Convolutions and circular convolutions
The circular convolution of two signals of period N is defined by :

The discrete Fourier transform of the circular convolution is the product of the discrete Fourier transforms.

For two signals F and H with length M>=32, it is faster to calculate their convolution, using a FFT. For that, we defines the two signals 2M-periodical:

and it is checked that their circular convolution coincides with the traditional convolution

for 0<=n<2M. The circular convolution itself is computed by in 3 stages : the FFT of the two signals, the product of the FFTs, and then an inverse-FFT.
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