As of May 31, 2023, we have updated our Code of Conduct.

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.

Filter by
Sorted by
Tagged with
1 vote
1 answer
29 views

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 ...
Finn Heijink's user avatar
4 votes
2 answers
75 views

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 ...
Ahson Yousef's user avatar
1 vote
1 answer
40 views

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 ...
Sajjad's user avatar
  • 145
0 votes
1 answer
39 views

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{...
Marco Marinho's user avatar
2 votes
2 answers
56 views

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 ...
mins's user avatar
  • 375
2 votes
1 answer
127 views

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 ...
Dan Boschen's user avatar
  • 45.9k
3 votes
1 answer
163 views

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 ...
Mason Wang's user avatar
0 votes
0 answers
23 views

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?
Volpina's user avatar
  • 173
4 votes
1 answer
41 views

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 ...
samueljohlal's user avatar
-3 votes
1 answer
71 views

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 ...
plk48's user avatar
  • 1
0 votes
0 answers
59 views

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 $...
Volpina's user avatar
  • 173
5 votes
1 answer
66 views

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} \...
Royi's user avatar
  • 50.4k
1 vote
1 answer
55 views

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. (...
Iscariot's user avatar
1 vote
2 answers
138 views

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 ...
OverLordGoldDragon's user avatar
3 votes
1 answer
91 views

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 $H$ ...
GeorgeIrwin's user avatar
0 votes
0 answers
42 views

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 ...
ndarkness's user avatar
  • 111
1 vote
1 answer
91 views

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 -$\pi/4$ $...
Madavan Viswanathan's user avatar
8 votes
1 answer
125 views

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} * \...
Royi's user avatar
  • 50.4k
1 vote
1 answer
55 views

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 ...
user67236's user avatar
1 vote
1 answer
46 views

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-...
0x15c's user avatar
  • 13
3 votes
2 answers
640 views

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 ...
Madavan Viswanathan's user avatar
0 votes
1 answer
70 views

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
O-Negative's user avatar
1 vote
1 answer
85 views

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-...
gebegb's user avatar
  • 11
0 votes
0 answers
37 views

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 ...
Volpina's user avatar
  • 173
1 vote
2 answers
139 views

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 ...
Volpina's user avatar
  • 173
0 votes
1 answer
42 views

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 ...
abt's user avatar
  • 1,021
0 votes
2 answers
81 views

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 ...
abt's user avatar
  • 1,021
1 vote
2 answers
129 views

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 ...
abt's user avatar
  • 1,021
0 votes
1 answer
70 views

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 ...
Daniel Polyakov's user avatar
6 votes
1 answer
221 views

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 ...
OverLordGoldDragon's user avatar
2 votes
1 answer
162 views

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 ...
twistfire's user avatar
  • 133
1 vote
0 answers
40 views

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 ...
Luis Fraga's user avatar
0 votes
0 answers
192 views

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 ...
Volpina's user avatar
  • 173
1 vote
2 answers
57 views

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 ...
Ali's user avatar
  • 95
1 vote
1 answer
87 views

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 ...
MeljahU's user avatar
  • 33
1 vote
1 answer
55 views

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 ...
Madavan Viswanathan's user avatar
1 vote
2 answers
204 views

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 ...
Piratemetaldrinkingcrew's user avatar
1 vote
2 answers
65 views

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] ...
Piratemetaldrinkingcrew's user avatar
0 votes
1 answer
33 views

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 ...
sh1's user avatar
  • 153
3 votes
1 answer
100 views

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 ...
xaberus's user avatar
  • 33
6 votes
2 answers
78 views

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 ...
Nightysky's user avatar
2 votes
1 answer
122 views

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: ...
Adam Katav's user avatar
0 votes
1 answer
29 views

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 ...
redroid's user avatar
  • 103
1 vote
1 answer
82 views

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 ...
Robert Moore's user avatar
1 vote
0 answers
54 views

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 ...
CompA's user avatar
  • 11
3 votes
1 answer
100 views

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^{*}[...
lord voldemort's user avatar
1 vote
1 answer
149 views

Before the fft2, why need fftshift for the kernel?

When I study some paper, I have some questions about usase of convolution theorem. ...
Jongkyu Lee's user avatar
2 votes
1 answer
90 views

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 ...
Miss Mulan's user avatar
1 vote
0 answers
41 views

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^...
Sabrina's user avatar
  • 11
0 votes
0 answers
19 views

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 ...
Krupip's user avatar
  • 111

1
2 3 4 5
20