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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Effect of BIBO-Instability on the frequency response of a ideal LPF
I recently came across this post stating that the continuous ideal LPF is BIBO-unstable since the impulse response is not absolutely integrable, and this post stating some examples.
I have been trying ...
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Is downsampling LTI for bandlimited inputs?
This question stems from the discussion we had on a previous question of mine.
The point of contention is whether the downsampling operator is time invariant or not. Which gives us a new condition to ...
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Is it possible to consider circular convolution in case of appending the guard interval as a suffix instead of a prefix
In OFDM system, the cyclic prefix is added into the head of time-domain signal to enable the circular convolution with the channel, and then perform one-tap frequency-domain equalization at the ...
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Discrete convolution of a causal signal with a delayed unit step
I am computing the discrete convolution of a signal $x[n] = a^nu[n]$ with a delayed unit step, say $h[n] = u[n-5]$.
If I place both directly into the discrete convolution formula I end up with:
$\frac{...
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What is the reason my DFT of a convolution of signals with disjoint spectrums is not zero everywhere?
Assuming the convolution in the time domain produces a signal which spectrum is the product of individual spectrums, when the two convoluted signals are sinusoids with different frequencies, the DFT ...
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Can time aliasing cause peaks?
For the following I use the terms “time domain signal” and “frequency domain signal” as a Fourier Transform pair. The question is for generalized cases of continuous-time signals that once sampled in ...
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Random Peak at the end Impulse Response
I am measuring a room's acoustic impulse response by playing a log sine-sweep through a speaker from 20hz to 24 khz, and then recording it using a microphone.
The sweep is 10 seconds long, followed by ...
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Proof for LTI Systems [duplicate]
Suppose we have a system $S$.If I know the impulse response $h(t)$ I can predict the output for any input $x(t)$ if a system is linear and time invariant.However how do we prove that statement?
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What architecture of CNN to solving a image regression problem (case study: solving Poisson equation)?
I've been working on solving Poisson problem using CNN model (you can ignore Poisson problem part if you not familiar and jump to image processing/CNN part). More specific, I am solving electric ...
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Parseval's theorem, Energy
I was wondering, how can Parsevals theorem (energy in time domain is equal to the energy in frequency domain) hold for sampling. I take three sampels from a sinc-function. This reduces the energy in ...
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LLTV Systems breakdown(2)
In this question I proved that for a linear linearly time varying system $S$ such that if $t_{2} = t_{1}+t_{0}$ then $h(t,t_{2}) = h(t,t_{1})+h(t,t_{0})\rightarrow$ $h(t,t_{0}) = g(t_{0})h(t) $ where $...
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How to Solve a Composition of Convolutions from Regularized Least Squares Model in Frequency Domain
Assume we need to solve the model:
$$ \arg \min_{\boldsymbol{x}} \frac{1}{2} {\left\| \boldsymbol{h} \ast \boldsymbol{x} - \boldsymbol{y} \right\|}_{2}^{2} + \frac{\lambda}{2} {\left\| \boldsymbol{g} \...
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Impulse response of a discrete time cascading system
My lecturer has decided that in order to pass our signal analysis class, we have to give a presentation on the blackboard in front of the entire class, so its kinda critical that i get this right. (...
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Efficient 2D convolution/cross-correlation along only one axis (1D output)
I wish to convolve/cross-correlate two images
and
but, only horizontally, yielding 1D output.
So, first output point would be sum(x * h), second ...
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Solving linear equation of discrete convolution kernels using black box model for the convolution
In Solving inverse problem using black box implementation of the kernel the solution depends on solving the equations of the form:
$${\left( {H}^{T} H + \lambda {G}^{T} G \right)} x = y$$
Where $H$ ...
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How can I compute virtual array via convolution?
I am starting to learn MIMO transceivers and I would like to compute the virtual array of my configuration. To do so, I am following these set of equations 2 and 3, to achieve (3) I was trying to use ...
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Frequency response of an LTI system described by the diagram below
I am trying to solve the below problem:
To begin with the frequency response of the ideal low pass filter with $\omega_c= \pi/4$ is given by $$
H(\omega) =
\begin{cases}
1 & \text{if -$\pi/4$ $...
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The Different Solutions for Filter Coefficients Estimation for Periodic Convolution and Full Convolution
As a continuation of the question Least Squares Solution Using the DFT vs Wiener Hopf Equations raised by Dan Boschen.
The question is, given the model:
$$ \boldsymbol{y} = \boldsymbol{h} * \...
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Simplification of convolution
Let's assume that there are two convolutions:
$y_1 = (h_2[n]\cdot x[n])*(\bar{h_1}[n]\cdot\bar{x}[n])$
$y_2 = (h_3[n]\cdot x[n])*(\bar{h_2}[n]\cdot\bar{x}[n])$
where "$\bar{x}$" is complex ...
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A question about time-shifted convolution
I have 2 time-shifted signals,$f(t-t_0)$ and $g(t-t_0)$. Assuming that $y=f(t)*g(t)$, which is the convolution of the signals.
By definition, I have $f(t-t_0)*g(t-t_0)=\int_{-\infty}^{+\infty}{f(\tau-...
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How can an impulse generate an output in the past time frame?
I am studying signal processing and currently doing signals & systems. While going through convolution and especially the impulse response , there are problems where LTI systems wherein the input ...
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Transfer function $h(t)$ of a positive feedback system
I want to find the transfer function h(t) of the below positive feedback system. I came out till this.
How can i get the inverse laplace of this function? say β = 1 and γ = 1
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Convolution of two functions using FFTW
I'm trying to perform a discrete convolution of two functions, $f(x) = 1$ and $g(x) = \exp(-x)$ of length nsize using FFTW. I have followed the procedure for zero-...
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Linear Linearly Time Varying Systems properties?
Yesterday I asked a question about LTV Systems and how the impulse response h(t,t0) is found.
I was thinking about it and realized there is a subsclass of LTV systems which I call Linear Linearly Time ...
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Why time invariant system in order to know any output for any input using the impulse response?
Suppose we have a system $S$.We give it the input $\delta(t)$ and get a response $S(\delta(t))$.If the system is linear and time invariant we can calculate every output $y(t)$ from any input $x(t)$ by ...
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Tabular method of convolution only applicable for discrete time?
https://www.youtube.com/watch?v=C_kwjJLepLg&ab_channel=NesoAcademy
Above youtube video mentions a tabular method for finding convolution in case of discrete time.
But i am bit confused? Is this ...
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Confusion regarding MATLAB code of convolution animation?
I am trying to understand a MATLAB code of convolution animation.
Please check above link especially code in lines 15 and 16. I think author has mistakenly swapped comments of line 15 and 16. Please ...
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Relation between filter and convolution?
https://www.quora.com/How-is-signal-filtering-done-with-convolution
What is the relation between convolution and a filter?
Is it mainly that convolution process is used to determine the output of an ...
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Real-time convolution with Gaussian noise
I have a brain activity simulator that is capable of receiving various stimuli. Both generated signals and input stimulus are causal: a single sample is created every time step. I use a sinusoidal ...
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Equivalence between "windowed Fourier transform" and STFT as convolutions/filtering
I've heard, that "windowed Fourier transform" is but one perspective on STFT, and that STFT is fundamentally convolutions of windowed complex sinusoids with the input, i.e. bandpass ...
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Matched filter, convolution with signals of various patterns. Explanation of results
I am trying to use matched filters for signal detection and advanced processing - to get additional information from the signal after the convolution with various templates.
The task I have is pretty ...
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Deconvolution of a ground-penetrating radar signal for further convolution with a desired source signal
I am following the instructions of this paper (https://www.earthdoc.org/content/journals/10.3997/1873-0604.2003015) to process a ground-penetrating radar (GPR) signal (a discrete signal sampled at a ...
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Discrete convolution tabular method
In the time discrete convolution the order of convolution of 2 signals doesnt matter :
$x_{1}(n)\ast x_{2}(n) =x_{2}(n)\ast x_{1}(n) $ When we use the tabular method does it matter which signal we put ...
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how to find type of a binary sequence
I want to know how I can find the type (algorithm) of a binary sequence at hand.
For instance, I'd like to know whether the following (binary) sequence is m-sequence, Barker, Gold, etc.
AC DD A4 E2 F2 ...
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How to perform an analytical computation of the convolution sum for a discrete-time system?
I am trying to follow some notes on "Analytical Computation of the Convolution Sum (Graphical Method)" but am getting stuck on what I am doing, or if what I am doing is correct.
There are 5 ...
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Convolution of $(3/4)^nu(n-2)$ and $2^nu(-n-5)$
I am trying to convolve the two discrete sequences
$$\left(\frac34\right)^nu(n-2)$$
and $$2^nu(-n-5)$$
where $u(n)$ is the unit step function.
Here is how I approached the problem ,using the ...
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Converting a triangle from the frequency domain to the time domain
I’ve been given a triangular signal that looks like this:
$$ X^{F}(\omega) = (2 -|\omega|) \cdot W_{[-2,2]}(\omega)$$
(this is just my interpretation of the signal from a picture I’ll add). I was ...
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Discrete-time system: divergent response to exponential input
I’ve been given the following Difference Equation and tasked with finding the response to $x_0[n] = (-p)^n$ - I’ve managed to $h[n]$ but the convolution itself failed.(The given system is IAR).
$$y[n] ...
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How to derive filter design (with parameters) from existing FIR weights
I made a thing which involves a FIR filter, and in that process I cobbled together some random numbers for the convolution which I figured would work the way I wanted.
Now I want to be able to take ...
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How to get DFT spectral leakage from convolution theorem?
I have an issue, where my numerically calculated leakage from a DFT of a simple cosine does not match the theoretical prediction from the convolution theorem. I will try to present the example using ...
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Analyzing 2 2D Kernels Which Approximates a Gaussian Kernel
I'm new to image processing and am working on mask operations.
I was given two kernels A and B, and performed convolutions respectively on an image.
Then, I have to get the difference of output image ...
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scipy convolve and fftconvolve return different output [closed]
I'm writing an autocorrelation function using and I noticed a difference between fftconvolve and convolve that should use fft if it's faster.
This is my function with convolve:
...
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Averaging 2D signal with ignored samples
I have a 2D signal, and I want to compute a new signal by calculating a weighted mean of each sample's neighbours. However, I also have a 2D bitmask, the same size as the original signal, which ...
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Find $E[Z^2(t)]$ when $Z(t) = X(t) - Y(t)$ where $Y$ is the output of a LTI system with WSS process $X$ as its input
I received this as a practice problem (part b only).
I was able to figure out that $E[Z^2(t)]$ = $R_X(0)+R_Y(0)-2R_\text{XY}(0)$ but did not see how to continue.
Checking the answers, I saw this line ...
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Combining audio and image filters in matlab
I am trying to write audio and image filtering together code in my project.
Purpose: The main aim of this project is to combine audio with image filters; like for example passing low frequencies of an ...
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Convolution of a mirrored signal [duplicate]
I want to compute the following convolution sum:
$$r_h[k] = h[k] * h^{*}[-k]$$
To do that first let $g[k] = h^{*}[-k]$
\begin{equation}
r_h[k] = \sum_n h[n]g[k-n]
\end{equation}
where $g[k-n] = h^{*}[...
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Before the fft2, why need fftshift for the kernel?
When I study some paper, I have some questions about usase of convolution theorem.
...
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Convolution of 2 discrete time signals
My background: until very recently in my studies I was dealing with analog systems and signals and now we are being taught discrete signals.
I am stuck at this question:
Suppose the impulse response ...
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Proof symmetry after 2D-convolution with $1/\lvert \mathbf x\rvert$ implies 2D-symmetry [closed]
Let be two 2D functions $f(x,y)\geq 0 \ \forall (x,y)\in \mathbb R^2$ and $g(x,y)=\frac{1}{\sqrt{x^2+y^2}}$.
I have, furthermore,
$$\int_{\mathbb R^2} f(t_1,t_2)g(x-t_1,y-t_2)dt_1dt_2=\int_{\mathbb R^...
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Frequency domain equivalent to center oriented rotated convolution?
I have a convolution kernel which I need to apply to an image. However, at each pixel in the image, I'm convolving using a rotated kernel, with respect to the center (think hands on a clock, with the ...
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