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Questions tagged [convolution]

Convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions.

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Mathematics behind bandwidth of product of two signals

I'm just starting to learn about signal processing and I've seen these two posts: 1.What is the bandwidth of product of two signals? 2.Convolution in frequency domain, what is the output bandwidth ...
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Circular Convolution Matrix of $ {H}^{H} {H} $

We all know that Discrete Fourier Transform (DFT) corresponds to circular (not linear) convolution. That is to say, if $x(n),h(n)$ and $y(n)$ is the original signal, the filter and output signal in ...
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Contradiction while using the convolution sum for a non-LTI system

In a recent quiz, we were given the following problem: The cascaded LTI systems $\mathcal{T}_1$ and $\mathcal{T}_2$ respectively have impulse responses $h_1[n]=\delta[n+3]$ and $h_2[n]=\delta[5−n]$....
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Reading a Wav File

I need to read two .wav files. One of them is a song, and the other one is impulse response. Then, I have to convolve them. In fact, I have read them by using ...
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Why can convolution only be applied to compute the output of a linear filter?

We apparently cannot compute the output of a bilateral filter (BF) using convolution (with the image) because the BF is a non-linear filter. In general, why can convolution only be applied to compute ...
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Interpreting results of multiplying signal and wavelets in the frequency domain

I have followed a lot of stuff on mike cohens website and have managed to make a filterbank of Morlet wavelets and convolve with an incoming block of samples. This of course is a computationally heave ...
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Why isn't bilateral filtering shift-invariant?

I have a source (that I can't share) that states that bilateral filtering isn't shift-invariant (that is, it depends on the input signal), hence we cannot use convolution and the Fourier convolution ...
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55 views

Convolution of Two Impulse Signals

I have encountered convolution of two different impulse signals. ...
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82 views

How Much Zero Padding Do We Need to Perform Filtering in the Fourier Domain?

Consider an $M\times N$ image $f$ and an $G \times K$ filter $h$. Given that convolution in the spatial domain corresponds to multiplication in the Fourier domain, then we can perform a convolution of ...
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Graphical DT Convolution

Attached is the question 1 part B, solution and my attempt. My attempt seems to be not correct. can someone comment?
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Can anyone please describe the relation between linear convolution and circular convolution? [duplicate]

It would be great if anyone could help. I am not able to find any relation amongst them, to me they are different things altogether.
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MATLAB - How do I get the Filter Function to get the output Energy Spectrum?

The image was from a question I posted on reddit, so ignore the title. I'm trying to write a program that plots these graphs I know that the first plot is just a plot of the source-signal so the "...
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1answer
56 views

Why Does 2D FFT of Gaussian Looks More Sharper than Gaussian Itself?

I am trying to understand why 2D FFT is done on a Gaussian process in a particular code. From my understanding from these posts: https://www.researchgate.net/post/...
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1answer
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What is the Fastest Way Ever to Do 2D Correlation?

Here is what i gathered so far: Any sliding window classification, image filtering or similar can be fastly done by a FFT (flip the signal and do convolution). Also, if the template/filter kernel is ...
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Wavelet Transform Implementation Method

I have been watching the wonderful youtube videos here: https://www.youtube.com/watch?v=4TTpwIZrUAo&list=PLn0OLiymPak2G__qvavn3T8k7R8ssKxVr&index=3 detailing morlet wavelets and fit ...
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1answer
50 views

Discrete Time Fourier Analysis

Suppose we're given the following: $ x[n] = 2 + (-1)^n $, and are given the impulse response $ h[n] = u[n] a^n $, of an LTI system where $ |a| < 1$. We're asked to find the output $y[n]$, if $x[n]$...
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Discrete Time Convolution Example

How did we get this final answer in example in fig attached. I understand that delta(n) is a DT unit impulse where it is 1 at n = 0 and zero elsewhere. I understand that u[n] is a unit-step where it ...
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HRIR and DT Convolution

You have an experimentally-measured HRIR and an audio signal. And you wish to implement filtering using scientific libraries in Python such as numpy, scipy and matplotlib(for plotting) Question A) ...
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What is the betwwen [i,j] and [u,v] in explinations of correlation and convolution (picture attached)?

I don't know how to write 'summation' symbol here hence posting the picture. Can someone explain to me the difference between i,j and u,v in this explanation of correlation and convolution? I know ...
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NLMS algorithm for a MISO structure

I am trying to implement an NLMS algorithm for a multi-input single-output(MISO) structure. We take a reference signal x, then we made a new set of P input signals from it as follows: x_op (k) = x(k)...
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How to find Fourier series coeffecients of convolution of two periodic continuous functions with different time periods?

Above given is my solution Plz check if it is correct and I got struck at last step .Plz help
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1answer
34 views

Confusion in the derivation of convolution formula [closed]

$$x(t)=\int_{-\infty}^{\infty}x(\tau)\delta(\tau-t)d\tau=\int_{-\infty}^{\infty}x(\tau)\delta(t-\tau)d\tau$$ Due to linearity, $$y(t)=T\{x(t)\}=\int_{-\infty}^{\infty}x(\tau)T\{\delta(\tau-t)\}d\tau=\...
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GCC-PHAT (Generalized cross correlation) always peak at delay=0 on real audio signal

I have studied the GCC-PHAT algorithm to estimate TDOA on audio signals at 2 mics. Here is my MATLAB implementation: ...
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For complex values, why use complex conjugate in convolution?

Taken from Adaptive Filter Theory (2014) written by Haykin page 110 : $$y(n) = \sum_{k=0}^{\infty} w_k^*u(n-k), \quad n=0,1,2,...$$ where $u$ and $w$ are complex values. My question is why use ...
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68 views

Support of the convolution of two rectangular signals

I'm trying to convolve two rectangular signals in the frequency domain $$H_1(\omega) = u[\omega +.2\pi] - u[\omega -.2\pi]$$ and $$H_2(\omega) = u[\omega +.1\pi] - u[\omega -.1\pi]$$ My result is a ...
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How to implement freq convolution layer?

I am referring the paper https://pdfs.semanticscholar.org/31c7/4962122ba5fe1c469101b5bc2ae6d88c9c18.pdf. In the paper, for CLDNN network first layer is freq convolution. How to implement the same for ...
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Deconvolution of Synthetic 1D Signals - How To?

I convolved a square wave with a Gaussian wave using linear convolution. Can I get the original square wave back by deconvolving my output with the Gaussian function? I took the FFT of both signals, ...
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34 views

Wide-Band Lorentzian FDTD Algorithm

I want to convert a simulated gain/absorption of a material, which can be understood as a discreet (dispersive?) function $g_i(f_i)$ ($f$ is for frequency) or $g_i(\lambda_i)$, into $\tilde g(t)$ for ...
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Convolution in the Hartley Domain

The convolution Theorem of the Hartley Transform is given by $$ Y_{Ha}(k) = X_{Ha}(k)H_{Ha}^{e}(k) + X_{Ha}(-k)H_{Ha}^{o}(k) $$ where, $$ H_{Ha}^{e}(k) = \frac{H_{Ha}(k) + H_{Ha}(-k)}{2} $$ $$ H_{...
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Cannot figure out the convolution operation in this problem

A linear system S has the relationship $y[n]=\sum_k {x[k]*g[n-2k]}$, k ranging from $-\infty$ to $\infty$, between its input $x[n]$ and output $y[n]$, $g[n]=u[n]-u[n-4]$. Determine $y[n]$ when $x[n]=...
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Applying a filter on an input sequence in matlab

Given a input sequence $x = {x_1, ... x_n}$ and a filter with l elements $h = [h_1, ..., h_l]$ with l < n. We want to filter the input sequence with the specified filter. My first thought was to ...
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Resources for learning Sound Processing [closed]

Does anyone know of any resources that explain simply, these are the data objects and variable definitions involved when doing sound processing? I took a class on image processing where we learned ...
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58 views

Why convolution in time and frequency domain are not equal?

I was writing this Jupyter Notebook. Then, I unexpectedly faced two visually similar output, but their numerical results were very different. This is the code I used for convolution in the time ...
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2answers
63 views

Convolution of real with complex signal

Let $x[n]$ be real signal and $y[n]=\exp(j3\pi n)$ be a complex signal Would the convolution between those two signals be $$x[n] * \Re(y[n]) + jx[n]*\Im(y[n])$$?
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How to find the impulse response of filter that outputs the autocorrelation of the input?

I am trying to solve question 9.61 in the attached image. I guess, by evaluating the autocorrelation for a specific instance, say $ t = 0 $ , that the impulse response, $h(t)$, should be : $$ h (t)...
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Convolution of signals sampled on a logarithmic grid

Is there a practical accelerated algorithm or a theoretical discrete (Fourier) transform based method to convolve discrete-time signals sampled on a logarithmic grid? What I mean is representing a ...
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1answer
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How to increase the sharpness of the image using convolution matrix?

I am using 3 X 3 convolution matrix to obtain an sharpness image. But the output result obtain from the above matrix is not much sharpen image. How to increase the sharpness of the image ? Ya i am ...
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27 views

Convolution with rectangular function

I have a system $h(t)=4e^{-4(t-4)}u(t-4)$ and I want to response of the system to $x(t)=rect(2(t+4))$. I have followed those steps: $y(t)=x(t){*}h(t)$ $=rect(2(t+4)){*}4e^{-4(t-4)}u(t-4)$ $=4[u(t)-...
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2answers
61 views

How does an LTI system produce multiple values from a unit impulse

I understand that in a discreet system, an impulse is 1 at the origin point and 0 everywhere else. I've seen many examples showing the impulse response of an LTI system to be many points, have many ...
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1answer
55 views

Explain the formula of convolution and convolution theorem

As stated in the title, I have two questions Why convolution is defined as $(f*g)(x) = \int_{-\infty}^\infty f(t) g(x - t) dt$ instead of just $\int_{-\infty}^\infty f(t) g(x + t) dt$ ? Why we need ...
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Noising audio in MFCC space

I am training up an audio recognition neural network using MFCCs. Its been shown to be very beneficial to artifically add noising and reverb of the original audio when training a neural network (Data ...
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1answer
72 views

Upsampling signal using convolution-based interpolation filters

I am currently reading this paper which discusses several image interpolation methods, such as nearest neighbor and linear interpolation, using convolution filters. I first want to do this in 1D with ...
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1answer
96 views

Image Processing/ Computer Vision: How is separability of filters implemented?

I am trying to convince myself that a separable 2D filter can be implemented via two 1D filters. So, I took the example of following Sobel filter: $1/8\begin{bmatrix}-1&0&1\\-2&0&2\\-...
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1answer
53 views

Circular convolution of a non causal signal

I know how we compute the $N$ point circular convolution of a two causal signals, but what about a signal such as $\{1,-1,2,1\}$ where, the position of 2 is the $0^{th}$ index and the other sequence ...
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1answer
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The proof of the dual convolution/multiplication properties? [closed]

I've been trying to find a rigorous proof of the dual convolution / multiplication, but I found nothing, can you give me a hand with this? \begin{align} f(t) * g(t) &\overset{\mathcal F}{\iff} F(...
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Inverse z-transform of a modulus square

Suppose we have the z-transform of $x[n]$ is $X(z)$ and that of $y[n]$ is $Y(z)$. Then we know that the inverse z-transform of $G(z)=X(z)Y(z)$ is $g[n]=x[n]*y[n]$, where $*$ is convolution. What will ...
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47 views

Why using the impulse respond of an LTI to characterize its output?

We all know that every LTI, is defined by its transfer function, so we can determine the output of any system, (using common transforms). It is also known that we can determine the output of any LTI ...
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1answer
33 views

Inverse DFT in terms of original signals for product of two DFTs

Given $x[n]$ and $h[n]$ that are zero for $n<0$ and $n>15$, their linear convolution being $y[n]=x[n]*h[n]$ and their discrete time Fourier transforms are $X(e^{j\omega})$ and $H(e^{j\omega})$, ...
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2answers
75 views

How to understand the discrete and continuous convolution in matlab?

For example,I want to calculate the convolution of two continuous signal in matlab as the image shows. Indeed, I chose to discrete the signal to compute in matlab. Obiviously, the 1st and 3rd are ...
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80 views

How do you apply a filter after DFT on an image?

Let's say size of the image is 100 x 100 and the kernel matrix is 5x5. I took the DFT of both the image and the kernel. But how do I multiple these two matrices? And which parts involve in these ...