The convolution theorem

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.

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.

https://en.wikipedia.org/wiki/Convolution_theorem#Functions_of_discrete_variable_sequences

The convolution theorem

Recommendations