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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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Step-by-Step calculation of stationary wavelet transform gives shifted results?

Good morning, I am doing an SWT by hand to understand it better, and have a couple of questions. Maybe someone here has experience with this? I am using the book "Conceptual Wavelets" by Fugal, ...
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Find the output for the input $ e^{-t}u(t) $ and impulse response $ \sin 3t u(t) $

Find the convolution between $ e^{-t}u(t) $ and $ \sin 3t u(t) $. I have tried to solve it the following way. Please help me find the correct solution Solution:
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Find the convolution between $ e^{-t} u(t)$ and the gate pulse shown in the figure

Find the convolution between $ e^{-t} u(t)$ and the gate pulse shown in the figure. I have tried to solve it in the following manner. My answer does not match with the one given in the textbook. I am ...
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Find the convolution between $ e^{-t} u(t)$ and $ e^{-2t} u(t-3)$

Find the convolution between $ e^{-t} u(t)$ and $ e^{-2t} u(t-3)$ I have tried to solve it in the following manner. My answer does not match with the one given in the textbook. I am not sure if I am ...
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Zero padding in frequency domain, any tricks to speedup?

there are many situations when one has to carry some operations on spectra, like splitting a spectrum Z wide in two Z/2 spectra, or vice versa merging two Z sized spectra in a 2Z sized one. The only ...
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How to manually implement convolution with FFTs?

I'm trying to manually implement a convolution using FFTs and it isn't working as expected. I know I'm probably missing some subtlety with padding, shifting, or conjugation, (all of which I've tried ...
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convolution expression h(n,k) = h(n-k)

As a new to DSP concepts want to understand the meaning of impulse response and why we do $h(n-k)$ in convolution and $h(n+k)$ in correlation.
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How to perform dechirping of SAR image in MATLAB?

I have the transmitted pulse and the raw SAR image before range compression (dechirping). I understand the pulse compression its a convolution along the columns but I am not able to make it work. I've ...
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Synthetic Aperture Radar (SAR). How to do Range Compression?

I am trying to perform range compression to a raw SAR image [fast times, sensor position], Dr in code. I have the transmitted signal (chirp), g in code, and literature says range compression is ...
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U-nets : how exaclty is upsampling performed

In U-nets I would like a more straight-forward/detailed explanation in how the upsampling part ("right part of the U") is performed. I read that it can be done by "transposed convolution layers" aka....
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Transposed convolutional layer

Can someone define the weights in a transposed conv2D kernel used to perform interpolation (NN or bilinear or whatever)? The idea is to get "convinced" that one can perform upsampling (interpolation) ...
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Variance of zero-mean signal after convolution for SIR computation

my goal is to scale desired, interfering signal at the receiver in order to achieve desired SIR (signal to interference ratio) for beamforming (source separation) application. Let be: $s(t)$ a known ...
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LTI, causal, discrete time system output

Consider a discrete time LTI causal system $S: y = S(u)$, with its impulse response $h:{Z} \rightarrow R:h(n)=3^{n+1}{H(n)}$ with $H$ the Heaviside function. We know the values of input: $$u(0) = 2$$...
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Do $|s(t)|$ and $|S(f)|$ uniquely determine $s(t)$?

Consider a signal $s(t)$. My question is if you know $|s(t)|$ and $|\mathcal{FT}[s(t)](f)| = |S(f)|$ or equivalently $|s(t)|^2$ and $|S(f)|^2$ is it possible to determine $s(t)$? That is, is $s(t)$ ...
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How do I find the convolution of the following signals? [closed]

$h(t)$ is the inputted to convolve the $x(t)$ The signal written in unit step are: $x(t) = (5-t)u(t-3) - (5-t)u(t-5)$ $h(t) = 2u(t-1) - 2u(t-3)$ So to convolve I first change the function to: $h(...
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Formula for PSD across an axis of a 2D output

Consider a 2D stationary input $e(x,y)$ and a 2D real convolution function $h(x,y)$. Let $S=h*e$ be the result of the convolution of $e$ by $h$. If needed, we may assume $e$ is isotropic (spectrum ...
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What does the convolution mean, what is the convolution philosophy [closed]

I would like to know why the convolution is necessary. that is, who said that multiplying numbers with others and then adding them would tell us something? If you could give me analogies without ...
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2D convolution of image with filter as successive 1D convolutions

I want to prove (or more precisely experiment with) the idea that a 2D convoltion as produced by the Matlab conv2() function between an image I (2D matrix) and a kernel (smaller 2D matrix) can be ...
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DFT of a function and array convolution

I saw some questions (and answers) on this subject, but they were all about a specific example and I'm not sure I understood. I'm trying to understand the meaning of computing the DFT of an array ...
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turn circular convolution into linear convolution by zero padding: A special case

We know that, multiplying a kernel and signal spectrum in Fourier domain will lead to a circular convolution and not a linear convolution, so in order to it become linear convolution we must zero pad ...
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How do impulse response guitar amp simulators work?

I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample. I tried to ...
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Deriving the Langrangian interpolation polynomials in Cook-Toom convolutions

I'm working through Blahut's 'Fast Algorithms for Signal Processing'. Trying to develop an intuition for the Cook-Toom algorithm for convolutions as used by Lavin and Gray in their Winograd paper for ...
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DTFT of window function applied to input signal

$$x[n] = cos(\omega_1n) + cos(\omega_2n)$$ $w[n] = 1/N$ for $0 \leq n < N, 0$ for everything else Find the DTFT of $y[n]=x[n]w[n]$ expressed by the DTFT of $w[n]$, $W(\omega)$ I was thinking ...
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When to Apply Circular Convolution Formulas?

Context I am studying the family of Discrete Trignometric Transforms (DTT): Discrete Cosine Transforms (DCT) and Discrete Sine Transforms (DST). And trying to understanding more their properties, I ...
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How is 2D convolution calculated?

I wish to implement the 2D convolution on an FPGA, so Ineed to understand how it is calculated in practice. The main difficulty that I found apparently 2 different ways showcases how to do it. The ...
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1answer
56 views

Convolution Integral of Harmonic Signal (Cosine) with the Sinc Function

I was asked to show that this convolution integral results in the answers also given in the image. Not quite sure how to approach this integral, everything seems to be coupled together. Does anyone ...
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Shift vector function in MATLAB

I am working on my own shift vector function that will be used later to compute the convolution of two signals. The function has to shift the vectors either left or right depending on the magnitude ...
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755 views

Can every type of linear filter be modelled by a convolution?

I have an input time series going through a filter that creates another time series as output. If I assume in first approximation that my filter is linear, does it necessarily mean that I can model ...
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Convolution of Signal with a Gaussian Filter / Kernel

Following up on Analytical Solution for the Convolution of Signal with a Box Filter, I am now trying to convolve a Gaussian filter with the sine signal by hand. My method is to use the definition of ...
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Solving equation with convolution

I have the measured signal $y(t)$ that can be modeled in the frequency domain as $Y(f)$: $$Y(f) = X(f)\cdot A(f) - [X(f)\cdot B(f)] \ast C(f)$$ where $\ast$ is the convolution. I know $A(f)$, $B(f)$,...
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What is the peak resonance of convolving with a sine FIR filter?

I'm trying to improve my understanding of FIR filters. As an experiment, I've manually created an FIR filter, whose coefficients follow exactly one period of a sine wave. I'm wondering what is the ...
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Analytical Solution for the Convolution of Signal with a Box Filter

I have an exercise in which I am trying to filter an input signal $y(x) = \sin(x)$. Ideally, I would like to apply a box filter to this signal. Previously, I successfully convolved the input signal $...
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1answer
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Partitioned overlap-add convolution - strange behavior at buffer boundaries

I've implemented a convolution reverb that operates in real-time, one audio buffer at a time (using FFTS for the fft bits). However, there's some strange behavior at the start of every buffer. ...
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Understanding convolution of Chirp z algorithm

I dont´t understand how works the convolution part of the Chirp z. I understand how the DFT is transformed \begin{align*} x(k) = \sum_{n=0}^{N-1} x(n) W_N^{kn} \end{align*} to this expresion: \...
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How does minimum-latency partitioned convolution reverb work when you receive input samples in chunks, rather than one at a time?

I'm writing a reverb system where I receive an input block of samples 480 elements long, do some operation on them, and pass the block on to the next effect. I've been reading up on partitioned ...
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Representing a continuous LTI system as a discrete one

I am aware that there are different ways to represent a continuous time system in discrete domain (e.g. bilinear transform, impulse invariance transform). But my problem is as follows: Given an ...
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Why Are There Two Different Common $ 3 \times 3 $ Kernels for the Laplacian?

I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ...
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Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?

I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ...
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Convolution between two vectors. Length and normalization

I have an RIR vector $h[n]$ with $N$ samples and an audio source $x[n]$ with $M$ samples. I wish to simulate a 5 seconds audio segment with $x[n]$ randomly located within (timewise). Using MATLABs <...
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Difference between the two forms of input-output relationships of an LTI system

$$y(t)=f(t)*h(t)\tag{1}$$ $$y(t)=H(s)e^{st}\tag{2}$$ $$H(s)=\int_{-\infty}^{\infty}h(t)e^{-st}dt\tag{3}$$ Let $f(t)$ in Eqn $(1)$ be $e^{st}$. In many worked out examples, I have found that the two ...
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Faster Algorithm to convolve/correlate two sparse 1-D signals in python (or any language)

I have two signals which I need to correlate or convolve. Each signal is sampled non-uniformly and the values of the signal I have with me are the timestamp and the magnitude of the signal at that ...
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108 views

Determining LTI system response to a scale change

We know that for an LTI system, if $y(t)$ is the output for $x(t)$ then the response for $x(t-2)$ will be $y(t-2)$ and so on. But my question is what will be the system response for the input $x(-2t)$...
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MATLAB Convolution

I am designing an IIR notch filter using pole-zero placement method. I am trying to convolve the two zero locations using ...
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Conflict with the properties of convolution

excuse me in advance for the lenghty question, consider the following signals: $x_1[n]$, $x_2[n]$, $y[n]$ and $z_1[n] = x_1[n] * y[n]$ $z_2[n] = x_2[n] * y[n]$ In addition, we know that: $x_2[n] =...
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How to convolve $u(-t)$ with other signals?

How can I convolve the following $u(t+1)*u(-t)$ I know that convolution with $u(t)$ gives the integral of a function but what change occurs due to $u(-t)$?
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Serial filtering using FFT

lets say I have 3 audio filters for a realtime DSP application. For simplictity each has length 256 (as well as the input signal). The filters should work in series. Starting with filter IR h1(n) and ...
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What is the point spread function and optical transfer function and what uses are they in image processing

So I seem to really be struggling with the concepts of the point spread function (PSF) and optical transfer function (OTF) and what they are used for in image processing. Everything I seem to google ...
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Given local responses by a bank of equally spaced (log-)Gabor filters, how can we estimate the response of an intermediate-scale filter?

Consider a grayscale image convolved with a bank of 2D wavelet quadrature pairs – in my case, log-Gabor filters. I have eight filters. For simplicity, let's say they are all vertically oriented, and ...
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Convolution Theorem: Hamming Window on a Time Series and Fourier Domain

If we have a set of time series data, y, consisting of 100 data points. One can apply a N (odd) Hamming window as a weighted moving average to decrease the noise. Say, if we choose 7 point Hamming ...
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Does class imbalance affects for 1D CNNs?

I'm trying to develop a 1D CNN model for a high imbalance dataset. I tried giving sample_weights trying to compensate for the class imbalance. But it always classifies into one class.