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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 …
user541686's user avatar
5 votes
1 answer
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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( …
user541686's user avatar