum_{n=- \infty}^{+\infty}x(nT)\delta(t-... | https://dsp.stackexchange.com/questions/40433/laplace-transform-of-product-of-signal-and-impulse-train |
Question: <p>An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise.</p>
<p>Now sticking to the mathematical notation of Laplace transform, we have for a causal function <span class="math-container">$x(t) = u(t)$</span>:
<span class="math-c... | https://dsp.stackexchange.com/questions/56793/why-is-the-roc-of-laplace-transform-independent-of-imaginary-part-of-s |
Question: <p>I have this differential equation that models a causal LTI system:
<span class="math-container">$$
\ddot{v}(t) - \dot{v}(t) - 2v(t) = \ddot{u}(t) + 2\dot{u}(t) + u(t)
$$</span></p>
<p>I was asked to find the impulse response both by using Laplace transform and by solving the ODE.</p>
<p>The first method is... | https://dsp.stackexchange.com/questions/93642/impulse-response-of-a-causal-lti-system-without-using-laplace-transform |
Question: <p>Suppose a continuous signal <span class="math-container">$x(t)$</span>, the Laplace transform of <span class="math-container">$x(t)$</span> is <span class="math-container">$X(s)$</span>. Suppose the ideally-sampled signal of <span class="math-container">$x(t)$</span> is <span class="math-container">$\hat{x... | https://dsp.stackexchange.com/questions/95098/what-is-relationship-between-the-laplace-transform-of-the-ideally-sampled-signal |
Question: <p>A couple of confusions have been occurred. The Signal I'm considering is <strong>f(t) = sin(t)*u(t)</strong></p>
<ol>
<li><p>Fourier Transform of it can be derived.
<em><span class="math-container">$-i \pi (\delta (\omega -1)-\delta (\omega +1))$</span></em></p></li>
<li><p>According to my mathematica co... | https://dsp.stackexchange.com/questions/53875/can-a-fourier-transform-exist-even-if-the-j-omega-axis-is-not-in-the-region-of |
Question: <p>I'm following Oppenheim's book. In exapmles, the laplace transforms of of the following signals </p>
<p><span class="math-container">$e^{-t}u(t)$</span> and <span class="math-container">$e^{-t-1}u(t+1)$</span> </p>
<p>is given as <span class="math-container">$\frac{s}{(s+1)}$</span> and <span class="math... | https://dsp.stackexchange.com/questions/60662/determining-stability-of-a-continuous-time-system-using-laplace-transform |
Question: <p>Given the input $$x(t)=u(t)$$ and the corresponding output signal measured as $$y(t)= 2 e^{-3t} u(t)$$ determine the impulse response $h(t)$.</p>
<p>This what have done so far:
$$ h(t)= \mathscr{L}^{-1} \left\{ \frac{Y(s)}{X(s)} \right\} = \frac{2/(s+3)}{1/s}
= \frac{2s}{s+3} $$. </p>
<p>I need to find t... | https://dsp.stackexchange.com/questions/42004/lti-system-with-laplace-transform |
Question: <p>Fourier transform has different types like continuous Fourier transform (CFT), Discrete time Fourier transform (DTFT) and Discrete Fourier transform ( DFT).</p>
<p>CFT can be used in case of continuous aperiodic signals while DFT for discrete aperiodic signals . </p>
<p>On the other hand, Laplace transf... | https://dsp.stackexchange.com/questions/31415/can-use-of-fourier-transform-be-minimized-completely-with-the-help-of-laplace-an |
Question: <p>A system given by <span class="math-container">$\frac{s-1}{(s+1)(s-2)}$</span> has to be inverse transformed so that it is anticausal and nonstable. The answer given is <span class="math-container">$h(t)=-\frac{1}{3}(2e^{-t}+e^{2t})u(-t)$</span></p>
<p>Why the minus sign at the beginning?</p>
Answer: <p>... | https://dsp.stackexchange.com/questions/60664/inverse-laplace-transform |
Question: <p>Imagine transfer function obtained by Laplace transform, for example:</p>
<p>$G(s) = \dfrac{1}{s+1}$</p>
<p>Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider this operation valid for this example).</p>
<p>What is the unit of the $\omega$? So far what I... | https://dsp.stackexchange.com/questions/43733/meaning-and-unit-of-frequency-in-laplace-fourier-transform |
Question: <p>In an example, an equation describing a causal LTI-system is</p>
<p><span class="math-container">$$
(D^2 + 5D + 6) y(t) = (D+1) x(t)
$$</span></p>
<p>where <span class="math-container">$y(t) = y_{zs}(t) + y_{zi}(t)$</span> and the initial conditions are <span class="math-container">$y(0^-) = 2, \dot{y}(0^-... | https://dsp.stackexchange.com/questions/71810/why-can-you-use-the-one-sided-laplace-transform-to-solve-differential-equation-d |
Question: <p>Let's say I have a function called $f(t)$ in time domain as: </p>
<p>$$f(t) = \exp(-3t)\cos(5t)$$</p>
<p>And the Laplace transform of this function call it $F(s)$ becomes:</p>
<p>$$F(s)=\frac{(s + 3)}{(s + 3)^2 + 25}$$</p>
<p>I want to plot the 3D plot of $\lvert F(s)\rvert$ as a surface above the $s$-... | https://dsp.stackexchange.com/questions/40628/how-can-i-plot-a-3d-graph-of-a-given-laplace-transform-of-a-function |
Question: <p>Consider the function $f\left(\frac{t - b}{a}\right)$. We want want to calculate its Laplace transform. There are two approaches:</p>
<ul>
<li><p>Firstly, </p>
<ol>
<li>let $g(t) = f\left(\frac ta\right)$. </li>
<li>Then $\mathcal{L}\left\{f\left(\frac{t-b}{a}\right)\right\} = \mathcal{L}\left\{g(t - b)\... | https://dsp.stackexchange.com/questions/38991/laplace-transform-of-f-left-fract-ba-right |
Question: <p>If we have an LTI system, with an input signal <span class="math-container">$x(t)$</span>, impulse response <span class="math-container">$h(t)$</span> and output <span class="math-container">$y(t)$</span>, I was under the assumption that if the input and impulse response were continuous in time, then you w... | https://dsp.stackexchange.com/questions/64539/when-to-use-fourier-laplace-and-z-transforms |
Question: <p>could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is placed in these transforms.</p>
<p>While looking through <a href="http://1drv.ms/1tbV45S" rel="noreferrer">http... | https://dsp.stackexchange.com/questions/19004/why-is-a-negative-exponent-present-in-fourier-and-laplace-transform |
Question: <p>The Laplace transform of a cosine starting at <span class="math-container">$t=0$</span> is given by</p>
<p><span class="math-container">$$F(s) = \frac{s}{s^2 + \omega_0^2}$$</span></p>
<p>If I sub in <span class="math-container">$s = j\omega$</span>, I get the Fourier transform of a cosine starting at <s... | https://dsp.stackexchange.com/questions/58364/why-does-subbing-s-j-omega-into-the-laplace-transform-of-a-cosine-wave-yield |
Question: <p><span class="math-container">\begin{align}
L[e^{-at}u(t)] &= \frac{1}{s+a}\\
L[\cos(\omega_{o}t)u(t)] &= \frac{s}{s^{2}+\omega^{2}_{o}}\\
L[e^{-at}\cos(\omega_{o}t)u(t)] &= \frac{s+a}{(s+a)^{2}+\omega_{o}^2}
\end{align}</span>
Everywhere <span class="math-container">$e^{-at}$</span> is multipli... | https://dsp.stackexchange.com/questions/84473/name-of-property-of-laplace-transform |
Question: <p>I am given the Laplace transform of the output of a LTI system: $$Y(s) = \frac{1}{s((s+2)^2+1)}$$ Asked is what the steady state response $y_{ss}(t)$ would be. I think that $y_{ss}(t) = \lim_{t\to\infty} y(t)$, since after waiting infinit long, the system should be in steady state. (Right?)</p>
<p>I thoug... | https://dsp.stackexchange.com/questions/36020/how-to-calculate-the-steady-state-response-y-sst-of-a-lti-system-given-the |
Question: <p>Is there any way, we can use MATLAB for finding and displaying Laplace or Z transform Region of convergence?</p>
Answer: <p>Matlab can only compute expressions for the uni-lateral (one-sided) versions of the Laplace transform and Z-transform. It doesn't explicitly determine the ROCs, but since both transf... | https://dsp.stackexchange.com/questions/83285/finding-and-displaying-laplace-or-z-transform-rocregion-of-convergence-using-m |
Question: <p>In control systems, the Laplace transform is often used to analyze the stability and the performance of <a href="http://en.wikipedia.org/wiki/LTI_system_theory" rel="nofollow">LTI system</a>. For instance, the LTI system is stable if and only if the <a href="http://en.wikipedia.org/wiki/Transfer_function" ... | https://dsp.stackexchange.com/questions/18053/wavelet-transform-in-control-systems |
Question: <p>If we give a input <span class="math-container">$x(t)=u(t)$</span> to a system <span class="math-container">$\mathcal{S}$</span> we get an output <span class="math-container">$y(t) = e^{-t} u(t)$</span>.<br />
After we Laplace-transform both the input and the output we get the transfer function
<span class... | https://dsp.stackexchange.com/questions/84485/transfer-function-and-laplace-domain |
Question: <p>I am trying to calculate the step response of the following given:
Should I use Laplace transform or Fourier transform?
<a href="https://i.sstatic.net/36JZu.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/36JZu.jpg" alt="enter image description here" /></a></p>
Answer: | https://dsp.stackexchange.com/questions/81291/step-response-of-a-given-input-and-output-laplace-or-fourier |
Question: <h2>SPEAKER AS RLC CIRCUIT</h2>
<p><a href="https://circuitdigest.com/electronic-circuits/simulate-speaker-with-equivalent-rlc-circuit" rel="nofollow noreferrer">I read this article here</a> which demonstrates a simulation of a speaker as a simple RLC circuit where the RLC components are in parallel:</p>
<p><... | https://dsp.stackexchange.com/questions/91516/laplace-transform-of-this-simple-parallel-rlc-circuit-for-audio-speaker-simula |
Question: <p>I'm working with loudspeaker impedance analysis. Electrical behavior of loudspeakers can be modeled with RLC networks. But real loudspeakers have components, that exhibit some non-linear and frequency dependent behaviors, that make them difficult to model with simple LTI systems.</p>
<p>One of the problem... | https://dsp.stackexchange.com/questions/45918/how-to-transform-a-fractional-order-laplace-transfer-function-into-a-digital-fil |
Question: <p>After studying z transform from different books and literature on internet I want to ask few which makes me confuse. </p>
<p>a) From the Discrete Time Fourier Transform we have drive equation for z transform. $$ X(z)= \sum _ {n=-\infty}^{+\infty} x[n]z^{-n}$$ where $z$ is represented in polar form $z=re^{... | https://dsp.stackexchange.com/questions/27385/question-about-z-transform |
Question: <p>Why do we have Laplace transform of a step function and integrator is same.</p>
<p>\begin{align}
\mathcal L\left[u(t)\right] &= \frac 1s\\
\mathcal L \left[ \int dt\right] &= \frac 1s
\end{align}</p>
<p>Please clear my doubt on this.</p>
Answer: <p>This is because the impulse response of an ... | https://dsp.stackexchange.com/questions/42723/laplace-of-step-and-integration-are-same |
Question: <blockquote>
<p><a href="https://i.sstatic.net/7paLk.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/7paLk.jpg" alt="Problem 9.14"></a></p>
</blockquote>
<hr>
<p>I have solved the problem 9.14 in Oppenheim's Signals and Systems textbook, but my solution and the one in Slader is different. P... | https://dsp.stackexchange.com/questions/63377/roc-of-the-function-in-the-problem-9-14-of-oppenheims-signals-and-systems-textb |
Question: <blockquote>
<p>System for estimating the tracking error in an A-D converter.
<a href="https://i.sstatic.net/9Evhk.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/9Evhk.png" alt="enter image description here"></a></p>
<p>Let $e_i(t)$ be ramp function with slope $e_i'$ and assume that t... | https://dsp.stackexchange.com/questions/44939/from-where-this-laplace-transform-for-tracking-error-came |
Question: <p>The mathematical formula of the Laplace and Z transforms are same with just one difference. I.e. in the first we use $t$ for continuous-time signal and in the latter uses $n$ for discrete-time signal. I don't think that there are any other differences. </p>
<p>While discussing Fourier transform for conti... | https://dsp.stackexchange.com/questions/24099/why-z-transform-is-considered-as-separate-transform |
Question: <p>Given a system with a known frequency response in the S-domain. Is there a way to find whether the system is linear and time invariant?</p>
<p>My current understanding is that we need to take the inverse Laplace transform of the system and prove linearity in the time domain.</p>
<p>Edit:<br />
As per the c... | https://dsp.stackexchange.com/questions/78176/can-we-tell-if-a-system-is-linear-and-time-invariant-from-its-frequency-response |
Question: <p>We all know that $a^nu(n)$ has unilateral $\mathcal Z$-transform. But what is the $\mathcal Z$-transform of $a^n$? (bilateral) When i tried to solve, i got answer as 'zero'.</p>
<p>But bilateral Laplace transform of $e^t$ doesn't exist. Both are exponentials in discrete and continuous domain respectivel... | https://dsp.stackexchange.com/questions/25489/bilateral-mathcal-z-transform-of-exponential |
Question: <p>I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is <a href="http://bwrcs.eecs.berkeley.edu/Classes/icdesign/ee240_sp10/lectures/Lecture22_Offset_Cancel_2up.pdf" rel="nofollow noreferrer">here</a> (PDF page 6, slide marked 11); I'll explain... | https://dsp.stackexchange.com/questions/88214/laplace-domain-transfer-function-from-system-sampled-at-discrete-times |
Question: <p>I have the following transform for <span class="math-container">$t>0, a_i>0$</span>
<span class="math-container">$$f(t)=\sum_{i=0}^d a_i \exp(-t a_i)$$</span></p>
<p>And I need to invert it for a set of target values <span class="math-container">$b$</span>:</p>
<p>Find <span class="math-container">$(... | https://dsp.stackexchange.com/questions/86922/discrete-version-of-this-transform |
Question: <p><a href="https://i.sstatic.net/bjZR8.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bjZR8.png" alt="enter image description here"></a></p>
<p>I need to solve what is underlined in red for $x_i$, nut currently I'm interested in the right side of the equation only.</p>
<p>On the left I sart... | https://dsp.stackexchange.com/questions/40087/why-do-these-2-methods-give-different-solutions |
Question: <p>Laplace domain is also known as <em>"s domain"</em>.</p>
<p>Is there any difference between <em>"s domain"</em> and <em>"frequency domain"</em>? Can we use both terms interchangeably?</p>
<p>If we want to convert a time domain signal to frequency domain, can we use Laplace tra... | https://dsp.stackexchange.com/questions/84250/s-domain-vs-frequency-domain |
Question: <p>I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components.</p>
<p>If it would be a sum of some sinusiod waves, it would be easy to Fourier-transform it, and then find the <a href="https://en.wikipedia.org/wiki/Kronecker_delta" rel="no... | https://dsp.stackexchange.com/questions/56644/is-there-an-analogy-of-the-fourier-decomposition-in-the-laplace-space-to-decompo |
Question: <p>Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as:
$$H(s) = \frac{1}{s - (-1-j)}$$</p>
<p>So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good.</p>
<ul>
<li><p>Now does that mean if the Laplace transform of the input to the system is $s = 1+j$ the ... | https://dsp.stackexchange.com/questions/40629/a-question-about-the-meaning-of-pole-in-time-domain |
Question: <p>I'm trying to find the zero-state response (ZSR) of an LTI system to a one sided periodic input, like a square wave that is equals to zero for $t < 0$.</p>
<p>I know that I can use the Fourier series of said input function to find the steady-state (SS) response, however I'm having trouble understanding... | https://dsp.stackexchange.com/questions/30712/lti-system-response-to-periodic-input |
Question: <p>I want play and record a sine sweep.
When i have both signals the recorded one and the send one i can create a Transferfunction.
That is what i know so far.</p>
<p>$$
H_0 = \frac{OUT}{IN} = \frac{Y}{X}
$$</p>
<p>Where i'm stuck is that when i read about the Transfer function it is all about the $Laplace... | https://dsp.stackexchange.com/questions/27963/dft-fft-transfer-function |
Question: <p>A continuous time domain system is well described by the Laplace transform. It allows to express any continuous signal x(t) as the integral sum of weighted complex and exponentially growing/decaying sine waves <span class="math-container">$e^{st} = e^{\sigma t} \cdot e^{j\omega t}$</span>:</p>
<p><a href="... | https://dsp.stackexchange.com/questions/75831/why-is-z-and-not-%cf%89-the-variable-of-interest-for-discrete-time-systems |
Question: <p>I'm working on a discrete updating algorithm as follows:</p>
<p><span class="math-container">$x[n+1]=Kx[n]$</span><br />
Here <span class="math-container">$K$</span> is a constant.</p>
<p>The continuous counterpart of this algorithm translates to:</p>
<p><span class="math-container">$\dot{x(t)}=Kx(t)$</spa... | https://dsp.stackexchange.com/questions/82466/what-is-the-difference-between-delay-and-difference-properties-of-z-transform |
Question: <p>I am trying to simulate a plant on a microcontroller. The transfer function of the plant is</p>
<p><span class="math-container">$$ G_{p} \left( s \right) = \frac{2}{\left( s + 3 \right) \left( s - 1 \right)} \tag{1} \label{1}$$</span></p>
<p>The step response for this function from Octave is</p>
<p><a href... | https://dsp.stackexchange.com/questions/88753/not-getting-the-same-step-response-from-laplace-transform-and-its-respective-di |
Question: <p>For digital signals, the fourier transform is taken along the unit circle of the Z-transform.<br />
The equivalent to the Z-transform in continuous signals is the Laplace transform, but in that case the fourier transform is taken along the imaginary axis.</p>
<p>Why the difference? Why don't we take the z-... | https://dsp.stackexchange.com/questions/95816/why-is-the-digital-frequency-response-taken-on-the-unit-circle-while-the-analog |
Question: <p>I'm trying to create a digital filter in code(C) but any language is fine. Now I've got an analogue filter that I have represented by an equation in the Laplace domain and I want to try and implement it digitally. </p>
<p>So my filter has this form in the Laplace domain:
$$\frac{as+b}{cs^2+ds}$$</p>
<p>I... | https://dsp.stackexchange.com/questions/18329/creating-a-digital-filter-from-laplace-to-mathcal-z-transform-zero-order-ho |
Question: <p>I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one.</p>
<p>I am currently studying the textbook <em>An Introduction to Laplace Transforms and Fourier Series</em>, second edition... | https://dsp.stackexchange.com/questions/66998/validity-of-applying-heaviside-function-for-signal-processing-applications |
Question: <p>I was reading pdf by caltech and in one of its section, Fourier transform of Unit step signal is calculated but I am confused, how this can be possible if region of convergence for Laplace transform (<span class="math-container">$1/s$</span>) of unit step signal does not contain imaginary axis?</p>
<p>And... | https://dsp.stackexchange.com/questions/67974/fourier-transform-of-unit-step |
Question: <p>For designing any analog filter and various other outputs of filter we use <strong>laplace transform</strong>,I can visualise a laplace transform like for ex.<br>
<code>s[X(s)]</code> can be implemented as differentiator fetched with signal <code>x(t)</code>while implementing differentiators we generally... | https://dsp.stackexchange.com/questions/22494/visualising-a-z-transformed-transfer-function |
Question: <p>As we have in Laplace transform that the roots decide the stability of the system i.e. if the roots are complex and lie in the left side of the plane you get a sinusoidal response with decreasing amplitude </p>
<p>similarly is there any significance of the roots , zeros and ROC of the z-transform and the... | https://dsp.stackexchange.com/questions/22556/what-is-the-significance-of-z-transform |
Question: <p>The discrete wavelet transform is applied in many areas, such as signal compression, since it is easy to compute. I notice that, However, the continuous wavelet transform (CWT) is also applied to different subjects. In my opinion, the CWT is redundant and hence difficult to compute. So what are the advanta... | https://dsp.stackexchange.com/questions/76624/continuous-wavelet-transform-vs-discrete-wavelet-transform |
Question: <p>How does Synchrosqueezing Wavelet Transform work, intuitively? What does the "synchrosqueezed" part do, and how is it different from simply the (continuous) Wavelet Transform?</p>
Answer: <p>Synchrosqueezing is a powerful <em>reassignment</em> method. To grasp its mechanisms, we dissect the (con... | https://dsp.stackexchange.com/questions/71398/synchrosqueezing-wavelet-transform-explanation |
Question: <p>I need to implement the discretized continuous wavelet transform from scratch. Could someone please point me to useful papers and references available online for this?</p>
Answer: <p>In 1D, some of the standard references are:</p>
<ul>
<li><a href="http://www.sciencedirect.com/science/article/pii/S016516... | https://dsp.stackexchange.com/questions/37528/implementing-continuous-wavelet-transform |
Question: <p>i have N samples obtained by sampling a signal with lot of frequency contents. How will i apply daubechies wavelet transform to obtain the frequency and its location? i need to write a program which will process the signal and gives the frequency and location as the result.</p>
Answer: <p>Looks like you n... | https://dsp.stackexchange.com/questions/28629/daubechies-wavelet-transform |
Question: <p><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/STFT_and_WT.jpg/500px-STFT_and_WT.jpg" alt="STFT and Wavelet"></p>
<p>Wavelet transform gives good time resolution for high-frequency events and good frequency resolution for low-frequency events. </p>
<p>=> I want to have complete oppos... | https://dsp.stackexchange.com/questions/24766/opposite-of-wavelet-transform |
Question: <p>I have a question related to wavelet transform: we know that while the Fourier transform is good for a spectral analysis or which frequency components occurred in signal, it will not give information about at which time it happens. That's why the wavelet transform is suitable for the time-frequency analys... | https://dsp.stackexchange.com/questions/15148/disadvantages-of-wavelet-transform |
Question: <p>Continuous wavelet transformation has been quite widely used for various applications. Most of the papers that I found were using CWT for non-stationary signals. Can we use CWT for stationary signal analysis? if not what are the drawbacks in using Continuous wavelet transform?</p>
Answer: <p>Stationarity ... | https://dsp.stackexchange.com/questions/58615/continuous-wavelet-transform |
Question: <p>I want to implement Wavelet Transform from the scratch, that mean breaking the wavelet transform into its equations to implement in any Programming language. Matlab Comes with built-in functions to implement Wavelet Transform but It is really hard to understand which processes are exactly involved in the i... | https://dsp.stackexchange.com/questions/8781/implementing-wavelet-transform-using-equations |
Question: <p>I want to perform 2D haar discrete wavelet transform and inverse DWT on an image.<strong>Will you please explain 2D haar discrete wavelet transform and inverse DWT in a simple language and an algorithm using which I can write the code for 2D haar dwt</strong>?The information given in google was too technic... | https://dsp.stackexchange.com/questions/2149/wavelet-transform |
Question: <p>I have a little bit confused on the difference between stationary wavelet transform and un-decimated wavelet transform.</p>
<p>So, can anyone tell me, if there is a difference between them?</p>
Answer: <p>The translation invariant version of the DWT is known by a variety of names, including stationary wa... | https://dsp.stackexchange.com/questions/27836/stationary-vs-undecimated-wavelet-transform |
Question: <p>How wavelet transform is different from STFT. </p>
<p>I'm not able to understand what is resolution in frequency domain means?</p>
Answer: <p><a href="https://i.sstatic.net/SyTNn.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/SyTNn.png" alt="STFT vs CWT"></a></p>
<p>In the STFT, you appl... | https://dsp.stackexchange.com/questions/54551/wavelet-transform-and-stft |
Question: <p>So I have this problem where I need to measure the phase of a signal and correct for a delay associated with the travel time of the signal while simultaneously determining the transfer function of my system (with the delay corrected).</p>
<p>So I thought I probably need a wavelet transform so that I can d... | https://dsp.stackexchange.com/questions/30895/transfer-functions-from-wavelet-transform |
Question: <p>I was reading on windowed fourier transform and wavelet transform, and i was thinking that the windowed fourier transform is a subset of wavelet transform. Is that true?</p>
Answer: <p>Define the Fourier transform as <span class="math-container">$$ x(t) = \mathscr{F}^{-1}\big\{ X(\omega) \big\} \triangl... | https://dsp.stackexchange.com/questions/13779/relationship-between-windowed-fourier-transform-and-wavelet-transform |
Question: <p>Does the Fast Wavelet Transform(FWT) produce the same coefficients as the Discrete Wavelet Transform(DWT) if configured for the same depths? Or is the the FWT just an approximation of the DWT?</p>
Answer: <p>If the discrete wavelet transform can be implemented with a FIR filter bank, with appropriate ext... | https://dsp.stackexchange.com/questions/71394/does-the-fast-wavelet-transform-produce-the-same-coefficient-as-the-discrete-wav |
Question: <p>I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification.</p>
<p>My question is if the Wavelet transform or Discrete Wavelet transform is a time frequency representation (or time... | https://dsp.stackexchange.com/questions/78846/should-i-use-window-with-hop-size-in-wavelet-transform-or-discrete-wavelet-trans |
Question: <p>One of the books on "Conceptual Wavelets" by Fugal explains some major differences between the undecimated discrete wavelet transform (UDWT) vs. discrete wavelet transform (DWT). In UDWT the scale of wavelet is increased continuously just like the continuous wavelet transform, but the scale increases in dy... | https://dsp.stackexchange.com/questions/61728/clarification-regarding-discrete-wavelet-transform |
Question: <p><strong>Main Question: Why would iterative wavelet/inverse-wavelet transforms cause a shift along the x-axis for undecimated (shift-invariant) wavelet transforms?</strong></p>
<p>I am attempting to remove backgrounds from signals using an iterative wavelet transform method similar to this approach which I... | https://dsp.stackexchange.com/questions/14086/shifting-of-shift-invariant-wavelet-transforms |
Question: <p>Is wavelet a Nonlinear transform, or Not?<br>
specifically, continuous wavelet transform with morlet function.<br>
I am studying behavior of a dynamic system, and it has nonlinear behaviour. can I employ wavelet transform? </p>
Answer: <p>A transform being linear has very little to do with its ability t... | https://dsp.stackexchange.com/questions/12926/nonlinear-wavelets-transform |
Question: <p>Referring to the <a href="https://en.wikipedia.org/wiki/Fast_wavelet_transform#cite_note-1" rel="nofollow noreferrer">Fast Wavelet Transform</a>, this transform is implemented as a QMF filter bank. This algorithm consists of high/low pass filtering and subsampling. However, a wavelet transform is typically... | https://dsp.stackexchange.com/questions/71263/where-is-the-mother-wavelet-defined-in-the-fast-wavelet-transform |
Question: <p>I have learned about STFT and wavelet transform recently, and wavelet transform seems better than STFT in my opinion.
So, I wonder if there is any advantage of using STFT than WT, and if so, what are practical applications of STFT?</p>
Answer: <p>Wavelet transforms and short-term/short-time Fourier transf... | https://dsp.stackexchange.com/questions/79586/advantage-of-stft-over-wavelet-transform |
Question: <p>I have just started reading about wavelets for a data compression problem that I want to perform. I am reading about Discrete Wavelet Transform (DWT) but I can't understand where the wavelet family that has to be set is used.</p>
<p>This is the DWT schema</p>
<p><a href="https://i.sstatic.net/rr56r.png" re... | https://dsp.stackexchange.com/questions/76594/discrete-wavelet-transform-dwt-and-wavelet-family |
Question: <p>Does anyone know if there exist a kind of convolution theorem for the discrete wavelet transform (decimated or undecimated)? </p>
<p>In other words can I find a simple form of
<span class="math-container">$W\left[ \int f(t) g(x-t) \, dt\right] $</span> where <span class="math-container">$W$</span> is the ... | https://dsp.stackexchange.com/questions/52839/wavelet-transform-of-a-spatial-convolution |
Question: <p>I read in <a href="https://books.google.com.eg/books?id=49FBDwAAQBAJ&pg=PA79&lpg=PA79&dq=DWT+shift+variance+property+due+to+the+downsampling+process+lack+of+directional+selectivity.&source=bl&ots=wnhZpeTQcY&sig=ACfU3U3heH_2sefjO995Jqn52pJ7udyrug&hl=en&sa=X&ved=2ahUKEwjtq... | https://dsp.stackexchange.com/questions/61213/discrete-wavelet-transform-disadvantages |
Question: <p>I'm trying to perform wavelet transform and make a 3D plot like :</p>
<p><a href="https://i.sstatic.net/GHooq.gif" rel="nofollow noreferrer"><img src="https://i.sstatic.net/GHooq.gif" alt="enter image description here"></a></p>
<p>With the wavelet transform function :</p>
<p>$$
\textrm{CWT}_x^\psi (\tau... | https://dsp.stackexchange.com/questions/31936/wavelet-transform-3d-plot-for-cop |
Question: <p>I am currently working on an audio watermarking project in MATLAB. I currently have a code I am using to construct a nxn 3 Band Wavelet Transform matrix. However, when I try to construct a matrix that is larger in size, I get the error "Maximum variable size allowed by the program is exceeded" or "Out of M... | https://dsp.stackexchange.com/questions/9777/3-band-wavelet-transform-in-matlab |
Question: <p>I am unable to understand the <strong>discrete wavelet transform</strong> on images. I followed Robi Polikar's tutorial and got a brief idea about the theory. But I'm unable to understand w.r.t images.</p>
<p>Using Matlab's <code>ndwt2('chess.jpg', 2, 'haar')</code> function on the chess board , I obtaine... | https://dsp.stackexchange.com/questions/29138/discrete-wavelet-transform |
Question: <p>I'm confused about the difference between a wavelet transform and a wavelet decomposition is. For example</p>
<pre><code>load woman
[cA1,cH1,cV1,cD1] = dwt2(X,'db1');
[c,s] = wavedec2(X,2,'db1');
</code></pre>
<p>What's the difference between these two matlab commands, and when would you want to do one ... | https://dsp.stackexchange.com/questions/10675/difference-between-a-wavelet-transform-and-a-wavelet-decomposition |
Question: <p>I have a rough overview on Discrete Wavelet Transform (DWT). However, I am confused about Discrete Wavelet <em>Decomposition</em> and did not find a good reference yet which explains this well. What is it actually about? Is it somehow part of DWT or an inverse operation to it?</p>
Answer: <p>The <strong>d... | https://dsp.stackexchange.com/questions/59382/difference-between-discrete-wavelet-transform-and-discrete-wavelet-decomposit |
Question: <p>I was thinking sometime back about how to explain the Continuous Wavelet Transform ELI5. So this is what I came across.</p>
<p>The correlation of two exact signals is 1. So if I have an input signal $f(x)$ made up of an array of frequencies, how can I find out what frequencies exist at what points? Well, ... | https://dsp.stackexchange.com/questions/15662/intuition-behind-the-continuous-wavelet-transform |
Question: <p>I am having trouble understanding on how to read the plot plotted by a wavelet transform,</p>
<p>here is my simple Matlab code,</p>
<pre><code>load noissin;
% c is a 48-by-1000 matrix, each row
% of which corresponds to a single scale.
c = cwt(noissin,1:48,'db4','plot');
</code></pre>
<p><img src="http... | https://dsp.stackexchange.com/questions/7911/reading-the-wavelet-transform-plot |
Question: <p>I am new to the concept of wavelet transforms. Can somebody please help me in understanding this ? and also how to implement it in c. Is Short term Fourier transform more efficient than Wavelet Transform for finding Transients ?</p>
Answer: <p>I would say that a matching Mother wavelet could be the best f... | https://dsp.stackexchange.com/questions/28018/implementing-wavelet-transform-for-finding-transients-in-the-power-supply |
Question: <p>I'm working on a speech recognition project. The first step of this project is to find phoneme in the speech signal. To do that, I found <a href="https://www-users.cs.york.ac.uk/~suresh/papers/PSOS.pdf" rel="nofollow noreferrer">this paper</a> that discusses about it.</p>
<p>In the paper, wavelets are use... | https://dsp.stackexchange.com/questions/36914/bandpass-filter-using-wavelet-transform |
Question: <p>In control systems, the Laplace transform is often used to analyze the stability and the performance of <a href="http://en.wikipedia.org/wiki/LTI_system_theory" rel="nofollow">LTI system</a>. For instance, the LTI system is stable if and only if the <a href="http://en.wikipedia.org/wiki/Transfer_function" ... | https://dsp.stackexchange.com/questions/18053/wavelet-transform-in-control-systems |
Question: <p>The implementations of Synchrosqueezing wavelet transform in Python (<a href="https://github.com/OverLordGoldDragon/ssqueezepy" rel="nofollow noreferrer">ssqueezepy</a>) and <a href="https://www.mathworks.com/help/wavelet/gs/wavelet-synchrosqueezing.html" rel="nofollow noreferrer">MATLAB</a> both write i... | https://dsp.stackexchange.com/questions/86713/why-are-wavelet-transforms-implemented-in-python-matlab-often-called-continuous |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.