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The Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies, known as a frequency spectrum.
19
votes
Why is the Fourier transform so important?
Another reason:
It's fast (e.g. useful for convolution), due to its linearithmic time complexity (specifically, that of the FFT).
I would argue that, if this were not the case, we would probably be do …
5
votes
1
answer
584
views
Why idft(dft(a) * dft(b)) not equal to convolve(a, b)?
I'm a little confused... I always thought the DFT of a convolution was equal to a product of DFTs, but when I tried this in Python:
from scipy import *
a = [1+0j, 2+0j]
b = [4+0j, 5+0j]
print list( …