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Question: <p>If <span class="math-container">$y(t) = x(t)*h(t)$</span>, then what is the expression for <span class="math-container">$y(t+a)$</span>?</p>
<p>Is it <span class="math-container">$x(t+a)*h(t+a)$</span> or <span class="math-container">$x(t+a)*h(t)$</span>?</p>
Answer: <p>From your confusion of <span class... | https://dsp.stackexchange.com/questions/52560/convolution-of-shifted-signal |
Question: <p>I have studied convolution in time domain and frequency domain. But doesn't know the 3rd method and technique </p>
Answer: | https://dsp.stackexchange.com/questions/63829/what-are-three-different-techniques-to-convolve-a-signal |
Question: <p>If you have a discrete signal, say</p>
<blockquote>
<p>[1,0,0,1]</p>
</blockquote>
<p>and you convolve it linearly with itself, you will quickly get a Gaussian distribution.</p>
<p>Why does it not hold for circular convolution?</p>
Answer: <p>Convolving <span class="math-container">$x = [1,0,0,1]$</span> ... | https://dsp.stackexchange.com/questions/83945/why-does-linear-convolution-with-itself-converges-to-gaussian-but-not-circular |
Question: <p>I know exactly what is periodic convolution. But i don't know if circular convolution means to be the same thing!</p>
Answer: <p>You did not give specific details on how you define periodic or circular. Assuming standard definitions, the answer is <strong>yes</strong>.</p>
<p>Standard infinite-support da... | https://dsp.stackexchange.com/questions/38450/is-periodic-convolution-same-as-circular-convolution |
Question: <p>I have 2 time-shifted signals,<span class="math-container">$f(t-t_0)$</span> and <span class="math-container">$g(t-t_0)$</span>. Assuming that <span class="math-container">$y=f(t)*g(t)$</span>, which is the convolution of the signals.</p>
<p>By definition, I have <span class="math-container">$f(t-t_0)*g(t-... | https://dsp.stackexchange.com/questions/87358/a-question-about-time-shifted-convolution |
Question: <p>Let's assume that there are two convolutions:</p>
<p><span class="math-container">$y_1 = (h_2[n]\cdot x[n])*(\bar{h_1}[n]\cdot\bar{x}[n])$</span></p>
<p><span class="math-container">$y_2 = (h_3[n]\cdot x[n])*(\bar{h_2}[n]\cdot\bar{x}[n])$</span></p>
<p>where "<span class="math-container">$\bar{x}$</sp... | https://dsp.stackexchange.com/questions/87361/simplification-of-convolution |
Question: <p>I want to implement a Length N moving average filter using block convolution algorithm(overlap save algorithm)</p>
<p>I am copying block convolution algorithm(overlap save algorithm) from Proakis, DSP using MATLAB 3rd Ed</p>
<pre><code>function [y] = ovrlpsav(x,h,N)
% Overlap-Save method of block convoluti... | https://dsp.stackexchange.com/questions/68515/implemenation-of-length-n-moving-average-filter-using-block-covolution-algorithm |
Question: <p>I memorized the convolution formula, all good. I started doing examples and in one of them I had to calculate the convolution of a shifted function with another one.</p>
<p>I know the property $$H(x)=f(x)\ast g(x)\\H(x-k)=f(x)\ast g(x-k)=f(x-k)*g(x)$$</p>
<p>So I had no trouble finding the result but I h... | https://dsp.stackexchange.com/questions/43339/question-about-convolution-of-shifted-function-simple |
Question: <p>I am attempting to combine two consecutive 2D convolutions into a single 2D convolution. Ideally, a convolution operation is a linear transformation, so it should be possible to merge two linear transformations into one.</p>
<p>In practice, I have performed all the necessary calculations to derive the fuse... | https://dsp.stackexchange.com/questions/89456/fusing-convolutions |
Question: <p>If I have a delta function of the following type</p>
<p>$$ n\delta(5n-20) * 3^{5n}u[n] $$ How can I calculate this convolution?</p>
<p>I have thought of the property $$ \delta[n-n_0] *x[n] = x[n-n_0] $$</p>
<p>Then if I say $$ k=5n $$ and $$ t[n]= 3^{5n}u[n] $$</p>
<p>It should be that the convolution... | https://dsp.stackexchange.com/questions/46363/convolution-of-delta-function-in-discrete-time-with-parameter |
Question: <p>I have a signal sampled at a period of 0.01 and a channel impulse response sampled at 0.1250. I convolved the signal with the channel impulse response.</p>
<ul>
<li>It is right to perform the convolution between two signals with diffrent sample times?</li>
<li>If it is, how can I calculate the sample ti... | https://dsp.stackexchange.com/questions/63927/sample-time-in-convolution |
Question: <ol>
<li><p>Why are we using circular convolution in DSP? </p></li>
<li><p>What's the main solid reason for the use of it in digital
processing? </p></li>
<li><p>Why does the concept of circular convolution come more often than
linear convolution?</p></li>
</ol>
Answer: <p>Given a discrete-time <strong>LTI</... | https://dsp.stackexchange.com/questions/35155/why-is-circular-convolution-used-in-dsp-why-not-linear-convolution |
Question: <p><img src="https://i.sstatic.net/Md1Ow.png" alt="enter image description here"></p>
<p>Dear all,</p>
<p>Please find attached image,
I am not able to understand why is the underlined term is to be included.
Shouldn't it be simply the exponential term?</p>
Answer: <p>The $u(t-2)$ term needs to be included ... | https://dsp.stackexchange.com/questions/13309/convolution-in-continious-time |
Question: <p>I have the input signal $x(t)$ <img src="https://i.sstatic.net/XxdCL.png" alt="enter image description here"></p>
<p>And impulse response $h(t)=20 e^{-1000t} u(t)$ in which u(t) is the unit step function.</p>
<p>When I try a convolution, I thought the solutions would be something like:</p>
<p>$
\begin{a... | https://dsp.stackexchange.com/questions/19934/is-there-a-convolution-mistake-in-my-method |
Question: <p>I am computing the correlation with MATLAB using the convolution fonction with a signal flipped before feeded into the function. Here are the results.</p>
<p><a href="https://i.sstatic.net/sTydl.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/sTydl.jpg" alt="enter image description here"></... | https://dsp.stackexchange.com/questions/31642/convolution-massive-spike-in-noise-section |
Question: <p>I am taking the convolution of $x(n)=\left\{2,1,-1,-2,3 \right\}$ with $n=0$ at the third position with $h(n)=\left\{1,2,0,3 \right\}$ with $n=0$ at the second position. The answer is $y(n)=\left\{2,5,1,-10, -10, -3, 6, -9 \right\}$ with the $n=0$ at the fourth position. I studied convolution more than a d... | https://dsp.stackexchange.com/questions/44401/identifying-origin-in-convolution-table |
Question: <p>I have just started convolution sum. I am able to do Mathematical convolution sum. But I am unable to make a figure of it in my mind. So I tried to go through the graphical convolution.
Below is the picture
<a href="https://i.sstatic.net/Zwgjn.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/... | https://dsp.stackexchange.com/questions/49578/difficulties-while-understanding-convolution |
Question: <p>I am struggling trying to understand the 3rd line of the expression below. The second line can be simply visualized by letting the kernel size be 3 and $i=2$ for eg. </p>
<p>Then
$ y_2 = \sum_a x_{2+a-1}k_a = x_2k_1 + x_3k_2 + x_4k_3$</p>
<p>In the 3rd line, there is a change of variable letting $u=i+a-... | https://dsp.stackexchange.com/questions/49906/convolution-change-of-variables |
Question: <p><a href="http://matlabtricks.com/post-3/the-basics-of-convolution" rel="nofollow noreferrer">Here</a> is an example of convolution given:</p>
<p><a href="https://i.sstatic.net/xWkbq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/xWkbq.png" alt="enter image description here"></a></p>
<p>I ... | https://dsp.stackexchange.com/questions/52891/using-matlabs-conv-function |
Question: <p>Attached is the question 1 part B, solution and my attempt. My attempt seems to be not correct. can someone comment?<a href="https://i.sstatic.net/AUfW9.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/AUfW9.png" alt="Question"></a></p>
<p><a href="https://i.sstatic.net/SFjWF.png" rel="nofol... | https://dsp.stackexchange.com/questions/56392/graphical-dt-convolution |
Question: <p>For my signals and systems homework, I was met with the following problem:</p>
<p>Consider a CT system with impulse response given by</p>
<p><span class="math-container">$$h(t) = e^{-|t|}$$</span></p>
<p>and a step input <span class="math-container">$x(t) = u(t)$</span>. Using the definition of convoluti... | https://dsp.stackexchange.com/questions/63741/is-there-a-process-for-deriving-special-cases-of-convolution |
Question: <p>As far as i have studied and understood, convolution is the process by which we can get/determine output of LTI systems
While reading one web link about convolution, i came across certain notation ,that i couldn't understand as shown highlighted in attached photo</p>
<p><strong>1)Are these notations refer... | https://dsp.stackexchange.com/questions/63971/confusions-regarding-convolution |
Question: <p>I have attached a snapshot from "signal processing first "
Where author says that properties of LTI systems are same as properties of convolution as shown in attached snapshot </p>
<p>Are these properties exactly same for both cases,convolution and LTI systems?and we don't need to apply any scaling etc?</... | https://dsp.stackexchange.com/questions/66460/properties-of-convolution-same-as-lti-systems |
Question: <p>Unfortunately indexing the output of convolution product confuses me. Suppose <span class="math-container">$x[n]$</span> is of length <span class="math-container">$15$</span> (i.e. <span class="math-container">$0 <= n <= 14$</span>) and <span class="math-container">$y[n]$</span> has the length of <sp... | https://dsp.stackexchange.com/questions/68530/how-to-index-output-of-convolution-product |
Question: <p>Edit,this is the <strong>exact phrasing</strong> of my question</p>
<blockquote>
<p>Let <span class="math-container">$\lambda\in\mathbb{R^n}$</span>.Prove that</p>
<p><span class="math-container">$f\star_{\lambda}g\in L^2(\mathbb{C^n})$</span> for all functions <span class="math-container">$f$</span> and <... | https://dsp.stackexchange.com/questions/76627/prove-that-the-twisted-convolution-of-f-and-g-lies-in-l2cn |
Question: <p>I'm just starting out in signal analysis and I've come across this effect. When I use convolution of a sinusoid with any other, either triangular pulse, rectangular pulse or decreasing exponential (regardless of whether they are causal) a transient segment appears in the output signal. Is this effect of th... | https://dsp.stackexchange.com/questions/89536/convolution-output-signal-transient-correction |
Question: <p>Convolution of two sine waves (or tones as called in audio) is theoretically not defined as the integral is infinite. Taking finite duration windowed sine waves and doing there convolution computationally always contains a fundamental frequency equal to that of the lower frequency sine wave. I am not getti... | https://dsp.stackexchange.com/questions/18480/what-is-convolution-of-two-sine-waves-tones |
Question: <p>If two signals do convolution in frequency domain, would the output width/BW be related to the width/BW input signals?
Would it be addition or any other?</p>
Answer: <p>For signals <span class="math-container">$x(t)$</span> and <span class="math-container">$y(t)$</span> having domains <span class="math-co... | https://dsp.stackexchange.com/questions/43828/convolution-in-frequency-domain-what-is-the-output-bandwidth |
Question: <p>I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what Dilip meant and it was simply not true...</p>
<p>Could someone confirm that it really isn't true what Dilip Sa... | https://dsp.stackexchange.com/questions/8530/a-better-explaination-for-theres-no-flipping-of-the-impulse-response |
Question: <p>Mathematically speaking, when convolving a <span class="math-container">$N$</span>-points signal with a <span class="math-container">$M$</span>-points signal, the resulting signal contains <span class="math-container">$N+M-1$</span> points.</p>
<p>In practice, the <span class="math-container">$N$</span>-po... | https://dsp.stackexchange.com/questions/94494/is-there-any-meaning-to-the-extra-points-introduced-by-a-convolution-product |
Question: <p>In the numerous PlayStation emulators there are out there, this small piece of code is used to resample the input to feed to the reverb, which only works at 22050 Hz:</p>
<p><a href="https://github.com/libretro-mirrors/mednafen-git/blob/master/src/psx/spu_reverb.inc#L69" rel="nofollow noreferrer">https://g... | https://dsp.stackexchange.com/questions/94669/this-isnt-a-typical-convolution-what-is-it-then |
Question: <p>If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?</p>
Answer: <p>There's not particularly any "physical" meaning to the convolution operation. The main use of convolution in engineering is in describing the output of a <a href="http://e... | https://dsp.stackexchange.com/questions/4723/what-is-the-physical-meaning-of-the-convolution-of-two-signals |
Question: <p>The equation to approximate an input signal with a unit impulse in Continuous Time, is shown below, before we take the limit $\hat{x}(t)=\frac{lim}{\Delta\rightarrow0}\sum^{\infty}_{-\infty}x(k\Delta)\delta_\Delta(t-k\Delta)\Delta$ <-- why is there a final $\Delta$ multiplying the $\delta_\Delta(t-k\Del... | https://dsp.stackexchange.com/questions/16410/why-the-delta-at-the-end-of-the-approximation |
Question: <p>We are currently learning about convolution in my signals and systems class, and one of our textbook problems is to compute the convolution of $x(t) = e^{-\alpha t} u(t)$ and $y(t) = e^{-\beta t} u(t)$. After working out the integral, I obtained the following result</p>
<p>$$
x(t) * h(t) = \frac{e^{-\alph... | https://dsp.stackexchange.com/questions/28671/unit-step-function-present-in-convolution-result |
Question: <p>\begin{align}
x(n)&=\left(-1\right)^n u(n)\\
h(n)&= u(n-1)+u(n-2)\\
y(n)&= x(n)*h(n)\\
y(n)&= \sum_{k=-\infty}^\infty \left(-1\right)^k u(k)\left[u(n-k-1)+u(n-k-2)\right]
\end{align}
Graphically it looks like the output is $u(n-1)$ but I can't do the math to get it into the closed form. </... | https://dsp.stackexchange.com/questions/28831/does-the-output-of-this-system-have-a-closed-form-expression |
Question: <p>I would like to know why the convolution is necessary.</p>
<p>that is, who said that multiplying numbers with others and then adding them would tell us something?</p>
<p>If you could give me analogies without mathematics, it would be a great help for non-mathematicians.</p>
Answer: <p>I'm somewhat in th... | https://dsp.stackexchange.com/questions/62233/what-does-the-convolution-mean-what-is-the-convolution-philosophy |
Question: <p>In the book Applied Digital Signal Processing by Manolakis and Ingle, page 45, section 2.5.1 "Properties of convolution", the author says:</p>
<p>"If we consider a system with impulse response <span class="math-container">$h[n] = \delta[n]$</span>, direct substitution into the convolution fo... | https://dsp.stackexchange.com/questions/96007/why-is-only-the-term-for-k-n-is-nonzero-relevant |
Question: <p>I am implementation a convolution reverb method for audios array in Python using <code>scipy.signal.convolve</code>. I choose the fft mode, which essentially a product of the rfft of the two signals then ifft back.</p>
<p>What I am not sure is how to perform the convolution without changing the amplitude o... | https://dsp.stackexchange.com/questions/68748/convolution-for-audio-how-to-control-amplitude |
Question: <p>I need to identify a matched filter, and so have gone through the mathematics to do this as listed here <a href="https://en.wikipedia.org/wiki/Matched_filter" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Matched_filter</a> which derives the optimal filter <span class="math-container">$h$</span> ... | https://dsp.stackexchange.com/questions/68876/matched-filter-do-i-need-to-know-the-signal-i-am-trying-to-find |
Question: <p>I need to improve my model of Convolutional Neural Network (CNN). The goal is to recognize facial expression.
I've been using some strategies like dropout for regularization and Adam optimazer, but i can get a good accuracy. Therefore I'm trying to implement PCA.</p>
<p>I use to filters for convolution, ma... | https://dsp.stackexchange.com/questions/69130/pca-with-cnn-tensorflow |
Question: <p>I need help with understanding a proof from a paper. Following is the description:</p>
<blockquote>
<p>Let</p>
<p><span class="math-container">$$r_{1}(t) = \int \int h_{1}\left(\tau, \nu\right) e^{j 2\pi \nu (t - \tau)} s\left(t - \tau\right) d\tau d\nu$$</span></p>
<p><span class="math-container">$$r(t) =... | https://dsp.stackexchange.com/questions/69561/twisted-convolution-simplifying-multiple-integral-via-substitution |
Question: <p>Let's say I have 2 sequences a and b in the time domain. Both are length N. A and B are the DFT of a and b. If I do a circular convolution of A and B in freq domain (A o B), then the IDFT of the result will be a x b in the time domain. Correct?
Now what happens if I do linear convolution of A and B in the ... | https://dsp.stackexchange.com/questions/71142/linear-convolution-in-the-dft-domain |
Question: <p>Hi I'm trying to solve the problem when studying for an upcoming test. The given solution is <span class="math-container">$$y[n]= \frac{1}{b-a}(b^{n+1}-a^{n+1}) \quad \text{for } n\ge0 \ .$$</span> However, I'm not sure how to reach this point. We have to also verify using the z-transform. Any help would b... | https://dsp.stackexchange.com/questions/71154/finding-the-convolution-an-un-with-bn-un |
Question: <p>I have two datasets <span class="math-container">$X_1$</span> and <span class="math-container">$X_2$</span> in a sparse wavelet basis, and I have two filters <span class="math-container">$f_1$</span> and <span class="math-container">$f_2$</span>. I’d like to compute the inner product of the convolutions <s... | https://dsp.stackexchange.com/questions/71735/how-to-compute-inner-product-of-wavelet-transform-convoluted-with-signal |
Question: <p>In my systems and signals course I had been asked a question about finding the convolution of two sets.
I was given:</p>
<p><span class="math-container">\begin{align}
x[n] &= \{3,2,1\}\\
h[n] &= \{1,-2,3\}\\
\text{Find}\quad y[n] & = x[n]\star h[n]
\end{align}</span></p>
<p>I have no idea o... | https://dsp.stackexchange.com/questions/72626/convolution-of-two-sets |
Question: <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://dsp.stackexchange.com/questions/6199/convolution-and-dtft">Convolution and DTFT</a> </p>
</blockquote>
<p>$x_1(n)=x_2(n)=1$<br>
where $0 ≤ n ≤ N-1$</p>
<p>1)The linear convolution of the signal gives a triangle how you write it... | https://dsp.stackexchange.com/questions/6211/covolution-of-dtft |
Question: <p>I am trying to implement Wavelet transform in an embedded environment. The problem I face goes like this:</p>
<ol>
<li><p>Two vectors, A and B. A is input samples. B is vector co-efficients.</p></li>
<li><p>I take convolution of A and B, call it C.</p></li>
<li><p>Now I go back to B and up-sample the co-e... | https://dsp.stackexchange.com/questions/8389/reconstruction-from-convolution |
Question: <p>I am quite familiar with signal processing using Matlab. Now I am working in its open source alternative 'Scilab.' In Matlab, cconv() function is used to perform circular convolution between two sequences. I want to do circular convolution in Scilab. But I could not find an equivalent function for circular... | https://dsp.stackexchange.com/questions/10029/circular-convolution-in-scilab |
Question: <p>I am trying to further reduce the following expression (if there's a nicer way to write it):</p>
<p>$\sum_{k=-\infty}^{+\infty}\sum_{p=-\infty}^{+\infty} \sum_{l=-\infty}^{+\infty} w(k) \varphi_\mathrm{y}(l-p)\varphi_\mathrm{x}(k-n-l+p)$</p>
<p>where $\varphi_\mathrm{y}$ and $\varphi_\mathrm{x}$ are the ... | https://dsp.stackexchange.com/questions/10684/simplification-of-a-convolution-like-expression |
Question: <p>I am trying to implement a Savitzky-Golay filter by following <a href="https://en.wikipedia.org/wiki/Savitzky%E2%80%93Golay_smoothing_filter" rel="nofollow">this Wikipedia</a> page and in the first instance I have written the following Octave software code to create the convolution coefficients</p>
<pre><... | https://dsp.stackexchange.com/questions/10698/savitzky-golay-filter-coefficients-and-wikipedia |
Question: <p>Question 3.1 d from Chapter 3 of Oppenheim's Signals & Systems
I have </p>
<p>$$x[n]=(-1)^n{u[-n]-u[-n-8]}$$
$$h[n]=u[n]-u[n-8]$$</p>
<p>and the question asks for $y[n]$ which is the convolution of $x[n]$ and $h[n]$ namely </p>
<p>$$y[n]=x[n]\star h[n]$$</p>
<p>I'm stuck with the limits on the sum ... | https://dsp.stackexchange.com/questions/12690/convolving-time-reversed-discrete-input-with-time-reversed-discrete-impulse-resp |
Question: <p>Can you please explain or point the right way to think about how to implement two sound effects in a .wav file.</p>
<p>So I read a .wav file and converted it to int values (in <code>numpy</code> array) </p>
<pre><code>array([59383, 58290, 60629, ..., 52606, 51982, 56274], dtype=uint16)
</code></pre>
<p>... | https://dsp.stackexchange.com/questions/14514/how-do-i-combine-a-copy-of-a-signal-with-the-original-to-achieve-a-chorus-effect |
Question: <p>PROBLEM</p>
<p>Two real, causal time series</p>
<p>$$f_k = a^k \quad \text{and} \quad g_k = b^k$$</p>
<p>where $a \neq b$, $|a| < 1$, and $|b| < 1$, are given for $k = 0,1,2,...$</p>
<p>Find the linear convolution $h_n$ of the time series $f_k$ and $g_k$.</p>
<p>ATTEMPTED SOLUTION</p>
<p>I thin... | https://dsp.stackexchange.com/questions/16414/finding-linear-convolution-of-two-time-series |
Question: <p>I came across this below question, (which was a homework assignment question for Signal Processing class, which my friend mailed me for help solving), mulled over it for an hour and had no idea how to proceed with solving it. </p>
<p>Let $C(x) = A(x)B(x)$ where:</p>
<p>$$A(x)=\sum_{n=0}^{N_1}a(n)x^n$$ ... | https://dsp.stackexchange.com/questions/18136/how-to-derive-the-answer-to-this-convolution-problem |
Question: <p>can anyone please help me with finding Convolution for following problem .....</p>
<p>1) $h(n) = \delta[\sin(1 + |n|)]\quad \text{and}\quad x(n) = \sin(n^2)$</p>
<p>2) $h(n) = \delta[\sin(2\pi n/N)] \quad \text{and}\quad x(n) = n^2$ where $N$ is odd.</p>
Answer: <p><strong>HINT:</strong></p>
<p>I assum... | https://dsp.stackexchange.com/questions/18408/convolution-of-hn-xn |
Question: <p>In <a href="http://en.wikipedia.org/wiki/Overlap%E2%80%93add_method" rel="nofollow">overlap add method for convolution</a> a filter $x$ of length $M$ will get convolved with a signal $y$ of length $N$ where $M << N$, i.e., $z = x * y $.</p>
<p>Here the signal $y$ is sliced into subparts each of leng... | https://dsp.stackexchange.com/questions/19591/implementing-overlap-add-method-for-convolution-with-a-slice-of-the-filter |
Question: <p>How do we define convolution of: $$x(t)= \mathrm{sinc}(W t)$$ and $$y(t)= -j\mathrm{sinc}(2W t)$$ </p>
<p><strong>Answer:</strong> In the frequency domain, both of them are rectangular functions and multiplication of them is equal to the rectangular signal with smaller bandwidth i.e $x(t)$, which means co... | https://dsp.stackexchange.com/questions/19890/convolution-of-a-real-and-complex-signal |
Question: <p>I do not specialize in signal processing so I wonder if there is any references to the following procedure.</p>
<p>Let $[n]=\{0,1,\ldots,n\}$.</p>
<p>Consider the function $f:[n] \to \mathbb{R}$ and $g:[kr] \to \mathbb{R}$, such that $\operatorname{supp} g = \{0,r,2r,3r,\ldots,kr\}$. Assume for simplicit... | https://dsp.stackexchange.com/questions/23189/convolution-of-one-signal-with-an-evenly-spaced-signal |
Question: <p>Say we have a function of time ($S(t)$) of the length $T$, and then a customized impulse response (say $I(t)$) of the length $T+N$. The question is, when $S(t)$ is convolved with $I(t$), what are the possible frequency domain (or alternately time domain) representation of all of the possible resulting func... | https://dsp.stackexchange.com/questions/26379/limits-of-convolution |
Question: <p>Some textbooks like (Numerical recipes the art of scientific computing) derive the DFT as a Riemann sum of the CTFT. With this in mind it would be natural then to approximate the identity $$y(t)=x*h=\mathcal{F}^{-1}\big\{XH\big\}$$</p>
<p>with the mathlab code y=ifft(fft(x).*fft(h)) which roughly means th... | https://dsp.stackexchange.com/questions/26924/approaching-the-response-of-an-rc-circuit-via-y-ifftfftxffth-why-is-this |
Question: <p>I have been trying hardly to check if these equalities are true or false. However, I have not been able to conclude anything. Could you help me, please?</p>
<p>$$y[2n]=h[n]\star x[2n] $$</p>
<p>$$\mathfrak{F}(x[-n])e^{-jp\pi Fm}=\mathfrak{F}(x[-n+m]) $$</p>
Answer: <p>I'll try to get you started.</p>
<... | https://dsp.stackexchange.com/questions/28958/convolution-ft-properties |
Question: <p>I have a 2D image and I convolve it with a 2D kernel image using FFT. So far I was always using symmetric kernels (e.g., Gaussian with stddev_x = stddev_y). As a result, I never bothered thinking whether I have to flip my kernel image or not because it wouldn't have made any difference. However, now I want... | https://dsp.stackexchange.com/questions/29065/do-i-have-to-flip-my-kernel-when-performing-an-fft-based-convolution |
Question: <p>So I think I have my thinking correct on what I'm trying to do, but I just want to make sure I'm not assuming something that isn't true. Below is what I'm currently doing in the time domain.</p>
<p>$r(t)$ is my received signal<br>
$T$ is my period<br>
$MultCurrent = r(n)\cdot r(n-T)$<br>
$MultPrevious = r... | https://dsp.stackexchange.com/questions/29100/concept-check-on-doing-multiply-in-time-with-circular-convolution-in-frequency-d |
Question: <p>I need to calculate the following linear convolution </p>
<p>$$ y[n] = h_1[n] \circledast h_2[n] \circledast h_3[n] \circledast \cdots \circledast h_{k-1}[n] \circledast h_k[n]$$ </p>
<p>where $k$ exceeds $5000$ and the length of each $h_i[n]$ exceeds $100,000$. I tried the method which is based on the ... | https://dsp.stackexchange.com/questions/32445/an-effective-algorithm-for-convolution-of-very-many-long-signals |
Question: <p>Assuming that filtered signal $y(n)$ is given as</p>
<p>$$
y(n)=x(n)\star h(n)=\sum_{m=0}^{2N-1}x(m)h(n-m), \quad n \in[0,1,\ldots, 2N]
$$</p>
<p>where $\star$ is convolution parameter. $x(n)$ is discrete signal of lenght $2N$ and $h(n)$ is filter of the same lenght as $x(n)$. If I want to take for exam... | https://dsp.stackexchange.com/questions/32449/convolution-and-dft-size |
Question: <p>If I have $$x[n] = u[n] - u[n-4]$$ where $u[n]$ is the unit step function, and $$h[n] = e^{-i\frac{\pi}{2}n}$$</p>
<p>does $x[n] * h[n] = 0$? </p>
<p>I tried doing the convolution sum and I got: $1 - i - 1 + i = 0$ and I also just tried plotting points and think I got 0 also, but I'm not sure if I did ei... | https://dsp.stackexchange.com/questions/34195/convolving-complex-exponential-with-box-function-discrete |
Question: <p>We usually talk about "spectral analysis" but some resources (<a href="http://www.sciencedirect.com/science/article/pii/016516849390090W" rel="nofollow">this paper</a> or <a href="http://www.alma.inaf.it/images/Moments.pdf" rel="nofollow">this doc</a>) talk about "spectral line analysis".</p>
<p>Does this... | https://dsp.stackexchange.com/questions/26021/spectral-analysis-vs-spectral-line-analysis |
Question: <p>I am doing the spectral analysis of some antenna recorded signals by computing PSD (logarithmic absolute value of the FFT) and the spectrogram of the signal. The problem is that I get some unexpected spikes in the signal that appear through all the signal, as it can be seen in the next figure:</p>
<p><a h... | https://dsp.stackexchange.com/questions/35593/unexpected-peaks-in-spectral-analysis |
Question: <p>Suppose that I have a sensor that can acquire samples $X[k]$ of the Fourier transform of an unknown signal $Y[t]$. An example is MRI, where the acquired data is in $k-$space. Now suppose that the unknown signal $Y[t]$ is known to be real and non-negative. My question is: is there a principled way to incorp... | https://dsp.stackexchange.com/questions/9220/spectral-analysis-of-positive-signals |
Question: <p>I an interested in spectral analysis of a random signal.</p>
<p>Assume the signal <span class="math-container">$n(t)\sim\mathcal{N}(0,\sigma^2)$</span> is followed by the white Gaussian noise with zero mean and <span class="math-container">$\sigma^2$</span> variance.</p>
<p>The test signal is <span class... | https://dsp.stackexchange.com/questions/56226/chi-squared-distribution-variable-spectral-analysis |
Question: <p>First-time questioner...</p>
<p>I'm writing an application (hobby/non-commercial, asp.net c#) to process polling data (answers to a single yes/no question) automatically collected from a website. The answers accumulate (yes = +1, no = -1) in a running total that ticks upwards and downwards over time. The ... | https://dsp.stackexchange.com/questions/66314/spectral-analysis-on-polling-data |
Question: <p>I have two signals <span class="math-container">$x_1(t)$</span> and <span class="math-container">$x_2(t)$</span> both with a baseband bandwidth of <span class="math-container">$W$</span> Hz. <span class="math-container">$x_1(t)$</span> is transmitted over carrier frequency <span class="math-container">$f_1... | https://dsp.stackexchange.com/questions/85115/power-spectral-analysis-in-baseband-vs-bandpass |
Question: <p>I intend to perform spectral analysis with <code>R stat:spectrum</code> and then plot power spectrum.</p>
<p>My code is listed here:</p>
<pre><code> t <- seq(0,1024,by=0.1)
x <- cos(2*pi*t) + 0.75*sin(2*pi*4*t) + 2*sin(2*pi*6*t)
x.spec <- spectrum(x,log="no",span=5,plot=FALSE)
del <- 0... | https://dsp.stackexchange.com/questions/47271/how-to-use-function-spectrum-in-r-to-perform-spectral-analysis |
Question: <p>I'm currently doing an investigation where I am attempting to resonant frequencies of an Alto Saxophone at various different notes. I have taken audio recordings of the notes with a sample rate of $44100\textrm{ Hz}$, and exported them into CSV files. Now, I am attempting to analyze this data using the sig... | https://dsp.stackexchange.com/questions/35224/most-appropriate-spectral-analysis-method-for-a-recording-of-a-saxophone-note |
Question: <p>Say I have a signal of length <code>20s</code> that contains signal from various (unknown) biological sources, e.g. heartbeat (~0.2Hz), respiration (~1Hz), and possibly som very-low frequency oscillations (~0.05Hz). My sampling frequency is <code>fs=10Hz</code>. I conduct a periodogram PSD estimate (hannin... | https://dsp.stackexchange.com/questions/76662/minimum-discernible-frequency-in-power-spectral-analysis |
Question: <p>Im doing some beginners spectral analysis for a homemade reactive RGB LED project and was thinking of ways to improve the accuracy of the audio analysis. Im using a Playstation eye with a Raspberry Pi Zero W (limited performance) and ive read several articles to try to better my understanding. According to... | https://dsp.stackexchange.com/questions/54487/will-noise-cancellation-with-playstation-eye-improve-my-spectral-analysis |
Question: <p>What are the Pros and Cons of using Wigner-Ville Distribution for spectral analysis of a signal vs taking the STFT. When is it appropriate to use one over the other and is WVD used in real-time implementations?</p>
<p><strong>Update:</strong> Since no answers were received for the first few days of this po... | https://dsp.stackexchange.com/questions/86211/wigner-ville-distribution-wvd-vs-stft-for-spectral-analysis |
Question: <p>Is there any reason to choose a biased autocovariance sequence estimate over an unbiased estimate for power spectral density analysis? Why would we want to introduce bias into our estimate of the power spectral density?</p>
Answer: <p><strong>TL;DR</strong>
While bias does decrease resolution in spectral ... | https://dsp.stackexchange.com/questions/95335/which-sample-autocovariance-sequence-estimate-should-i-use-for-spectral-analysis |
Question: <p>I am having trouble with all of the forums that I have looked at thus far.
I have one day's worth of Sonic Anemometer data. I want to see the spectral analysis of this data. When the anemometer data was being logged it appears that the frequency ranges between 31 and 32 hz. I am looking to analyze this dat... | https://dsp.stackexchange.com/questions/23900/how-do-i-perform-spectral-analysis-fft-windowing-detrending-on-sonic-anemome |
Question: <p>I have been reading about non-linear non-stationary signal analysis methods and it seems to do this type of analysis the go-to method is the Empirical Mode Decomposition (EMD), then Hilbert Transform (HT) to get instantaneous phase and frequency.</p>
<p>However I have been doing some analysis on a non-lin... | https://dsp.stackexchange.com/questions/59797/non-linear-non-stationary-spectral-analysis-methods-when-and-where |
Question: <p>So it's widely known that the Cross Correlation of 2 signals helps us in figuring out the time delay in those signals by analyzing the peak of the correlation coefficient in the time domain.</p>
<p>For something I am working on, due to a short baseline in comparison to the wavelength of the signal in betw... | https://dsp.stackexchange.com/questions/68308/spectral-analysis-of-a-cross-correlation-function |
Question: <p>I'm trying to create spectral plots similar to one below (it's from the <a href="https://www.analog.com/media/en/technical-documentation/data-sheets/AD1896.pdf" rel="nofollow noreferrer">datasheet</a> of an AD1986 sample rate converter, page 8):</p>
<p><a href="https://i.sstatic.net/3Zoev.png" rel="nofollo... | https://dsp.stackexchange.com/questions/73360/spectral-analysis-with-high-selectivity-but-low-number-of-points |
Question: <p>I was tasked with comparing my own PSA algorithm's results with those of a different lab. The data which is being analyzed is NREM epochs of a sleep EEG. The match I have obtained is, to my eyes, very decent in terms of the overall trend.</p>
<p>PSA is calculated as follows: divide each <span class="math-c... | https://dsp.stackexchange.com/questions/96123/how-precisely-can-power-spectral-analysis-be-replicated |
Question: <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... | https://dsp.stackexchange.com/questions/86297/comparison-of-wvd-vs-stft-spectral-analysis-in-the-presence-of-noise |
Question: <p>I use a PC to record time series of some physical property. The problem is that, for some reason, I did not record the time series as a whole, rather I record first segment, then second, third, etc. Each segment is 500,000 points, representing ~30 min. However, they are not strictly consecutive: between ea... | https://dsp.stackexchange.com/questions/22930/spectral-analysis-of-a-time-series-with-missing-data-points |
Question: <p>I have two signals</p>
<pre><code>>> t = linspace(0, 10, 10000); % 0 to 10 seconds
>> u1 = 30*sin(2*pi*5*t); % Sine signal 1
>> u2 = 10*sin(2*pi*90*t); % Sine signal 2
>> u = u1 + u2; % Combine
>> spa(u, t); % Spectral analysis
>> grid on
</code></pre>
<p>And the spectra... | https://dsp.stackexchange.com/questions/84469/amplitude-ratio-is-larger-than-0-5-on-a-rc-filter-if-rc-1-7684e-03 |
Question: <p>I intended to use a discrete Fourier transform (DFT) on a time series sampled at uneven intervals. What I did was to calculate a DFT matrix where the elements are the values at the uneven locations like this</p>
<p><span class="math-container">$$
{\displaystyle {\begin{aligned}X_{k}&= \frac{1}{\sqrt{N}... | https://dsp.stackexchange.com/questions/54569/fourier-like-spectral-analysis-with-uneven-intervals-and-redesigned-dft-matrix |
Question: <p>I have a signal processing chain which goes:</p>
<ul>
<li>
<ol>
<li>Every 256 samples, take 512 samples of input buffer</li>
</ol>
</li>
<li>
<ol start="2">
<li>Apply a Hann window to the samples</li>
</ol>
</li>
<li>
<ol start="3">
<li>Copy the windowed samples into the real components of a complex array<... | https://dsp.stackexchange.com/questions/88402/stft-frequency-domain-processing-destroys-window-shape-makes-synthesis-glitchy |
Question: <p>Many books in signal processing, e.g. Papoulis [1], define power spectral density (PSD) as:</p>
<p>$$S(\omega)=\sum_{k=-\infty}^{\infty}R_{xx}(k)e^{-j\omega k}$$</p>
<p>Which is the fourier transform of the correlation function:
$$R_{xx}(\tau)=E[x(t)x(t-\tau)]$$</p>
<p>However, some authors in the cont... | https://dsp.stackexchange.com/questions/43155/clarification-concerning-power-spectral-density |
Question: <p>I am performing spectral analysis of a finite length signal that saturates to a non-zero value. The signal (<span class="math-container">$s(t)$</span>) can, practically, be write as
<span class="math-container">$s(t) = f(t) \big(1-H(t-t_0)\big) $</span>, where <span class="math-container">$t_0$</span> is t... | https://dsp.stackexchange.com/questions/72120/discrete-fourier-transform-of-a-finite-length-signal-which-saturates-at-non-zero |
Question: <p>I am studying the seismo-ionospheric anomalies associated with the Japan earthquake using total electron content derived from a GPS signal. I am trying to detect acoustic-gravity waves in the signal caused by the earthquake if possible.</p>
<p>I am trying to perform spectral analysis for this task using ma... | https://dsp.stackexchange.com/questions/93411/need-help-understanding-fft-for-timeseries-analysis |
Question: <p>My inquiry is regarding the so called <a href="https://en.wikipedia.org/wiki/Cepstrum" rel="nofollow noreferrer">cepstrum</a> analysis.</p>
<p>By conducting some experiments, i have real time data at my disposal. The acquisition rate is 1600Hz.</p>
<p>I wanted to try cepstrum analysis just out of curiosi... | https://dsp.stackexchange.com/questions/38837/cepstrum-analysis-cut-off-frequencies-displayed |
Question: <p>In nonparametric spectral estimation method what is meant by biased and unbiased Autocovariance sequence estimate and why most commonly biased one is used?
I have the answer to the second question from Peter Stoica (SPECTRAL ANALYSIS OF SIGNALS)but not getting what he wants to say. </p>
Answer: <p>In s... | https://dsp.stackexchange.com/questions/48407/what-is-meant-by-biased-and-unbiased-autocovariance-sequence-estimate |
Question: <p>I am a scientist at Indian Space Research Organization (ISRO) and will be representing my team. We work on Telemetry and Data Handling units for our Launch Vehicles.</p>
<p>We are preparing for our upcoming SSLV Launch (Small Satellite Launch Vehicle) and need some information to confirm if we are at par w... | https://dsp.stackexchange.com/questions/74666/indian-space-research-organization-extent-of-spectral-spread-1-3rd-octave-anal |
Question: <p>The discrete cosine transform(DCT) is a popular choice for spectral analysis in audio, video, image compression algorithms. This is primarily due its efficient "spectral compaction" property in comparison with Fast Fourier Transform(FFT). Is there a way to measure approximate "spectral compa... | https://dsp.stackexchange.com/questions/87162/dct-measures-of-energy-compaction-gain-achieved-using-dct-over-fft |
Question: <p>Whats a good rigorous grad level textbook on DSP focused on audio/spectral analysis? Coming from a half proof based half applied math/physics background; have done several research projects where I worked with spectra and did audio analysis but never really understood all the details I always see in posts ... | https://dsp.stackexchange.com/questions/95762/whats-a-good-grad-level-audio-dsp-textbook |
Question: <p>This is a general question on multitaper spectral analysis of signals and stationarity</p>
<p>I work with time series which are non stationary. In this regard I have two questions</p>
<ol>
<li><p>Is weak sense stationarity of second order sufficient to apply multitaper spectrum to compute valid estimates... | https://dsp.stackexchange.com/questions/19559/weak-sense-stationarity-sufficient-for-multitaper-spectrum-analysis |
Question: <p>I am reading an elementary book on signal processing - "<a href="https://books.google.co.in/books/about/Signals_Systems.html?id=LwQqAQAAMAAJ&redir_esc=y" rel="nofollow noreferrer">Signals and Systems</a>".</p>
<p>It never struck until recently, the math involving signal processing seemingly h... | https://dsp.stackexchange.com/questions/91794/what-math-should-i-study-to-really-understand-signal-processing |
Question: <p>What is meant by "spectral whitening" in DSP?</p>
<p>What effect does spectral whitening have when used in image processing? (visually or otherwise...)</p>
<p>Where might spectral whitening be useful in audio processing or analysis? What would a spectrally whitened audio signal sound like?</p>
Answer:... | https://dsp.stackexchange.com/questions/10183/what-is-spectral-whitening |
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 |
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