Signal Processing Stack Exchange
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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.

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?
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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?
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Is Periodic Convolution Same as Circular Convolution?

I know exactly what is periodic convolution. But i don't know if circular convolution means to be the same thing!
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A better explaination for 'there's no flipping of the impulse response'

I showed the question about flipping the impulse response to some math teachers and electrical engineers at an university. They read Dilip's answer and thought that it was hard to understand what Dilip meant and it was simply not true... Could…
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Can two nonzero signals $x[n]$ and $y[n]$ give a zero convolution

Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero signal? In other words, is it possible that…
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How can I calculate the cyclic (periodic) convolution?

I'd like to understand how to calculate the cyclic convolution as well as understand what that means exactly. How should I go about finding the output for various periods for a system? I have an example: $$ x(n) = \begin{cases} n & \textrm{for}…
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Breaking a convolution into smaller pieces

For a project I need to do convolution and i use gpu for calculations. Sometimes I have to deal with kernel sizes of 50x50 and this size of kernel is sufficiently large that it chokes the gpu. (not enough memory svailable by the gpu) I need to find…
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Convolving two signals

I saw a video where this guy used a program to do a frequency analysis on a voice signal and a sawtooth wave (I'm assuming this was FFT). Then he saved the plots as images and combined them pixel by pixel through multiplication using photoshop. He…
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Basic question: Why is the output of a system the convolution between the impulse response and the input?

I forgot a very simple fact and I am now struggling to find reference that proves this basic property? How would you prove that for a single in single out system, the system output is the impulse response convoluted with the input?
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What is convolution of two sine waves (tones)?

Convolution of two sine waves (or tones as called in audio) is theoretically not defined as the integral is infinite. Taking finite duration windowed sine waves and doing there convolution computationally always contains a fundamental frequency…
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What are three different techniques to convolve a signal

I have studied convolution in time domain and frequency domain. But doesn't know the 3rd method and technique
Uzair Abbas
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Convolution of delta function in discrete time with parameter

If I have a delta function of the following type $$ n\delta(5n-20) * 3^{5n}u[n] $$ How can I calculate this convolution? I have thought of the property $$ \delta[n-n_0] *x[n] = x[n-n_0] $$ Then if I say $$ k=5n $$ and $$ t[n]= 3^{5n}u[n] $$ It…
user33117
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Minimal number of additions in convolution

The Winnograd algorithm can be used to reduce the number of multiplications in convolution. Is there a known method of reducing the number of additions in convolution?
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the sub-range of circular and linear convolution

circular convolution $x_{_3p}[n]$ = $x_1[n]~\circledast_N ~x_2[n]$ is a period version of the linear convolution $x_{_3p}[n]=x_1[n] * x_2[n]$ The length of $x_1[n]$ and $x_2[n]$ are $L$ ($n\in[0,\ldots,L-1]$) and $P$ ($n\in[0,\ldots,P-1]$)…
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Convolution problem

This will be maybe quite easy fore somebody but I am not sure how to solve it. If I have a signal which is equal to $$ y(n)=x(n)\star g(n), \quad n\in[0,1,...,N] $$ where $\star$ is convolution operator, how do I get expression for taking every…
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