# 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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### Add echo as described by difference equation to audio signal (in MATLAB) [closed]

A simple linear system is echo. It can be described by equation $$y[n] = x[n]+ k\,x[n−d],$$ where $n$ represents sample index, $k$ represents an attenuation coefficient, and $d$ represents time lag....
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### Intuition behind commutativity of convolution in LTI systems

Why is convolution commutative, as it seems to treat two signals in a different way in an LTI system? If you imagine $y[n] = x[n] \star h[n]$ with $x[n]$ being an input signal and $h[n]$ being the ...
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### Convolution Strategy

I would like your help on a theoretical question regarding convolution. The point is to design a faster discrete-time convolution operator functioning on one-dimensional space so that y[n] = x[n] * h[...
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### Equalizing a temporal sound signal with a convolution

This question is more or less the following of a previous question. The aim is to equalize some sounds signals. By equalizing, I mean increasing or decreasing some frequency ranges, a bit like an ...
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### Basic Confusion About the DFT and Convolution

I am learning DSP (with Digital Images) and I have some elementary confusion about the convolution between two discrete periodic signals. Specifically, I have learnt that when filtering an image, we ...
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### What is the meaning of the sum of kernel components in digital image filtering?

When analyzing an image signal as a series of Dirac impulses in the continuous spatial domain, I applied continuous low pass filters (to reconstruct or smooth it) with area equal to 1 to preserve the ...
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### Graphical method for convolution?

Is graphical method the best way to solve convolution questions whether they be discrete or continuous? I was given a question: $$x[n]=1$$ $$0\leq n \leq 4$$ $$h[n]=\alpha^n$$ $$0\leq n \leq 6$$ ...
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### How to solve this question by using convolution?

I had previously posted this question but my method was wrong in it. Two signals are given: $$x[n]=2^nu[n]$$ $$h[n]=u[n]$$ I have to find $y[n]$. I have spent hours on this question but I am unable ...
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### Comparison of Linear Convolution and N point DFT

I am studying Discrete Fourier Transform currently and I have a doubt in that. Consider two sequences {1,2,3,4} and {0,1,0,0}. When I convolve them linearly, I get this {0,1,2,3,4,0,0}. However, if I ...
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### Impulse response when input to a system is differentiated, and its applicability to find response to general inputs

I will first give a short explanation of what I am asking, and then give a more comprehensive context. If we have a LTI dynamic system acted upon by inputs $y(t)$ and producing outputs $x(t)$, , we ...
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### Convolution of discrete time signal

I'm given a discrete time signal which is as follows: $$x[n] = \alpha^n u[n],\\$$ $$h[n] = u[n],\\$$ Why is unit function neglected in the following step: $$y[n] = \sum_{k=0}^{n} \alpha^{k}\\$$
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### Derivation of the Optimal Matched Filter - Convolution vs. Correlation

On the Wikipedia page for Matched Filters here, there is a matrix algebra derivation for an optimal matched filter. Now, considering the output of an LTI system is found using the convolution operator,...
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### What is about the circular convolution in OFDM

In an OFDM system, serial-to-parallel conversion for data is done, then the DFT is performed and then adding the cyclic prefix (CP). My question is related to that step of adding a CP. As I know, ...
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### How can I improve the Canny edge detection code?

I have converted this Matlab code for Canny edge detection into C# given that the Matlab version gives out a good output. The output from Matlab code is as follows: And my C# version's outputs are ...
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### How I can perform SIMO channel convolution in MATLAB

In OFDM system, I need to transmit a signal $x$ in SIMO channel $H$ of single Tx antenna and $4$ Rx antennas. The initial equation for that convolution is $r = Hx + n$ where $n$ is the noise. As ...
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### Matrix cross correlation in python

I'm currently performing matrix cross correlation in python using : C = scipy.signal.correlate2d(A,A) where A is a 2D matrix, typically a picture. As you can ...
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### What is the relation between kernel functions, kernels used in convolution and null spaces of a matrix?

I have recently started learning about machine learning and have come across kernels and null spaces. I understand that null space is the set of all vectors that satisfy the equation A.v = 0 (Where A ...
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### Correlation peformed by convolution

Background: The question here is related to images in particular and not signal/waveforms. I have been reading a lot of answers about the difference between convolution and correlation but I am stuck ...
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### Deconvolution Using Complex Division in The Frequency Domain

Consider these two signals: a = [1 1 0 0 0 0 0 0] b = [1 0 1 0 0 0 0 0] their convolution is c = a * b = [1 1 1 1 0 0 0 0] ...
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### Numerical error while implementing a periodic pulse signal

I'm trying to illustrate the principle of constructing a periodic signal using an elementary pattern. This is the code I use (python 2.7 + numpy + scipy.signal) : ...
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### Applying BCJR equalization for LDPC encoded information

I want to apply BCJR decoder for LDPC encoded information. How can I change the BCJR originally for convolutional codes for this purpose?