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The convolution theorem
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The convolution theorem

Creator
Creator
Seonglae Cho
Created
Created
2023 Apr 19 13:56
Editor
Editor
Seonglae Cho
Edited
Edited
2023 Nov 14 16:53
Refs
Refs
Convolution
The Fourier transform of the convolution of two functions is the product of their Fourier transforms and inverse too
Using the convolution theorem, we can interpret and implement all types of linear shift-invariant filtering as multiplication in frequency domain.
notion image
 
 
 
Convolution theorem
In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the pointwise product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain). Other versions of the convolution theorem are applicable to various Fourier-related transforms.
Convolution theorem
https://en.wikipedia.org/wiki/Convolution_theorem#Functions_of_discrete_variable_sequences
 
 

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The convolution theorem
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