Signal Processing Stack Exchange
Signal Processing Stack Exchange

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.

Convolution is similar to cross-correlation. The convolution can be defined for functions on groups other than Euclidean space. It has applications that include probability, statistics, computer vision, image and signal processing, electrical engineering, and differential equations.

Extracted from: http://en.wikipedia.org/wiki/Convolution

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What is the physical meaning of the convolution of two signals?

If we convolve 2 signals we get a third signal. What does this third signal represent in relation to the input signals?
Parag
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What is the difference between convolution and cross-correlation?

I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ. What is the difference between the two? Can you say that autocorrelation is also a…
Mien
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Flipping the impulse response in convolution

During convolution on a signal, why do we need to flip the impulse response during the process?
winuall
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Overlap-Add versus Overlap-Save

What differences or other criteria can be used to help decide between using overlap-add and overlap-save for filtering? Both overlap-add and overlap-save are described as algorithms for doing FFT based fast convolution of data streams with FIR…
hotpaw2
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How to circularly shift a signal by a fraction of a sample?

The shift theorem says: Multiplying $x_n$ by a linear phase $e^{\frac{2\pi i}{N}n m}$ for some integer m corresponds to a circular shift of the output $X_k$: $X_k$ is replaced by $X_{k-m}$, where the subscript is interpreted modulo N (i.e.,…
endolith
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Difference Between Correlation and Convolution in the Context of Image Processing

Could you please clearly explain what is the difference between correlation and convolution that is done by a filter on an image? I mean in terms of signal processing definition I know that convolution describes the output of an LTI system, that is…
the_naive
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What are the problems with designing an FIR filter using FFT?

I'm trying to get an understanding of the relationship between an FIR filter designed from "first principles" using a filter kernel with convolution, and a filter designed in one of two ways using FFT (see below). As far as I understand, the impulse…
bryhoyt
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Why convolution is required, or what is the philosophy behind convolution?

I am working in digital image restoration field. I have read all things about convolution, that, for an LTI system, if we know its impulse response, then we can find its output by just using convolution between input and impulse response. Can…
Mayank Tiwari
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How to find the convolution kernel in frequency domain?

I have a two vectors of spatial data (each about 2000 elements in length). One is a convolved version of the other. I am trying to determine the kernel that would produce such a convolution. I know that I can do this by finding the inverse Fourier…
Bowler
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How to Deduce a Linear System's Impulse Response from a Set of Input and Output Signals?

I want to know how to solve those types of problems.. is it by inspection ? Consider the linear system below. When the inputs to the system $x_1[n]$, $x_2[n]$ and $x_3[n]$, the responses of the systems are $y_1[n]$, $y_2[n]$ and $y_3[n]$ as…
Belbesy
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Why is circular convolution used in DSP? Why not linear convolution?

Why are we using circular convolution in DSP? What's the main solid reason for the use of it in digital processing? Why does the concept of circular convolution come more often than linear convolution?
vishaln
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Deconvolution of 1D Signals Blurred by a Gaussian Kernel

I have convolved a random signal with a a Gaussian and added noise (Poisson noise in this case) to generate a noisy signal. Now I would like to deconvolve this noisy signal to extract the original signal using the same Gaussian. The problem is that…
user1724
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What Are Linear and Circular Convolution?

I have some basic understanding of signals and convolution. As far as I know it shows the similarities of two signals. Could I get some explanation in plain English of: what are the linear and circular convolution why they are important practical…
Sturm
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How Does a Convolution Can Be Expressed as a Matrix Multiplication (Matrix Form)?

I know this question may not be very relevant to programming, but if I don't understand the theory behind image processing I'll never be able to implement something in practice. If I got it right Gaussian filters are convolved with an image for…
Matteo
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Why do linear systems show sinusoidal fidelity?

I am looking for a proof for sinusoidal fidelity. In DSP we study a lot about linear systems. Linear systems are homogenous and additive. One more condition it satisifies is that if a signal is a sine or cos wave then the output only changes the…
Hobyist
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