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What is the difference between convolution and correlation?

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sundarmeenakshi

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Convolution

What is the differance between convolution and correlation
 

Re: Convolution

correlation is used to compare the similarity of two signals, the result is a signal that shows this similarity and reaches its maximum at the time when the two signals match best. correlation can be used to measure the delay of a certain system.

convolution is used to compute the output of a certain linear system when a certain input signal is applied to it. this is done by applying convolution between the input signal and the impulse response of the system
 

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    sundarmeenakshi

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Re: Convolution

From mathematical point of view convolution of two function is:

x(t)*y(t)=∫x(Θ)y(t-Θ)dΘ

and correlation is

E[x(t)y(t)]=∫x(Θ)y(t+Θ)dΘ
 
Re: Convolution

Convolution is the operation / transformation that governs the i/p - o/p relationship in a LTI system.

Correlation is a statistical measure of how similar two waveforms or random processes are.

In the case of a matched filter, correlation and convolution becomes the same.
 
Convolution

convolution is specifically used for the multiplication of continous and discrete time signal in time domain and valid for LTI system but correlation is matching and comparision of signal and there are two types auto and cross correlation and its example in missile imaging

Added after 22 seconds:

convolution is specifically used for the multiplication of continous and discrete time signal in time domain and valid for LTI system but correlation is matching and comparision of signal and there are two types auto and cross correlation and its example in missile imaging and using correlators and matched filters for taht
 

Re: Convolution

Hi,
Convolution of two signals can be interpreted graphically as folows:
supose you take convolution between x(t) and y(t). Then in t domain just reverse the signal y(t) i.e. plot the signal y(-t). Now translate the signal y(-t) from -∞ to Γ. The overlap area is the convolution between x(t) and y(t). at the point Γ.

On the otherhand the correlation is the same thing, only thing is that, you dont have to invert the signal y(t) in t domain. Translate y(t) itself from -∞ to Γ. The overlap area gives the correlation between these two signals.
 

Convolution

Completly agree with asoom
 

Convolution

Correlation + Shifting = Convolution

This is the difference between the both.
 

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