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filter design | Converting Analog Filter into Digital Filter, why Bilinear Transform? | https://dsp.stackexchange.com/questions/68567/converting-analog-filter-into-digital-filter-why-bilinear-transform | <p>What's the advantage of using the Bilinear Transform?</p>
<p><span class="math-container">$$H_d(z) = H_c(s)\bigg|_{s=\frac{2}{T_s}\frac{z-1}{z+1}}$$</span></p>
<p>When you can just use this equation?</p>
<p><span class="math-container">$$H_d(\omega) = H_c(\Omega)\bigg|_{\Omega=\omega/T_s}$$</span></p>
<p>In other wo... | <p><span class="math-container">$$\left . H_d(z) = H_c(s) \right |_{s = \frac{2}{T\,s}\frac{z-1}{z+1}}$$</span> describes a transfer function in the <span class="math-container">$z$</span> domain that you can easily translate into a difference equation and realize in software.</p>
<p><span class="math-container">$$\lef... | 934 |
filter design | Pole/Zero Placement for Filter | https://dsp.stackexchange.com/questions/19062/pole-zero-placement-for-filter | <p>I'm attempting to design a FIR high pass filter than keeps signals above 200Hz and rejects signals below 60Hz with a sampling frequency of 500 samples/sec. This is my first time attempting this and I'm a little confused.</p>
<p>I started with looking at pole/zero placement. I'm not exactly sure how to go about this... | <p>This is how you can try to design a short and simple FIR filter by hand. Note that this method is just supposed to be enlightening, a really useful filter can be designed using some software. If you want a zero at 60 Hz you indeed need to place it at an angle of $0.24\pi$ on the unit circle of the $z$-plane. The gen... | 935 |
filter design | Filter design / Analysis apps | https://dsp.stackexchange.com/questions/18851/filter-design-analysis-apps | <p>There are a plethora of tools, both commercial and free, which I have found online for designing filters. The ones I have tried (so far) prompt for frequency response, number of steps (for FIR), then generate coefficients and a frequency response plot.<p>
<strong>Question</strong>: are there any particular sites or ... | <p>I believe that Octave and Python/Scipy are the most commonly used free software packages for digital signal processing (including filter design). They offer of course much more than you might be looking for. On the other hand, if you want to play around with the coefficients and get some quick feedback, it might be ... | 936 |
filter design | Polyphase filter notation | https://dsp.stackexchange.com/questions/1340/polyphase-filter-notation | <p>Hi I am a little confused on what the notation of the following statement means.</p>
<p>$$ H_{k}(z)= H(W_{4}^{k} z), k = 0,...,3$$</p>
<p>It comes from a question in which I have designed a FIR low-pass filter $H(z)$ and my goal is to implement a DFT filter bank scheme like this:</p>
<p><img src="https://i.sstati... | <p>Hk are modulations of the low pass filter (band pass instead of low pass).</p>
<p>$$
(W_{4}^{k}) = e^{-2j\pi k /4}.
$$
For $z = e^{j\omega}$: $$H(W_{4}^{k} z) = H(e^{j(\omega-2\pi k/4)})$$
This means that the filters $H_k$ are shifted in frequency- these are the band pass filters you want to get using your filter... | 937 |
filter design | How to determine cut off frequency for high pass filter using spectral density? | https://dsp.stackexchange.com/questions/24707/how-to-determine-cut-off-frequency-for-high-pass-filter-using-spectral-density | <p>I have filtered out the low frequency noise from the signal. For further analysis, I want to compare it with FIR filters (for which I require cut off frequency). Hence, I took the power density spectrum of noise using Welch method and found its peak and used the same as cut off frequency. The PSD looks like this <im... | 938 | |
filter design | Design IIR Butterworth filter using bilinear transform | https://dsp.stackexchange.com/questions/25673/design-iir-butterworth-filter-using-bilinear-transform | <p>Write listing in MATLAB which design a low-pass IIR filter basis on Butterworth (Rp=2dB, Rr=40dB, fp=1000 Hz, fr=1300 Hz, fs=5000 Hz) as a prototype and using bilinear transform without built-in functions. Control the point(fr,Rr). Plot the response characteristic (linear scale, and dBs scale). </p>
<p><a href="htt... | 939 | |
filter design | describing a block diagram // How do I describe multiplying a signal through multiple branches formally? | https://dsp.stackexchange.com/questions/30292/describing-a-block-diagram-how-do-i-describe-multiplying-a-signal-through-mul | <p>Let's say I made this block diagram and I want to explain it:</p>
<p><a href="https://i.sstatic.net/rIxpl.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/rIxpl.png" alt="enter image description here"></a></p>
<p>FYI: $x$ is a signal and each $y$ box is a matrix</p>
<p><strong><em>I want to say that... | <p>What I would do is:</p>
<ul>
<li>Add $m$ multiplier blocks, using a circle with a $\times$ inside</li>
<li>Each multiplier would have inputs $X$ and $Y_k$</li>
<li>Each multiplier would have output $f_k$</li>
<li>Be consistent in the use of bold typeface, uppercase and lowercase</li>
</ul>
<p>Then I would say some... | 940 |
filter design | Doubts about Notch filter design | https://dsp.stackexchange.com/questions/53695/doubts-about-notch-filter-design | <p>I am following the process that is described in this question: <a href="https://dsp.stackexchange.com/questions/31028/transfer-function-of-second-order-notch-filter">Transfer function of second order notch filter</a> , I want to create a notch filter with the band suppressed equal to <span class="math-container">$f_... | <p>This Octave / Matlab code gives you a 2nd ord notch filter at <span class="math-container">$\omega_n = \pi/6$</span></p>
<pre><code>r = 0.99; % notch radius (closer to 1 stiffer)
wn = pi/6; % notch radian frequency...
% Create the 2nd order NOTCH filter coefficients b() and a()
b = r*conv([1, -... | 941 |
filter design | What is importance of the conjugate reciprocal and none reciprocal zeros in FIR Type 2 Filters? | https://dsp.stackexchange.com/questions/62794/what-is-importance-of-the-conjugate-reciprocal-and-none-reciprocal-zeros-in-fir | <p>In DSP class we have <a href="http://ce.sharif.edu/courses/93-94/1/ce763-2/resources/root/Lecture%20Notes/Lec09-FiltersIntroduction2.pdf" rel="nofollow noreferrer">this</a> slide:</p>
<p><a href="https://i.sstatic.net/IfhM4.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/IfhM4.jpg" alt="enter image d... | <p>Consider</p>
<p><span class="math-container">$$ h[n] = \sum_{k=0}^{M} b_k \delta[n-k] ~~~~\longleftrightarrow ~~~~H(z) = \sum_{k=0}^{M} b_k z^{-k} $$</span></p>
<p>where <span class="math-container">$b_k$</span> are impulse response coefficients, and and <span class="math-container">$H(z)$</span> is the correspondi... | 942 |
filter design | FIR filter | how can I change the axis to unnormalized? | https://dsp.stackexchange.com/questions/80673/fir-filter-how-can-i-change-the-axis-to-unnormalized | <p>I don't understand why my output graphs and not showing the real frequencies, tried to change it in a number of ways with no luck. so far I'm stuck.</p>
<p>This is what I have done so far while implementing a LowPassFilter using the frequency sampling method:</p>
<pre><code>M=63
Wp=0.25*pi ... | <p>To change to frequencies in units of Hz for the filter multiply the frequency axis by half the sampling rate, as below where fs is the sampling rate:</p>
<pre><code>plot(w/pi * fs/2,20*log10(abs(H)));
</code></pre>
<p>For your lower plot you are not sampling high enough such that the desired frequencies are in the f... | 943 |
filter design | Implementing HPF using frequency sampling method | https://dsp.stackexchange.com/questions/80704/implementing-hpf-using-frequency-sampling-method | <p>I'm on it for a few hours trying to tweak it in all sort of ways but the output comes out scrambled and I can't understand why.</p>
<p>I am trying to implement an HPF with a stopband frequency of 500Hz and passband frequency of 600Hz.
This is what I've done so far:</p>
<pre><code>M=131072; %the nu... | <p>You have no concept of a sample rate in your code. Everything in digital signal processing is relative to the sample rate. You either need to work in normalized frequency (from <span class="math-container">$-\pi$</span> to <span class="math-container">$\pi$</span>) or absolute frequency (from <span class="math-conta... | 944 |
filter design | Finding The Coefficients of the digital filter? | https://dsp.stackexchange.com/questions/2760/finding-the-coefficients-of-the-digital-filter | <p>I want to design a digital filter for pulse shaping. Pulses are of 100us Fall time. and the sampling rate is 100MegaSamples/sec. and the Shaping time is 5us. What should my coefficients be??? And how to obtain them using matlab or any other related software.</p>
| 945 | |
filter design | Bireciprocal lattice wave digital filter | https://dsp.stackexchange.com/questions/15112/bireciprocal-lattice-wave-digital-filter | <p>I have posted this question "Electrical Engineering", but this seems a more appropiate place. I am trying to model a bireciprocal Cauer filter in LTspice but I don't get the expected results. More precisely, using this formula for the coefficients</p>
<p><span class="math-container">$\gamma=\frac{re(p_i)−1... | <p>Let's try to sort of answer this from the BLWDF point of view (without much of the WDF-theory, since this can to a large extent be skipped as you know which structure you want).</p>
<p>Starting from a second-order BLWDF allpass section (based on symmetric two-port adaptors without any negations in the feedback), th... | 946 |
filter design | Equiripple Filter-Design | https://dsp.stackexchange.com/questions/23770/equiripple-filter-design | <p>I have a requirement to design minimax filter with linear programing (<code>linprog</code> in MATLAB).
To build the filter I must choose vector $\omega$ (frequency sample), how many values I need to take to get the optimal result? How to spread them across the interval $[0,\pi]$?</p>
| <p>There is no real rule, but you would usually choose around $10N$ frequency points, where $N$ is the desired filter order. Distribute the points equidistantly over pass band(s) and stop band(s). This does not mean that they are equidistant in the interval $[0,\pi]$ because usually there is at least one "don't care" r... | 947 |
filter design | How to transform lowpass fir filter to bandpass fir filter without using a built in function in matlab | https://dsp.stackexchange.com/questions/25672/how-to-transform-lowpass-fir-filter-to-bandpass-fir-filter-without-using-a-built | <p>The FIR low-pass filter was designed in MATLAB which characteristics are listed below. Coefficient of this filter was written in variable h. Basis on this filter design a band-pass filter with central frequency 1/5(normalized to fs) keeping the same gain and bandwidth. Give the listing in MATLAB(no using buitl-in fu... | <p>Mathematically, applying a FIR with impulse response $h_\mathrm{lpf}[n]$ to digital signal is convolution:</p>
<p>$y = x * h_\mathrm{lpf}$, or thanks to the properties of the (discrete) Fourier transform,</p>
<p>$Y = X\cdot H_\mathrm{lpf}$, as convolution becomes multiplication.</p>
<p>Now, making a bandpass out ... | 948 |
filter design | Filter design, relationship between energy and stop-band ripple | https://dsp.stackexchange.com/questions/33922/filter-design-relationship-between-energy-and-stop-band-ripple | <p>I read some example of design LPF which I didn't understand something.
The stop-band in that example is $\frac { 22 }{ 25 } $ from the over-all frequency, and I want to filter some white noise.
After we found out in that example that the energy of the white noise in the stop band area is $0.22\%$ from the overall ... | <p>$\delta_s$ is the stop-band (hence the ${}_s$ subscript) attenuation.</p>
<p>A signal in the stop-band with amplitude $1$ would have amplitude $\delta_s$ after filtering.</p>
<p>Since power goes quadratic with amplitude, and if you feed in white noise, $\frac{22}{25}$ of the original energy will be in stop band, a... | 949 |
filter design | how to make CIC compensation filter | https://dsp.stackexchange.com/questions/19584/how-to-make-cic-compensation-filter | <p>I gotta wrap my head around to design CIC compensation filter</p>
<p>I'm studying by referring these materials:</p>
<ol>
<li>Altera, "Understanding CIC compensation filters</li>
<li>Hardware Efficient FIR Compensation Filter
For Delta Sigma Modulator Analog to Digital Converters.
Circuits and Systems, 2005. 48th ... | <p>I have a simple compensation approach that I've used to implement a reasonable estimate of an inverse $\textrm{sinc}$ for use as a CIC compensator as well as other inverse $\textrm{sinc}$ applications. This approach makes use that the $\textrm{sinc}$ function in the passband can be reasonably approximated by a weigh... | 950 |
filter design | Cut out harmonics that occur in the main signal | https://dsp.stackexchange.com/questions/95365/cut-out-harmonics-that-occur-in-the-main-signal | <p>I have a signal like this:<a href="https://i.sstatic.net/82I9mzrT.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/82I9mzrT.png" alt="enter image description here" /></a>
The frequency I need is in the range of 5.5 kHz-6.5 kHz. I select the band I need, as Dan Boschen showed me in <a href="https://dsp.... | <p>I believe you are seeing the effects of aliasing. An anti-alias filter is required to select a band of interest and reject potential alias frequency zones prior to A/D conversion and similarly prior to any rate conversion.</p>
<p>If that isn’t clear, please update your question to include the sampling rate and speci... | 951 |
filter design | Designing narrow-band notch filter with high sampling frequency | https://dsp.stackexchange.com/questions/94797/designing-narrow-band-notch-filter-with-high-sampling-frequency | <p>I want to design a narrow-band filter for a signal that has been sampled at 125 [kHz].</p>
<p>The specifications are:</p>
<ul>
<li>Passbandfrequency1: 58 [Hz]</li>
<li>Stopbandfrequency1: 59 [Hz]</li>
<li>Stopbandfrequency2: 61 [Hz]</li>
<li>Passbandfrequency2: 62 [Hz]</li>
</ul>
<p>Ripples are standard, and attenua... | <p>A 5th order elliptic filter can theoretically do that (With a ripple of 1 dB)</p>
<pre><code>fs = 125e3;
[z,p,k] = ellip(5,1,60,[58 62]*2/fs,'stop');
</code></pre>
<p>A filter that aggressive will have a lot of tradeoffs: the impulse response will be insanely long and there are serious stability concerns.</p>
<p><a ... | 952 |
filter design | What's the use of the ripple in the Equiripple method and their effect in the filtering process? | https://dsp.stackexchange.com/questions/38652/whats-the-use-of-the-ripple-in-the-equiripple-method-and-their-effect-in-the-fi | <p>I read about the design methods of FIR filter which are:
windowing method, sampling frequency method and Equiripple method. And I don't understand the use of the ripple in the Equiripple method and their effect in the filtering process. Can anyone help me?</p>
| <p>There is ripple to three different degrees depicted in this plot:</p>
<p><a href="https://i.sstatic.net/HhkQz.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/HhkQz.png" alt="enter image description here"></a></p>
<p>ripple is the variance that the filter gain is from the target gain. in the above, ... | 953 |
filter design | Linear-phase crossover filters | https://dsp.stackexchange.com/questions/70913/linear-phase-crossover-filters | <p>Is it possible to design linear-phase filters that sum to a flat frequency response? If so is it practical to use them in real-time audio processing for as many as 10 bands?</p>
<p>My experience has only been with Linkwitz-Riley IIR filters, but I would like to explore the possibilities of linear phase or minimum p... | <p>Well, by definition of linear phase filter follows that <span class="math-container">$A(f)$</span> of the filter response <span class="math-container">$H(f) = A(f)e^{-j2\pi \frac{N}{2} fT}$</span> is a linear combination of cosines of different frequencies therefore is quite impossible to obtain a flat band (basical... | 954 |
filter design | changing filtering "speed" (cutoff frequency) of an IIR filter knowing only its coefficients | https://dsp.stackexchange.com/questions/68657/changing-filtering-speed-cutoff-frequency-of-an-iir-filter-knowing-only-its | <p>i got an IIR filter bu I have only the coefficients.
now i'd like to be able to change the filter characteristics of the low pass filter (the "cutoff" frequency) but all i got are a and b coefficients.
i'd like to be able to set a multiplier that will "scale" the filter by that amount. if i set ... | <p>Your probably your best option here is "frequency warping". You can calculate the poles and zeros from the coefficients, warp the poles and zeros and then recalculate the coefficients again.</p>
<p>Warping is a procedure the applies a conformal mapping to the poles/zeros. Specifically a conformal mapping t... | 955 |
filter design | what rule has coefficients to follow for an IIR filter to be stable? | https://dsp.stackexchange.com/questions/68838/what-rule-has-coefficients-to-follow-for-an-iir-filter-to-be-stable | <p>I'd like to play with IIR filters, but not by designing them with algorithm but rather play with the coefficients directly.
i got a stability problem though, because of course IIR filters are sensitive to design, and we have to make sure the filter is stable and will not go to infinity.
So is there a rule that have ... | 956 | |
filter design | IIR filter design in digital domain using the magnitude squared | https://dsp.stackexchange.com/questions/8021/iir-filter-design-in-digital-domain-using-the-magnitude-squared | <p>Does anyone have any good references for deriving parameters of an IIR Low pass/High Pass filter directly in the digital domain using the magnitude squared at the corner frequency? </p>
<p>I have been able to derive the parameters of a first order Low/High pass filter with $3\textrm{ dB}$ attenuation at the corner ... | <p>To solve the case that you mentioned...</p>
<p>You have 2 variables to determine, so you need two relationships to resolve the two variables. I'm going to use $k$ and $a$ as the variables to make this easy to type up.</p>
<p>$$H(z) = k\frac{1 + z^-1}{1-az^-1}$$</p>
<p>Start by considering the passband gain. Use... | 957 |
filter design | Types of rounding in coefficients quantization | https://dsp.stackexchange.com/questions/8571/types-of-rounding-in-coefficients-quantization | <p>Suppose we have create an IIR filter with matlab function "ellip", and then we want to quantize the coefficients using:</p>
<p>\begin{align*}
bq=Quantize('round',b,2^8); \cr
aq=Quantize('round',a,2^8);
\end{align*}</p>
<p>I have read that there are 4 major types of rounding:</p>
<ul>
<li>truncate</li>
<li>round<... | <p>The various rounding methods have a computation vs. quantization error tradeoff.</p>
<p><strong>Truncate</strong></p>
<p>Truncation is the simplest method. Everything after the decimal point is simply lopped off. For instance, both 2.1 and 2.9 become 2. This is very simple, but is the worst method in terms of q... | 958 |
filter design | DC component of a discrete filter | https://dsp.stackexchange.com/questions/14500/dc-component-of-a-discrete-filter | <p>I know that many books and papers talk about the DC offset/DC component of a filter. How do we define the DC offset mathematically, for the case of discrete filters?</p>
| <p>Here is a (working) link to a paper relevant to the OP: <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.80.2334&rep=rep1&type=pdf" rel="nofollow">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.80.2334&rep=rep1&type=pdf</a></p>
<p>It looks like when they say zero DC, they ... | 959 |
filter design | Filter design with 8-tap latency on recursion | https://dsp.stackexchange.com/questions/15522/filter-design-with-8-tap-latency-on-recursion | <p>I'm curious about the feasibility of designing a noise shaping filter (but might generalise to any recursive filter) with the constraint that the most recent output samples aren't available for several iterations of the filter.</p>
<p>The use case I have in mind is reducing the word length of an audio stream sample... | <p>This is tricky. Any filter with 8 tab latency between coefficients can be represented in the z-domain as a rational function in $z^{-8}$ . That's basically the same as saying the impulse response has 7 zeros between each non zero tap. Any filter with this property is periodic in the frequency domain. You can pick an... | 960 |
filter design | Speaker Recognition | https://dsp.stackexchange.com/questions/15719/speaker-recognition | <p>How can you filter out a person's voice from a group of people talking? </p>
<p>We have a sample of each person's voice from the group, and the sample of the entire group talking at once. Both samples are uploaded into matlab for analysis.</p>
<p>Is there a way to single out any one person's voice?</p>
| <p>IMHO,</p>
<p>Using several microphones (at least 2 like our ears) may help. There will be some constant delay in the time-domain between the recordings from different microphones. This will help you to amplify voice of a single person, because no 2 persons can occupy the same space :-) </p>
<p>To detect this time-... | 961 |
filter design | Slepian or DPSS window | https://dsp.stackexchange.com/questions/17777/slepian-or-dpss-window | <p>I am planning to use Slepian or DPSS window in my application where I want central lobe to be concentrated and also have low bandwidth:</p>
<p><a href="http://en.wikipedia.org/wiki/Window_function#DPSS_or_Slepian_window" rel="nofollow">http://en.wikipedia.org/wiki/Window_function#DPSS_or_Slepian_window</a></p>
<p>... | <p>If you follow the reference link no. <a href="http://en.wikipedia.org/wiki/Window_function#cite_note-JOSKaiserDPSS-45" rel="nofollow">43</a> from Wikipedia, then you will end up on <a href="https://ccrma.stanford.edu/~jos/sasp/Slepian_DPSS_Window.html" rel="nofollow"><strong>this website</strong></a> of Stanford Uni... | 962 |
filter design | Creating a digital filter, from Laplace to $\mathcal Z$-transform (zero order hold) to code? | https://dsp.stackexchange.com/questions/18329/creating-a-digital-filter-from-laplace-to-mathcal-z-transform-zero-order-ho | <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 then use ... | <p>The example I looked at used a tustin or bilinear conversion not a zero order hold(the default for matlabs "c2d" command). So this is more an answer to what i wanted to do rather than the question that i asked above.</p>
<p>I solved the following (converting the s domain function into code) by taking the s domain f... | 963 |
filter design | How to pad a windowed sinc filter in the frequency domain | https://dsp.stackexchange.com/questions/18580/how-to-pad-a-windowed-sinc-filter-in-the-frequency-domain | <p>I'm creating windowed sinc filters to apply them to certain signals that I'm dealing with. To design the filters, I'm using the approach described in the book "The Scientist and Engineer's Guide to DSP". Here's a brief resuming:</p>
\[h[i] =
\left\{
\begin{matrix}
Kw(i)\frac{\sin(2\pi f_c(i - \frac{M}{2}))}{i - ... | <p>You don't pad it in the frequency domain, you pad it in the time domain (i.e. before you calculate the FFT). You can put the zeros either symmetrically or after the filter. Either way works, it just results in a shift in the output.</p>
| 964 |
filter design | FIR filter design | https://dsp.stackexchange.com/questions/18622/fir-filter-design | <p>I am designing an FIR filter.my specs are fs=300MHz, Fc=45MHz, Fs=75MHz, passband gain=3dB , stopband attn=>40dB. what parameters I values of <em>a</em> have to provide in <em>firpm</em> for the minimum order filter design.
I am putting <em>a=[0.01 0.01]</em>. is it correct?</p>
| <p>I suppose you want a low pass filter. Such a filter has one passband and one stopband, and accordingly you need an <code>a</code> vector with 4 elements:</p>
<ol>
<li>the desired magnitude at frequency $0$</li>
<li>the desired magnitude at the passband edge ($f_c$)</li>
<li>the desired magnitude at the stopband edg... | 965 |
filter design | multiplications per second for FIR filter | https://dsp.stackexchange.com/questions/18699/multiplications-per-second-for-fir-filter | <p>In my filter the fs=300MHz. and no. of coefficients is 31. I have following queries.
(1) what will be the number of multiplications per second?
(2) can multiplication be done in one clock cycle?
(3) why normally multiplication per second is calculated and not addition/substraction per second in the filter implementa... | <p>To answer your questions:</p>
<ol>
<li>The number of multiplies is the number of taps times the number of sample per second. Given a sampling rate of 300MHz and 31 taps, you will have to do 9300 million multiplies per second.</li>
<li>As Paul R says, whether a multiply can be done in one cycle depends on the proce... | 966 |
filter design | Filtering an image with a helmholtz-type equation | https://dsp.stackexchange.com/questions/22821/filtering-an-image-with-a-helmholtz-type-equation | <p>I'm attempting to apply the following PDE as an image filter to smooth a discrete heightmap with a helmholtz-type equation as described in this <a href="http://www.researchgate.net/profile/Manuel_Gamito/publication/222551401_An_accurate_model_of_wave_refraction_over_shallow_water/links/00b4951a8b09d51acf000000.pdf" ... | 967 | |
filter design | Calculating the network function of a filter | https://dsp.stackexchange.com/questions/23431/calculating-the-network-function-of-a-filter | <p>Given a system, that behaves as a 1st order filter with network function $H(s)$. We input:
$$v_1 (t)=1+3\cos(10^4 t)$$</p>
<p>And we obtain as output:
$$v_2(t)=1+1.5\cos \left(10^4 t -\dfrac{\pi}{3}\right)$$</p>
<p>Say what kind of filter it is and find its network function $H(s)$.</p>
<p>I'm trying to solve this... | <p>You need to consider the system's frequency response</p>
<p>$$H(j\omega)=\frac{\kappa}{j\omega+a}\tag{1}$$</p>
<p>Now you know that $$H(0)=1\tag{2}$$ and $$|H(j\omega_0)|=\frac12\tag{3}$$ (with $\omega_0=10^4$). Note that $H(0)$ is real-valued, whereas $H(j\omega_0)$ will generally be complex-valued. From (1) and ... | 968 |
filter design | Are noncausal filters ever used in practice? | https://dsp.stackexchange.com/questions/25252/are-noncausal-filters-ever-used-in-practice | <p>Basically what it says in the title; I have just started reading about these things and find noncausal filters pretty interesting in concept, but also they do not seem like they would have any advantage worth sacrificing real-time processing. Since "I have just started reading about these things" I feel as if I shou... | <p>Yes.</p>
<p>The problem with a system that operates in (near) real time is that you can't look into the future. One way you can deal with this is if you only need a finite amount of look-ahead is to put some delays and then delay the output so you're still causal.</p>
<p>However, many filtering problems have non-c... | 969 |
filter design | Practical vs ideal lowpass interpolator | https://dsp.stackexchange.com/questions/26691/practical-vs-ideal-lowpass-interpolator | <p>Consider a signal with a sample rate $f_s = 44.1$ kHz. Let us upsample the signal by a factor of $L = 2$ and interpolate the zeros.</p>
<p>An ideal lowpass interpolator would have a gain of $L$ and a cutoff frequency of:</p>
<p>$$f_c = \frac{f_s}{L}$$</p>
<p>An ideal lowpass filter has an infinitesimally small tr... | <p>When designing a filter, you really care about its behavior in two regions:</p>
<ol>
<li><p><strong>Passband</strong>: You want little attenuation in this region, and maybe other properties as well, like linear phase, depending upon your application.</p></li>
<li><p><strong>Stopband</strong>: You want as much atten... | 970 |
filter design | comb filter design in wireless communication | https://dsp.stackexchange.com/questions/26974/comb-filter-design-in-wireless-communication | <p>How can I implement comb filter in reducing noise in wireless communication?
I am new in signal processing and right now I am still learning about the comb filter. Can I use it to reduce/filter noise in wireless communication?</p>
| 971 | |
filter design | Filter Design for Phase Response | https://dsp.stackexchange.com/questions/27779/filter-design-for-phase-response | <p>How can I design an all pass filter to have a constant phase shift over a bandwidth centered around a carrier?
I don't care about phase shift outside the band.
I would like to have the filter in time domain. This is not a straightforward job right?
Any keywords, design methods, external links are appreciated. </p>... | <p>It's instructive to see what an ideal filter adding a constant phase shift would look like. If $\theta$ is the desired phase shift, the corresponding ideal frequency response is</p>
<p>$$H(e^{j\omega})=\begin{cases}e^{-j\theta}&,\quad 0<\omega<\pi\\
e^{j\theta}&,\quad-\pi<\omega<0\end{cases}\tag... | 972 |
filter design | A C/C++ library for FIR filter design with "Don't Care region" | https://dsp.stackexchange.com/questions/28947/a-c-c-library-for-fir-filter-design-with-dont-care-region | <p>I need to get coefficients for my FIR filter.
I know my pass band lets say between 350 - 400 Hz
And my stop band(s) lets say 200 - 250 and 500 - 500 Hz,
The other regions in the spectrum I simply don't care. I want the Filter to be relaxed in this regions so be more effective in pass and stop bands. </p>
<p>I am... | 973 | |
filter design | how to design wavelets from splines | https://dsp.stackexchange.com/questions/29007/how-to-design-wavelets-from-splines | <p>Can any one tell me how to design wavelets from splines using matlab. whether we can make wavelets from higher order splines or only with B splines</p>
| 974 | |
filter design | What filter to use in audio analysis filterbank instead of FFT? | https://dsp.stackexchange.com/questions/29721/what-filter-to-use-in-audio-analysis-filterbank-instead-of-fft | <p>Standard bandpass filters can make super precise analysis filterbanks with 1024 to 4096 filters, on reaktor4. I tried in code to used cookbook BandPass and the result was aweful.</p>
<p>Does someone know a precise BandPass Filter that transmits narrow bands of an intended frequency without noise and irregularity? r... | <p>This has already been addressed in depth here:
<a href="https://stackoverflow.com/questions/5901483/simple-audio-filter-bank">https://stackoverflow.com/questions/5901483/simple-audio-filter-bank</a></p>
<p>and i found some c# code on the subject here:<br>
<a href="https://waveletstudio.codeplex.com/" rel="nofollow ... | 975 |
filter design | Adjusting corner frequency to constrain maximum disturbance in a high-pass filter | https://dsp.stackexchange.com/questions/29738/adjusting-corner-frequency-to-constrain-maximum-disturbance-in-a-high-pass-filte | <p>I have a first-order high-pass filter with transfer function:
$$G(f)=\dfrac{G_0 jf}{jf + f_c}$$</p>
<p>where $G_0$ is the gain at high frequencies.</p>
<p>If I input a sine wave with frequency 1 KHz and I want a maximum disturbance of 0.1% in the amplitude, how can I know the maximum value of the corner frequency ... | <p>You set $|G/G_0| = 0.001$ and $f = 1kHz$ and then solve your equation (in magnitude form) for $f_c$</p>
| 976 |
filter design | What is Local Mean Filter? | https://dsp.stackexchange.com/questions/31219/what-is-local-mean-filter | <p>The research paper "<a href="http://download.springer.com/static/pdf/256/art%253A10.1155%252F2010%252F680429.pdf?originUrl=http%3A%2F%2Fjivp.eurasipjournals.springeropen.com%2Farticle%2F10.1155%2F2010%2F680429&token2=exp=1464792290~acl=%2Fstatic%2Fpdf%2F256%2Fart%25253A10.1155%25252F2010%25252F680429.pdf*~hmac=1... | <p>They probably just wanted to say that the image was blurred (by some local method, e.g. convolution with a Gaussian kernel) in a more scientific way. </p>
<p>On the sharpening: They don't sharpen the image directly. What they do is to blur the image and the subtract the blurred version from the original. The result... | 977 |
filter design | FIR filter design sampling rate | https://dsp.stackexchange.com/questions/36103/fir-filter-design-sampling-rate | <p>Let's assume we have an $x(n)$ time sequence, whose $f_s$ sample rate is 20 kHz. We are required to design a linear-phase lowpass FIR filter that will attenuate the undesired high-frequency noise beyond 4kHz analog frequency. So we design a lowpass FIR filter and come out with an equation for the unit impulse respon... | 978 | |
filter design | FIR Filters - Type 3 | https://dsp.stackexchange.com/questions/40685/fir-filters-type-3 | <p>So I understand that a type 3 filter is not suitable for a highpass filter design, but is there any reason why it isnt suitable for a lowpass filter? </p>
<p>So ultimately, can a type 3 linear-phase FIR filter be used to design a lowpass filter? Why or why not? </p>
| <p>A type 3 FIR filter has odd symmetry and an odd number of taps. For this reason it has frequency response zeros at $\omega=0$ (DC) and $\omega=\pi$ (Nyquist), corresponding to transfer function zeros at $z=1$ and $z=-1$:</p>
<p>$$H(1)=\sum_{n=-M}^{M}h[n]=0\\
H(-1)=\sum_{n=-M}^{M}(-1)^nh[n]=0$$</p>
<p>where $N=2M+1... | 979 |
filter design | FIR filter design with flat passband but equi-ripple stop-band | https://dsp.stackexchange.com/questions/40822/fir-filter-design-with-flat-passband-but-equi-ripple-stop-band | <p>I am looking for a lowpass FIR filter with flat passband but equi-ripple stopband. In other words, it likes <a href="https://en.wikipedia.org/wiki/Chebyshev_filter" rel="nofollow noreferrer">Chebyshev_filter Type II</a> except that it is FIR instead of IIR. Linear-phase is preferred.</p>
<p>Thanks</p>
| <p>I suggest you the Parks-McClellan method. In Matlab you can use $\tt{firpm}$.</p>
<p>Matlab's (now obsolete function) $\tt{remez}$ also uses this scheme.</p>
<p>The FIR filter is optimally designed to approximate e.g. a Chebyshev filter such that the maximum error between the filter's response and the desired resp... | 980 |
filter design | Are all least square filters adaptive? | https://dsp.stackexchange.com/questions/42192/are-all-least-square-filters-adaptive | <p>Are least square filters, or filters that minimize error energy, the same as least mean square adaptive filters?</p>
| <p><strong>TL;DR:</strong> No, they are not necessarily the same.</p>
<hr>
<p><strong>Gory Details</strong></p>
<p>Least squares is just an optimization technique. It is used in a variety of ways.</p>
<p>For filter <strong>design</strong> it is used to select that realizable filter $H_r(e^{j\omega})$ that most clos... | 981 |
filter design | An explanation of "phase" of a filter | https://dsp.stackexchange.com/questions/43870/an-explanation-of-phase-of-a-filter | <p>I always read the word "phase" (like linear phase, phase shift...) in DSP but I'm still not sure what it supposes to mean, in intuition and also in practice.</p>
| <p>The phase of a sinusoid $s(t)=A_0\cos(2\pi f_0 t + \phi_0)$ is $\phi_0$ radians.</p>
<p>If this sinusoid goes through an LTI system with frequency response $H(f)$, then the ouptut is $y(t) = |H(f_0)| A_0 \cos(2\pi f_0 t + \phi_0 + \angle H(f))$. So, the phase of the output is different than the phase of the input -... | 982 |
filter design | Is initializing a digital filter's output with no "momentum" a non-trivial task? | https://dsp.stackexchange.com/questions/44350/is-initializing-a-digital-filters-output-with-no-momentum-a-non-trivial-task | <p>I'm working on implementing a filter with a very slow step response. This filter is implemented as a cascaded second-order-section filter (transposed direct form 2). I'm using the output of this filter as the input to a controller. Thus I'm trying to slow down how quickly the controller set point is able to change.<... | <p>If you want a stable linear time-invariant system to output constant $y$, it must have received input $x$ that is the ratio of the constant output and the zero frequency response of the system $H(1):$</p>
<p>$$y = H(1)x\quad \Leftrightarrow \quad x = \frac{y}{H(1)}$$</p>
<p>Or, you'd want to change the state of th... | 983 |
filter design | Transition bands and passband gain in digital filter design | https://dsp.stackexchange.com/questions/46454/transition-bands-and-passband-gain-in-digital-filter-design | <p>In an ideal design, a digital filter has a target gain in the passband and a zero gain (−∞ dB) in the stopband. In a real implementation, a finite transition region between the passband and the stopband, which is known as the transition band, always exists. The gain of the filter in the transition band is unspecifie... | <p>In an actual design you need to allow for a smooth transition from the passband to the stopband because the magnitude response of a realizable (i.e., causal and stable) filter is smooth; it can't jump. Of course you can try to approximate a jump in the magnitude, but you'll always get a smooth magnitude response (cf... | 984 |
filter design | About how to increase the FIR filter sampling frequency in FPGA? And what is the tradeoff of increasing the sampling frequency? | https://dsp.stackexchange.com/questions/46888/about-how-to-increase-the-fir-filter-sampling-frequency-in-fpga-and-what-is-the | <p>I am trying to implement a FIR filter on FPGA and trying to have a solid understanding of the FIR filter tap delay and sampling frequency.</p>
<p>Does the “one tap” delay equal to “1/Fs (sampling frequency)”? If I have N-tap, the total delay will be N/Fs? If the Fs sampling frequency is increased, the “one tap” del... | <blockquote>
<p>Does the “one tap” delay equal to “1/Fs (sampling frequency)”?</p>
</blockquote>
<p>Yes</p>
<blockquote>
<p>If I have N-tap, the total delay will be N/Fs?</p>
</blockquote>
<p>Depends on how you define "total" delay, but in general the answer is no. For a minimum phase filter the delay will be 1.... | 985 |
filter design | Creating a music note filter (notch/peaking) | https://dsp.stackexchange.com/questions/49426/creating-a-music-note-filter-notch-peaking | <p>I'd like to make a filter which essentially masks the spectrum except for frequencies around music notes in the standard tempered scale, i.e. $frequency \in 110 \times 2^\frac{i}{12}, 10 \le i \le 64$, in the case of a violin. The passband around each note should be narrow, perhaps 1% of the space between notes. The... | 986 | |
filter design | What is meant by Two pass FIR Filter?? (A basic question) | https://dsp.stackexchange.com/questions/50121/what-is-meant-by-two-pass-fir-filter-a-basic-question | <p>I have a confusion about what does a two pass FIR (bandpass) filter with order 40 means?? Passband frequencies are [8 13]. Type 2 FIR is same as two pass?? </p>
<p>I have check some previous literature which shows Linear-phase FIR filter can be divided into four basic types.</p>
<p>TYPE I symmetric length is o... | <p>You can't in general categorize a two-pass filter in any of those listed filter types. "Two-pass" means that the filter processes the data in two passes; the output of the first pass is used as the input of the second pass.</p>
<p>The two-pass filter's impulse response is the convolution of the impulse responses of... | 987 |
filter design | The desired frequency-response specifications | https://dsp.stackexchange.com/questions/50795/the-desired-frequency-response-specifications | <p>The complex function $ D (e^{-jw})$ is defined on the domain of approximation $\Omega$ .In most cases the domain $\Omega$ is the union of several disjoint frequency bands which are separated by transition bands where no
desired response is specified .We denote the union of all passbands by $\Omega^p$ and stopbands ... | <p>If you have to consider the whole frequency spectrum range in $[0,2\pi]$ for the design of the discrete-time filter, without assuming any type of symmetry, then you are considering the most general case of the filter and its coefficients will be <strong>complex</strong> valued. And nothing more can be said about the... | 988 |
filter design | CCDE processing vs. Scilab function | https://dsp.stackexchange.com/questions/50895/ccde-processing-vs-scilab-function | <p>I have used Scilab functions to produce a low-pass filter for an audio signal and the coefficients for the associated constant coefficient difference equation (CCDE). I then produced filtered signals by running the Scilab <code>filter()</code> function and by running my implementation of the CCDE on the audio signa... | <p>Scilab's filter, for <strong>short</strong> coefficient vectors, function implements a linear convolution in C code; that alone, since there's no python to actually be evaluated here, just multiplication and addition, is much much faster than writing something in a scripting language that can't 100% be just-in-time ... | 989 |
filter design | Design digital filter with model order reduction (MOR) and other methods | https://dsp.stackexchange.com/questions/51026/design-digital-filter-with-model-order-reduction-mor-and-other-methods | <p>IIR filters can be designed using different methods,such as: </p>
<ul>
<li>Analog Prototyping</li>
<li>Direct Design</li>
<li>Generalized Butterworth Design</li>
<li>Parametric Modeling</li>
</ul>
<p><a href="https://www.mathworks.com/help/signal/ug/iir-filter-design.html?lang=en#brbq5qb" rel="nofollow noreferrer"... | <p>If you're still new to digital filter design, I would not recommend you to dive into methods for model order reduction. First of all, they are not filter design methods, but they represent a second step to simplify an already existing model/system. Second, these methods are more applicable to control design, where y... | 990 |
filter design | Design of a Complex FIR Filter | https://dsp.stackexchange.com/questions/51930/design-of-a-complex-fir-filter | <p>For apply least-squares linear-phase FIR filter design,with frequency domain specification is not symmetrical.</p>
<p>The pass-band error function,</p>
<p>$$E(\mathbf{h})_p=\int_{\omega_{p_1}}^{\omega_{p_2}}| \mathbf{c}^T(\omega)\cdot \mathbf{h}-D(\omega)|^2d\omega \tag{1}$$</p>
<p>The stop-band error function,</... | <p>In the stopband(s), Eqs $(1)$ and $(2)$ are equivalent, because in the stopband the desired response equals zero: $D(\omega)=0$. The reason why you might want to split the error in passband and stopband error is to apply different weights, as shown in your Eq. $(3)$.</p>
<p>The function <code>freqz</code> computes ... | 991 |
filter design | Generation of Noise-shape filter from Power Spectrum Density | https://dsp.stackexchange.com/questions/52526/generation-of-noise-shape-filter-from-power-spectrum-density | <p>This is my very first time in dealing with signal processing, so I am sorry if I will not use a rigorous terminology.</p>
<p>I am dealing with some issues about noise modeling in matlab. I'm trying to figure out a way to construct a model (filter) of a noise from data. My first problem is that I have no <span class... | 992 | |
filter design | What frequency each bin of a Discrete Cosine Transform represents? | https://dsp.stackexchange.com/questions/55571/what-frequency-each-bin-of-a-discrete-cosine-transform-represents | <p>A practical example: I perform a DCT on a time series of discrete values that are spaced in time by 1/30 of a second. What frequencies each bin of this DCT represents? What is the formula to find that?</p>
<p>If I want to filter the DCT to remove all signal bins that correspond to frequencies below 0.4 Hz and abov... | 993 | |
filter design | Electret microphone RC filter design contradiction among information sources | https://dsp.stackexchange.com/questions/56295/electret-microphone-rc-filter-design-contradiction-among-information-sources | <p>I'm building a circuit for an electret microphone and I want to build a bandpass filter around the op-amp.
I was using <a href="https://youtu.be/ts-JqEVzvDo?t=394" rel="nofollow noreferrer">this source</a> until I have found that most sources ( e.g. <a href="https://www.maximintegrated.com/en/app-notes/index.mvp/id... | <p>First, the youtube source shows an 1st order active filter, maxim source shows 2nd order active filter and last source shows first order passive filter. That's three different designs.</p>
<p>A 1st order active filter can be implemented either in the negative feedback branch of the op amp (as in youtube source), th... | 994 |
filter design | Criterion to choose length of an accumulator and product | https://dsp.stackexchange.com/questions/59491/criterion-to-choose-length-of-an-accumulator-and-product | <p>I am designing an IIR filter with fixed-point arithmetic and I have to select the proper length for the accumulator and product. I would like to know a standard to follow in order to choose its length. I have selected the <em>Direct Form 1</em> topology to implement a 6th order digital filter (instead of a cascaded ... | <ol>
<li>Fixed point processing is very difficult. Floating point is A LOT easier. </li>
<li>The best algorithm and scaling approach depends a lot on your specific filter and the statistics of your signal. There is no "one size fits all" solution.</li>
<li>Cascaded second order sections are almost always the way to go.... | 995 |
filter design | Cascading filters at different sampling rates | https://dsp.stackexchange.com/questions/59608/cascading-filters-at-different-sampling-rates | <p>We are currently designing a type 2 compensator <span class="math-container">$G_1$</span> (1 pole at the origin, 1 zero and 1 pole) to stabilize a power factor correction (PFC) circuitry. The crossover frequency is low - 2-3 Hz - and the compensator is implemented using a biquad structure sampling at 10 kHz. For rip... | 996 | |
filter design | Is there any advantage on using a low span value in a RRC filter? | https://dsp.stackexchange.com/questions/59752/is-there-any-advantage-on-using-a-low-span-value-in-a-rrc-filter | <p>I know that in a RRC filter a high value of the span gives a better response, in the sense that the RRC filter response is more near to the ideal RRC filter response. However, would there be any advantage on using a small span?</p>
<p>Lets say, for example, that I am sending <code>100 BPSK</code> symbols, a value o... | <p>The advantage of a RRC filter with a smaller span is that it has fewer taps, so the filter requires fewer multiplies and additions per sample. Longer filters approximate the ideal RRC response more closely but require more computation. Shorter filters do not approximate the ideal RRC as well but require less compu... | 997 |
filter design | How to smooth filter response? | https://dsp.stackexchange.com/questions/61177/how-to-smooth-filter-response | <p>I have a filter designed in matlab with the function cheby2( N, Rs, Ws, 'stop'). The filter would give nice frequency response with for a given parameter set when the filter order is 2 or 4 (N=4). But if I increase the filter order to say 14 the magnitude plot of filter response is not at all smooth in fact in the s... | <p>You have a very narrow stop band which means that all the poles are crammed in a very small area of the complex plane, close to the unit circle. This can result in severe numerical problems, even for relatively small filter orders, even with floating point arithmetic.</p>
<p>Another important point that you might n... | 998 |
filter design | Is gradient vector of pole zero carry usful information? | https://dsp.stackexchange.com/questions/61429/is-gradient-vector-of-pole-zero-carry-usful-information | <p>Consider a transfer function (TF) with <span class="math-container">$n$</span> number of poles <span class="math-container">$(p_1,..p_n)$</span> and <span class="math-container">$m$</span> number of zeros <span class="math-container">$(z_1,..z_n)$</span>. One can write the magnitude of the frequency responce of the... | <blockquote>
<p>Does gradient vector of pole zero carry useful information?</p>
</blockquote>
<p>Yes. The partial derivatives can be used in creating iterative search algorithms for fitting IIR filters to arbitrary targets. Examples of algorithms that use the derivatives are Steepest Descent or Conjugate Gradient. <... | 999 |
time-frequency analysis | Introductory book on time-frequency analysis? | https://dsp.stackexchange.com/questions/15898/introductory-book-on-time-frequency-analysis | <p>I'm looking for an introductory book to time-frequency analysis. The book should be practical in nature and not mathematics heavy. Suggestions?</p>
| <p>I recommend this book:</p>
<p><a href="http://www.amazon.fr/Understanding-Digital-Signal-Processing-Edition/dp/0137027419" rel="nofollow">Understanding Digital Signal Processing, Richard G. Lyons</a></p>
<p>This book explains the basics concepts of digital signal processing, which includes time-frequency analysis,... | 1,000 |
time-frequency analysis | Introduction to fast algorithms for time–frequency analysis | https://dsp.stackexchange.com/questions/43744/introduction-to-fast-algorithms-for-time-frequency-analysis | <p>I had preliminary knowledge of digital signal processing from Oppenheim's <a href="http://dl.acm.org/citation.cfm?id=1795494" rel="nofollow noreferrer">Discrete-Time Signal Processing</a> and is studying time-frequency analysis now. May someone suggest introductory reference (textbook, website, review paper...) for ... | <p>If you are interested in discrete linear systems (either time-frequency or time-scale), you could invest in multirate filter banks, that provide tools for computing, optimizing, etc, such as the polyphase matrix or the lifting scheme. A tutorial paper is </p>
<ul>
<li><a href="http://www.systems.caltech.edu/dsp/pp... | 1,001 |
time-frequency analysis | Time Frequency Analysis Equation Derivation | https://dsp.stackexchange.com/questions/85395/time-frequency-analysis-equation-derivation | <p>I have been reading Leon Cohen's book "Time Frequency Analysis" as part of a project for university. On page twelve or equation (1.57) during his derivation of a representation of the average frequency in terms of the time-domain signal he provides the following relation which from my perspective came out ... | <p>They just express <span class="math-container">$S(\omega)$</span> (and its complex conjugate) by the Fourier transform of <span class="math-container">$s(t)$</span>:</p>
<p><span class="math-container">$$S(\omega)=\int s(t)e^{-j\omega t}dt\tag{1}$$</span></p>
<p>From which we get</p>
<p><span class="math-container">... | 1,002 |
time-frequency analysis | Time frequency analysis for a spreading signal | https://dsp.stackexchange.com/questions/56293/time-frequency-analysis-for-a-spreading-signal | <p>I am a beginner in digital communications: I am studying the spread spectrum communication and I have a question on the spreading signals. For example I have 2 spreading signals and I do a time frequency analysis.</p>
<p>Should the spreading signals overlap in time? And if yes, why?</p>
| <p>The overlap is not important, it is just necessary that the spreading sequences are pseudo-orthogonal.</p>
<p>Can someone confirm?</p>
| 1,003 |
time-frequency analysis | Why are analytic signals so important in Time-frequency analysis? | https://dsp.stackexchange.com/questions/46245/why-are-analytic-signals-so-important-in-time-frequency-analysis | <p>I am little confused about why we need analytic signals so bad in time-frequency analysis. What might happen if I use non-analytic signals to do time-frequency analysis?</p>
| <p>Assuming time-frequency aims a providing a separation (at least visual) between signal components, the main reasons could be:</p>
<ul>
<li>for quadratic distributions, which tend to yield interference between components, "cancelling" at negative frequencies reduce the quantity of components that can interfere.</li... | 1,004 |
time-frequency analysis | Time-frequency analysis | https://dsp.stackexchange.com/questions/19156/time-frequency-analysis | <p>I had this question in the exam without any further explanation.</p>
<p>Why the time translation invariance is an important feature for time-frequency distributions?</p>
<p>I am writing to ask whether anyone can please explain what is time translation invariance? And why is it important feature?</p>
| 1,005 | |
time-frequency analysis | Auto Correlation for Time Frequency Analysis | https://dsp.stackexchange.com/questions/31718/auto-correlation-for-time-frequency-analysis | <p>Given a signal $x(t)$, how do I implement a form of autocorrelation function defined as $a(t,T) = x(t-T)x(t+T)$, where $T$ is an arbitrary constant? </p>
<p>(a fast implementation would be ideal)</p>
<p>Edit:
This kind of signal I came across from seeing a "Parametric Symmetric Autocorrelation function", defined ... | <p>This line seems wrong:</p>
<pre><code>X = signal(X1_signal_indices).*conj(X1conj_signal_indices);
</code></pre>
<p>shouldn't it be</p>
<pre><code>X = signal(X1_signal_indices).*conj(signal(X1conj_signal_indices));
</code></pre>
<p>??</p>
<p>Note that there is some C code for implementing <a href="https://site... | 1,006 |
time-frequency analysis | Motivation of time-frequency analysis | https://dsp.stackexchange.com/questions/41194/motivation-of-time-frequency-analysis | <p>Can anyone give me an example of two signals with different temporal waveforms having the same Fourier transform (FT)? </p>
<p>Would the inverse Fourier transform still be able to recover correctly each signal?</p>
<p>Actually, I tried to check the question above, in matlab, using two chirp signals (same duration)... | <p>What a tricky question to overlook. Indeed I'm one of those who would immedieately press that Fourier transforms do lose time localization of the events as the comments stated. Yet it's certainly (mathematically and practically) true that any (transformable) signal waveform is <strong>exactly</strong> preserved unde... | 1,007 |
time-frequency analysis | Python tool for time-frequency analysis | https://dsp.stackexchange.com/questions/60366/python-tool-for-time-frequency-analysis | <p>I am trying to perform time-frequency analyses using the PyWavelets (pywt) toolkit for python. My ultimate goal is to perform time-frequency analyses for EEG signals but I am starting with something simpler.<br>
For a sanity test, I am creating a simple signal of length 2 seconds, with sample rate 250Hz, containing ... | <p>You can find a nice tutorial for time-frequency analysis in Numerical python by Johansson, chapter 17. link to github <a href="https://github.com/Ziaeemehr/signal_processing/tree/master/Numerical_Python_johansson" rel="nofollow noreferrer">repository</a>.</p>
<p>You can also check the <a href="https://docs.scipy.or... | 1,008 |
time-frequency analysis | Time-frequency analysis of a nonlinear system | https://dsp.stackexchange.com/questions/76817/time-frequency-analysis-of-a-nonlinear-system | <p>I have empirically developed a sensor failure detection system which works fine. The system receives inputs from different types of sensors. Because of noise characteristics, I use low pass filters on some sensors output. In the system, all these sensor readings form a signal which is constantly compared with a mode... | <p>If superposition works, then independent mode/component extraction is of interest. <a href="https://dsp.stackexchange.com/a/71399/50076">Synchrosqueezing</a> is well-suited for this task. Extracted features can ten be fed to an anomaly detection system - optionally with <a href="https://github.com/gregversteeg/gauss... | 1,009 |
time-frequency analysis | When was the time-frequency analysis invented? | https://dsp.stackexchange.com/questions/17909/when-was-the-time-frequency-analysis-invented | <p>It seems there are several papers from the seventies but backtracking from the references gets quickly difficult. Who calculated for the first time a time-frequency representation of a signal?</p>
| <p>According to the preface of <a href="https://books.google.com/books?id=sjN2qq99-WwC&lpg=PR1&pg=PR1#v=onepage&q&f=false" rel="nofollow noreferrer">Foundations of Time-Frequency Analysis</a>, a rough timeline is as follows:</p>
<ul>
<li>1930 - Early development of quantum mechanics by H. Weyl, E.Wigner... | 1,010 |
time-frequency analysis | Time Frequency Signal Analysis in Mathematica (MMA) | https://dsp.stackexchange.com/questions/19188/time-frequency-signal-analysis-in-mathematica-mma | <p>I want to know " Whether there is any Tool Box in Mathematica (MMA) for the Time-Frequency (TF) Signal Analysis".</p>
<p>I am well-versed in MMA Programming, so want to do TF Signal Analysis in MMA. I think if there is toolbox of TF Analysis, then it will be of very much great help in long programming.</p>
<p>Than... | <p>If you are using an older version of <em>Mathematica</em> (pre v.8) and are interested in wavelets - yes, you need an add-on to perform wavelet analysis. More about it <a href="http://library.wolfram.com/infocenter/TechNotes/4639/" rel="nofollow noreferrer">here</a>. If you are using v.8 or above then everything wav... | 1,011 |
time-frequency analysis | Time-frequency analysis of non-sinusoidal periodic signals | https://dsp.stackexchange.com/questions/4697/time-frequency-analysis-of-non-sinusoidal-periodic-signals | <p>Given the history of the sum of a time-varying mixture of periodic signals, say square waves, how would you efficiently estimate the number and frequencies of components active at a particular time? The amplitudes and frequencies of the components are arbitrary but fixed real numbers; if a component is active at a c... | <p>Let us start with the unsupervised methods...</p>
<p>A first approach would be to compute a spectrogram and factorize it with NMF (<a href="http://en.wikipedia.org/wiki/Non-negative_matrix_factorization" rel="nofollow">Non-negative Matrix Factorization</a>). If you are unfamiliar with this technique, it decomposes ... | 1,012 |
time-frequency analysis | Time Frequency Analysis by Frequency Contour Detection in Spectrogram | https://dsp.stackexchange.com/questions/64084/time-frequency-analysis-by-frequency-contour-detection-in-spectrogram | <p><a href="https://i.sstatic.net/tZou6.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/tZou6.png" alt="enter image description here"></a>I have an image of a spectrogram and I wish to detect the tracks/contours of prominent frequencies present in the spectrogram.</p>
<p>In the end, I want to be able to... | <p>The OP is interested in detecting the presence of frequencies in the 155 to 165 Hz frequency band within a block of data (or any other defined frequency band). The spectrogram is useful to observe multiple frequencies versus time, but if only one or even a few blocks of frequencies are desired for detection, then an... | 1,013 |
time-frequency analysis | Time domain analysis vs frequency domain analysis? Applications wise? | https://dsp.stackexchange.com/questions/68083/time-domain-analysis-vs-frequency-domain-analysis-applications-wise | <p>When do we use time domain analysis and when do we use frequency domain analysis? </p>
<p>As far i studied i know that when we need to study individual sinusoidal components of a signal, we choose frequency domain analysis. Is it the only application of frequency domain analysis? </p>
| <p>Frequency domain analysis has much broader application (more numerous to list) than just analyzing sinusoidal components of a signal. Frequency domain analysis appears as a mathematical tool whenever the equivalent operations in the time domain can be simplified, and vice versa. For example, convolution in one domai... | 1,014 |
time-frequency analysis | Frequency Analysis (DFT / FFT) of a Signal Without a Constant Sampling Frequency (Non Uniform Sampling in Time Domain) | https://dsp.stackexchange.com/questions/32137/frequency-analysis-dft-fft-of-a-signal-without-a-constant-sampling-frequency | <p>I'm a stack exchange user for some time and now I'm registering to ask a simple question (I think!).</p>
<p>I have a vibration signal with an amplitude and time (sampling frequency not constant) in a $10000\times 2$ double variable.</p>
<p>The data is available at: <a href="https://1drv.ms/x/s!AoCOij4si31tzgY89bh... | <h1>The DFT Matrix for Non Uniform Time Samples Series</h1>
<h2>Problem Statement</h2>
<p>We have a signal <span class="math-container">$ x \left( t \right) $</span> defined on the interval <span class="math-container">$ \left[ {T}_{1}, {T}_{2} \right] $</span>.<br />
Assume we have <span class="math-container">$ N $</... | 1,015 |
time-frequency analysis | How can I compute a time-frequency cross-spectrum in MATLAB? | https://dsp.stackexchange.com/questions/11503/how-can-i-compute-a-time-frequency-cross-spectrum-in-matlab | <p>MATLAB has a <a href="http://www.mathworks.com/help/signal/ref/spectrogram.html" rel="nofollow">spectrogram</a> function for the time-frequency analysis of a single signal. It also has a <a href="http://www.mathworks.com/help/signal/ref/cpsd.html" rel="nofollow">cpsd</a> function for estimating the cross-frequency s... | <p>I don't know of a function that does all of what you ask, but it is easy enough to write. They key step is to create short-time integrations on which the FFTs may be performed. As you say, cpsd then averages all these STIs, but you can write your own to skip that step.</p>
<p>The key function to do this is $y = b... | 1,016 |
time-frequency analysis | Python - time frequency spectrogram | https://dsp.stackexchange.com/questions/25115/python-time-frequency-spectrogram | <p>I have some 64 channel EEG data sampled at 256Hz and I'm trying to conduct a time frequency analysis for each channel and plot a spectrogram.</p>
<p>The data is stored in a numpy 3d array, where one of the dimensions has length 256, each element containing a microvolt reading over all sampled time points (total len... | <p>The idea of a spectogram is to split your signal into a number of blocks or frames, which are potentially overlapping. After windowing, an FFT is calculated per frame. The output of these FFTs are collected as column vectors in your graph. Thus, the x-axis is related to time and the y-axis is related to frequency. S... | 1,017 |
time-frequency analysis | Time-Frequency Analysis of Big Data - Data Size Reduction: averaging the most appropriate method? | https://dsp.stackexchange.com/questions/36839/time-frequency-analysis-of-big-data-data-size-reduction-averaging-the-most-ap | <p><strong>Explanation:</strong></p>
<p>I would like to analyse the data from an experiment, which investigates the performance of a mechanical component using sensors, that has generated <strong>2000 CSV</strong> files. Each file contains <strong>513 Rows</strong> x <strong>1220411 Cols</strong>, and they are in spec... | <p>So, first of all, CSV seems to me the least suitable format imaginable for this amount of data. It needs to be parsed, is memory hungry, and wastes precision, and isn't linearly addressable (ie. to get to the 99999. element, you need to parse the preceeding 99998 elements). </p>
<p>So I'd recommend keeping the stru... | 1,018 |
time-frequency analysis | Time domain and frequency domain analysis equivalence | https://dsp.stackexchange.com/questions/31299/time-domain-and-frequency-domain-analysis-equivalence | <p>Let us imagine an LTI system with physically realizable input (ruling out fancy mathematical functions and the concomitant complexities and paradoxes) completely known from -$\infty$ to $\infty$. We want to calculate the output. We can analyse it in time domain using the linear constant coefficient differential equ... | <p>now, even a steady-state sinusoid can be thought of, in the limit, as a sum of weighted pulses, each with a beginning and some kinda end. how do all of these <em>"transient"</em> signals add up to a steady-state sinusoid? but they do:</p>
<p>$$\begin{align}
x(t) &= \lim_{T \to 0} \sum_{n=-\infty}^{+\infty} x(... | 1,019 |
time-frequency analysis | Match Filter in Time-Frequency domain instead of just Time domain. Redundant, or better? | https://dsp.stackexchange.com/questions/2400/match-filter-in-time-frequency-domain-instead-of-just-time-domain-redundant-or | <p>Assume you have a signal, and within it, some pulses are present. A pulse is a simple tone. You know the pulses' duration and shape. (Let us assume that a pulse is made of a couple of cycles, and then to which all those cycles are multiplied by a hamming window. So the final pulse may look like the blue plot below: ... | <p>Think of the time - frequency ambiguity of your matched filter like so:</p>
<ul>
<li>Frequency ambiguity means it will respond to a range of frequencies</li>
<li>Time ambiguity means the response will be 'smeared' around the spatial location.</li>
</ul>
<p>If you you have 0% frequency ambiguity, the matched filter... | 1,020 |
time-frequency analysis | Does the instantaneous frequency contradict the uncertainty principle? | https://dsp.stackexchange.com/questions/38970/does-the-instantaneous-frequency-contradict-the-uncertainty-principle | <p>The uncertainty principle states that there is a trade off between time and frequency. So, finding frequency components at specific time is impossible. However, the instantaneous frequency measure the frequency as a function of time. Which means using the instantaneous frequency, the frequency components could be fo... | <p>The uncertainty principle works in the presence of (an uncertain amount of) noise or other signals (including possible harmonics), corrupting the exact phase, and thus the rate of change of phase of the signal of interest. If the phase is corrupt, or mixed with the phase of other signals, then deriving an instantan... | 1,021 |
time-frequency analysis | Natural frequencies | https://dsp.stackexchange.com/questions/86797/natural-frequencies | <p>Given the acceleration response time history of a multi-story structure, how can I find natural frequencies using time-frequency analysis techniques?
If you just provide some references or articles, I truly appreciate it.</p>
| <p>In general, you need the time history of the excitation in order to interpret the response, like Dan Boschen has said.</p>
<p>But under certain circumstances, the excitation of the system can be assumed to be minimum entropy (or quite similarly minimum energy), which allows one to identify an estimate of the system'... | 1,022 |
time-frequency analysis | Does Fast Continuous Wavelet Transform (fCWT) have theory-supported novelty or just simply a computation optimization? | https://dsp.stackexchange.com/questions/83469/does-fast-continuous-wavelet-transform-fcwt-have-theory-supported-novelty-or-j | <p>A recent publication, <a href="https://doi.org/10.1038/s43588-021-00183-z" rel="nofollow noreferrer">The fast Continuous Wavelet Transform (fCWT)</a>, enables real-time, wide-band, and high-quality, wavelet-based time–frequency analysis on non-stationary noisy signals.</p>
<p>I'm a beginner with wavelet and I'm work... | <p>I've modestly reviewed the paper.</p>
<p>I'm skeptical of its speedups and implementation accuracy. It includes time of sampling the wavelets in benchmarks, which is valid, but arguably the main use case is if wavelets are pre-computed and reused. Paper also make several dubious statements that suggest the authors d... | 1,023 |
time-frequency analysis | Comparison of WVD vs STFT Spectral analysis in the presence of Noise | https://dsp.stackexchange.com/questions/86297/comparison-of-wvd-vs-stft-spectral-analysis-in-the-presence-of-noise | <p>This question is an extension to the question about WVD vs STFT originally posted <a href="https://dsp.stackexchange.com/questions/86211/wigner-ville-distribution-wvd-vs-stft-for-spectral-analysis/86287?noredirect=1#comment182690_86287">Here</a>. During the QA it was pointed out that the WVD only works for noiseless... | 1,024 | |
time-frequency analysis | How critical is the selection of the window function in STFTs? | https://dsp.stackexchange.com/questions/1618/how-critical-is-the-selection-of-the-window-function-in-stfts | <p>I have a sum of periodic signals that I am trying to untangle using time-frequency analysis. I seem to get wildly different results depending on the window length and shape. This is a problem because I want to develop an automated, and hopefully sequential algorithm to do the job.</p>
| <p>Window functions have an inherent tradeoff between two of their frequency-domain properties:</p>
<ul>
<li><p><strong>Main lobe width:</strong> Any tapered window function will cause some "smearing" in the frequency domain. This is visualized by the width of the center lobe in the window function's frequency respons... | 1,025 |
time-frequency analysis | What does "real time" signal processing mean? | https://dsp.stackexchange.com/questions/18740/what-does-real-time-signal-processing-mean | <p>I thought this was supposed to be an obvious question, until I finally set up my real time system.</p>
<p>So basically I have a transmitter that sends 128 samples/second to a receiver. The transmitted information is stored as an object in MATLAB and continuously updated.</p>
<p>When people talk about real time sig... | <p>'Real time' is a concept from computer engineering. A real time system is one that is guaranteed, by design, to execute a function or routine in a certain time T, or less. For example, a real-time avionics system is proven to react to signals coming from certain instruments in a time below a given threshold.</p>
<p... | 1,026 |
time-frequency analysis | Disadvantages of wavelet transform | https://dsp.stackexchange.com/questions/15148/disadvantages-of-wavelet-transform | <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 analysis. It is ... | <p>If you consider the whole set of potential wavelet transforms, then you have a lot of flexibility. </p>
<p>For instance, should you use 1D continuous complex wavelet transforms, by analyzing the modulus and the phase of the scalogram, and provided you use well-chosen wavelets (potentially different for the analysis... | 1,027 |
time-frequency analysis | Calculating the spectrogram of the center of pressure time series in human standing balance | https://dsp.stackexchange.com/questions/66338/calculating-the-spectrogram-of-the-center-of-pressure-time-series-in-human-stand | <p>I have some biomechanical data of a few subjects standing on a force plate. The center of pressure along the x and y axes was measured. The total time of measurement was 30s and the sampling frequency was 100Hz. </p>
<p>I want to observe if there is any reduction of the density P(t,ω) in higher frequencies as time ... | 1,028 | |
time-frequency analysis | Bandpass filtering with passband changing with time | https://dsp.stackexchange.com/questions/56313/bandpass-filtering-with-passband-changing-with-time | <p>Is it possible to implement some sort of filter which adapts as a function of time?</p>
<p>Specifically, say I have a "noiseless" model of some signal which has the same frequency components at the same times as the signal I expect to measure, but with different phase and amplitudes (thus invalidating simple matche... | 1,029 | |
time-frequency analysis | time frequency localization using wavelet transform | https://dsp.stackexchange.com/questions/18058/time-frequency-localization-using-wavelet-transform | <p>I am currently doing analysis on Photoplethysmograph (PPG) data and I want to know the frequency (heart rate) at every time point so a windowed FFT might not be the best option. I am looking at wavelet to generate frequency and time information. I have been working with matlab example code however I have trouble det... | <p>What information are you trying to extract from your signal?</p>
<blockquote>
<p>I want to know the frequency (heart rate) at every time point</p>
</blockquote>
<p>If this is the information you want then any sort of frequency analysis is unlikely to be very useful. It will show you that you have a 1 or 2 hz per... | 1,030 |
time-frequency analysis | Uncertainty principle - Duration bandwidth principle | https://dsp.stackexchange.com/questions/42867/uncertainty-principle-duration-bandwidth-principle | <p>In one of <a href="http://nptel.ac.in/" rel="nofollow noreferrer">NPTEL</a> courses about time-frequency analysis, the professor said that the duration bandwidth principle is $\sigma_t^2 \sigma_\omega^2 \ge \frac{1}{4}$.</p>
<p>He added that the formula making use of time resolution and frequency resolution is a fa... | <p>Defining the Fourier Transform:</p>
<p><span class="math-container">$$ \mathscr{F} \Big\{x(t)\Big\} \triangleq X(f) \triangleq \int\limits_{-\infty}^{+\infty} x(t) \ e^{-i 2 \pi f t} \ \mathrm{d}t $$</span></p>
<p>and inverse:</p>
<p><span class="math-container">$$ \mathscr{F}^{-1} \Big\{X(f)\Big\} \triangleq x(t) ... | 1,031 |
time-frequency analysis | Detecting background noise from audio time-freq domain analysis | https://dsp.stackexchange.com/questions/81297/detecting-background-noise-from-audio-time-freq-domain-analysis | <p>I have a requirement to detect/reduce sidetalk/background noise in real-time audio. I am stuck in how can I detect this from audio time-frequency domain analysis. I am already getting the time-freq data from stft (I am using java for an easier way to integrate with our project). Can I do this without any machine/dee... | <p>After some r&d on this area, I found out that there is only one good way to approach the problem. That is Short Time Fourier Transform <strong>(STFT)</strong> as mere RMS of an audio frame is mixed energy of all frequencies present there. It can give an idea but will fail in many of the cases. but through STFT w... | 1,032 |
time-frequency analysis | Frequency analysis to determine low-pass cut off frequency | https://dsp.stackexchange.com/questions/50611/frequency-analysis-to-determine-low-pass-cut-off-frequency | <p>I collected some data for a practical application, where the signal represents force data obtained from an impact of a punch against a force plate attached to a quasi-rigid rig (it moves once the impact occurs). I have a few questions to understand how to deal with my data.</p>
<p>Features of the signal:</p>
<p>th... | <ol>
<li><p>I think you will get almost the same amount of frequency content for both the cases (fft of 60 ms and fft of 2 sec). The time series indicates that only from 0.6 to 1.2 sec there is vibration. But it's better to use the full signal while doing the FFT as there is no fear of losing any data. If you cut some ... | 1,033 |
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