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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27 views

Plot the sum frequency generation spectrum using convolution MATLAB

I am attempting to calculate the spectrum of a pulse that has undergone sum-frequency generation (in this case it is a gaussian, so it is correct to also say frequency doubling/Second harmonic ...
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What transformation preserves first term and averages the opposite conjugates?

I can't figure not find any reference on what is this transformation (what $X$ represents in relation to $A$). If $A=[a_1+jb_1, a_2+jb_2, a_3+jb_3, ..., a_n+jb_n]$, $X$ is defined as:$$X=\left[j b_1, \...
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Applying Convolution in Frequency Domain by Element Wise Multiplication on Time Domain

I'm studying the power spectrum. Right now, I am making a program to try to make sure that the "Fourier transform of the multiplication of some data and window function" and the "...
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Cumulative Distribution Function of 2-fold convolution

I'm looking for CDF of 2-fold convolution of $X$, with cdf: $F(x) = 0$ if $x < 0$ and $F(x) = 1 - ae^{-bx}$ if $x >= 0$ It looks like exponential, so I try somethings in here https://math....
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Why does convolution reverb work?

I've just begun learning about signal processing on my own, and after reading about convolution I'm curious about why convolution reverb works. That is given a recorded impulse $\hat{f}$ and an audio ...
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Does a FIR filter always perform a convolution operation?

I've come across this question in textbook. I guess it's basically asking are there any input or impulse response conditions that a FIR filter won't be able to compute. I can't think of any.
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Frequency Interpolation of DFT to create Zero-Padded IFFT

As a response to this question I have proposed interpolating new samples in a DFT (meaning the frequency samples of an existing DFT result) sufficient to be the new samples that if we were to take the ...
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51 views

Under which conditions will windowing with a rectangular window intime always lead oscillations in the spectrum?

I'm going through some conceptual questions about windowing signals. I came across the following: Assume a sinusoidal signal - under which conditions will windowing with a rectangular window ...
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Self-Adjoint Filter Doesn't Work

My understanding is that a symmetrical kernel is its own self-adjoint. For example, if we had the following kernel: ...
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42 views

Parameterization of a Idempotent Filter

I'm interested in if there has been research into how to parameterize filters so they are idempotent. I'm looking for the property shown below: $$ h \circledast h = h $$ I searched around and found &...
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Complex Filter (Modelling a Channel ) convolved with complex baseband modulation gives error *Plots inside -Updated*

I have a complex filter that is modelling the channel response, its not symmetrical on 0. The complex filter is convolved with a complex baseband modulation of QPSK. Plot 1 Zoom in on impulse response ...
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Image / Video Upscaling (Super Resolution) Algorithm Explanation (Image and Video Upscaling from Local Self Examples)

So, I'm trying to implement the classical algorithm described in this paper Image and Video Upscaling from Local Self-Examples and this presentation to serve as a baseline for comparison with AI/NN-...
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Computing a convolution using FFT and more than minimum number of samples

Assume vector s is a set of time samples of length 1000. Assume vector h is a set of samples of length 50. If I want to compute the convolution of those vectors, the result will be 1000+50-1 = 1049 ...
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Applying a 2D Convolution Using 2D FFT

So I was following the article Victor Podlozhnyuk (nVidia) - FFT Based 2D Convolution (Page 7). I have expanded the kernel to the correct way they have done it. However when it comes to the part on ...
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75 views

How to calculate signal after passing through the filter?

I have the amplitude response of the LPF (here it is generated in Python): ...
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When FFT fails to perform circular convolution?

I need to know of the applications that circular convolution is needed but FFT can not be used or FFT's convolution property fails.
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Gaussian Blur For Entire Image

I am trying to simulate the blurring process (defocus) of a sinusoidal. For this I have build my own Gaussian filter and performed the convolution in Fourier domain. The result of the blurred signal ...
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Does CNN need training data and validation data?

I am using a simple CNN model, and I want to run a test, input is an image of Bird, the output is either "0" or "1", where "1" means the output is correct, is a bird. Do ...
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82 views

Convolutions in log-scale axis [closed]

Suppose I have two signals $f[x]$ and $g[x]$ defined over a grid of $2N+1$ points ${x}_{i}$, so that the difference $|x_{i+1}-x_{i}|$ between points is logarithmically spaced with base 10. Thus, the ...
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Should i use window with hop_size in Wavelet Transform or Discrete Wavelet Transform?

I have a signal (audio - voice) with 1 second of duration with sample rate of 50000 Hz. It is big signal and I wish extract some features and apply pattern recognition or classification. My question ...
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Biexponential (double exponential) convolution of a function

Summary I am trying to run a convolution on some data that was originally calculated from a deconvolution (so the reverse). However I'm not getting the expected graph. Blue is expected, red is a ...
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37 views

Convolution of a discrete continuous function for reconstruction

From chapter 9 page 198 of https://github.com/t4world/Computer-Graphics/blob/master/Fundamentals-of-Computer-Graphics-Fourth-Edition.pdf I am confused as to what this book's description is saying ...
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How can I use an irrational transfer function to convolve a signal?

I have the irrational transfer function $$H(s)=\mathrm{e}^{-a\sqrt{s}}$$ With the inverse Laplace transform $$ h(t) = \frac{a\,\mathrm{e^{-a^2/(4t)}}}{2\sqrt{\pi}~t^{3/2}} $$ For $a > 0$ How can I ...
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Non-Uniformly Partitioned Convolution Implementation

I've succeded in implementing the uniformly partitioned convolution algorithm and now I'm looking to implement the non-uniformly partitioned version. I've had no luck with running parallel threads on ...
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Multi-thread Audio Processing With C and JACK

I'm currently trying to create a NUPOLS (Non-Uniformly Partitioned OverLap Save) convolution reverb processor using C and JACK. According to the literature I've consulted; this is equivalent to ...
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MATLAB filter and conv Functions

I'm trying to get familiar with MATLAB's filter and conv functions. To start, I created a signal that was 1000 zeroes followed by a 13 sample long Barker code. I then convolved it with the same Barker ...
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64 views

Value of $\sum\limits_{n=-\infty}^{\infty}(x*x)[n]$

If $x[n]=(0.5)^nu[n]$ and $y[n]=(x*x)[n]$ then what is the value of $\sum\limits_{n=-\infty}^{\infty}y[n]$ ? I calculated the $\mathcal{Z}$-transform of $x[n]$ and then applied the accumulation ...
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How to handle zeros before FFT convolution / deconvolution?

I would like to calculate the input function (unknown) by deconvolution of the output and the "system response" signals. The output is a finite signal from a measure device so it presents ...
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1answer
52 views

Expression of the convolved image

I have an image of a 2D-sinusoidal pattern $f(x, y)$ with wavelength $\lambda$ which I would like to convolve with a 2D circular pill-box function $h(x,y)$ of radius $r$. The image is given by $$ f(x,...
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Why do the lengths of the sampled signals $x_1, \: x_2$ have to be $\text{length}(x_1)+\text{length}(x_2)-1$?

We know that convolution in time is equivalent to multiplication in frequency (Fourier). $$x_1(t) \ast x_2(t) \leftrightarrow X_1(\omega)X_2(\omega) \tag1$$ However, for a sampled signal, this ...
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Real Time Partitioned Convolution Not Working

EDIT: Scroll down for actual working code. I'm working on implementing a real-time convolvution reverb JACK client on C and I've been trying to follow a number of sources (including Gardner and Wefers ...
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60 views

Approximating inverse of unstable difference of Gaussians filter

I am trying to invert a difference of Gaussians (DoG) filter. The inverse is not stable and so I am trying to find an approximation applied to a specific input. The DoG filter increases contrast at ...
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64 views

Impacted of a conjugated filter

What is the effect of using a conjugated FIR filter? I have a use case where a weight vector, x, can be estimated using the least squares approximation: $$Ax=b$$ $$ A^HAx = A^Hb$$ $$ x = (A^HA)^{-1} ...
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How to Use Convolution Theorem to Apply a 2D Convolution on an Image

How do I actually apply the convolution theorem? I have my fourier transformed image matrix, and a Fourier transformed kernel, but how do I actually multiply these together to achieve the intended ...
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1answer
75 views

Prove Convolution Property for DFT using duality

If $x_1[n]$ and $x_2[n]$ are finite length sequences of length $N$ $$\mathcal{DFT}(x_1[n] \circledast x_2[n]) = X_1[k]X_2[k]$$ where $X_1[k]$ and $X_2[k]$ are the DFTs of$x_1[n]$ and $x_2[n]$, ...
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Prove Discrete Time Fourier Series Multiplication property

Note: This is not a homework problem. I'm just stalled at a point because I think I might be interpreting the duality property incorrectly. If $x_1[n]$ and $x_2[n]$ are periodic with period N, then if ...
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36 views

What does shift and multiply-accumulate mean in terms of Convolutional Neural Networks?

While reading this paper, I came across the following paragraph - "Our intuition is: the convolution operation consists of shift and multiply-accumulate. We shift in the time dimension by ±1 and ...
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Real time estimation of room impulse response using the sine sweep method

I am working on real time Room Impulse Response estimation using sine sweep. $x(n)$ is my sine sweep signal. $f(n)$ is its amplitude modulated inverse. $beep$ consists of 3 sine sweeps with a delay ...
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How can we find Room Impulse Response in real-time using Sine Sweep Method?

I want to calculate the room impulse response in real-time using sine sweep method. For that, I generated a sine sweep $x$ & its amplitude modulated inverse signal $f$. Then I played that $x$ ...
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On discrete fourier coefficient convolution of indivdual periodic signals with different frequencies

It is a well-known result that when two signals with the same period $T$ get multiplied in the time domain, the resulting signal's Fourier coefficients are given by the discrete convolution of ...
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log(conv) vs conv(log)

Suppose an arbitrary, strictly positive $x[n]$, transformed as $$ x_l[n] = \log(1 + C x[n]) \tag{0} $$ where $C$ is freely chosen. Given the following, where $h[n]$ is a Gaussian lowpass filter (or ...
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Prove that the twisted Convolution of $f$ and $g$ lies in $L^2(C^n)$?

Edit,this is the exact phrasing of my question Let $\lambda\in\mathbb{R^n}$.Prove that $f\star_{\lambda}g\in L^2(\mathbb{C^n})$ for all functions $f$ and $g$ in $L^2(\mathbb{C^n})$.What Happens when $...
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Convolve with a box filter in time domain

To low pass filter a signal, we have to convolve it with a sinc function because it's the same as multiplying the Fourier transform of the signal with a rect function, resulting in the high frequency ...
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How this convolution integral is solved to obtain autocorrelation function of current for shot noise?

I am studying shot noise characteristics from this source: Here the author writes that autocorrelation function is given by: $$R_I(\tau)=\bar{h}*h*R_Z(\tau)$$ where $R_Z(\tau)=q^2(\lambda^2+\lambda \...
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Multiple 1D gaussian filter

Given $$ \begin{cases} &f_0(x)=1 \\ &f_{n+1}(x)= (\varphi*(f\mathbb{I}_{[a_n,b_n]}))(x)=\int_{-\infty}^{+\infty}\varphi(x-t)f_n(t)\mathbb{I}_{[a_n,b_n]}(t)dt = \int_{a_n}^{b_n}\varphi(x-t)f_n(...
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673 views

Generate the Matrix Form of 1D Convolution Kernel

As a follow up to Generate the Matrix Form of 2D Convolution Kernel, could someone explain how to generate the matrix form of a 1D convolution kernel? How different convolutions shapes are handled? ...
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1answer
111 views

Fast computation of a convolution integral with Gaussian kernel

Given a convolution integral with gaussian kernel $$ g(y) =\int_a^b\varphi(y-x)f(x)dx=\int_{-\infty}^{+\infty}\varphi(y-x)f(x)\mathbb{I}_{[a,b]}(x)dx $$ where $\varphi(x)= \frac{1}{\sqrt{2\pi}}\exp{\...
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1answer
60 views

Perform Transposed Convolution in Spectral / Frequency Domain?

I'm doing some experimentation on performing end to end generative modeling in the frequency domain. I've got a working convolutional layer, but do not yet have a Conv2DTranspose equivalent. Please ...
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convolving an LTI with filters

I just started learning signal processing and one of the very first topics I begun with is convolution. I want to learn signal processing practically, therefore I opted to work with circuits(also a ...

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