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Trivial, or just straightforward? I don’t think that it’s trivial to know why multiplying by this powers-of-roots-of-unity matrix is interesting, and does the t
by joppy 5y ago
Trivial, or just straightforward? I don’t think that it’s trivial to know why multiplying by this powers-of-roots-of-unity matrix is interesting, and does the things that it does.
- hasmanean 5y agoThe Correlation of two signals a and b is just multiplying them (if they are vectors, multiply each element of a by the corresponding element of b) Corr(a,b) = sum(a. * b) The correlation of a signal s with a sine wave of frequency f just gives the signal power at that frequency. Repeat for a set of regularly spaced of frequency values from 0 to Fs/2 (the maximum frequency you can work with with data sampled at Fs) and you have the DFT. You can even clump the sine waves into a matrix and your DFT gets reduced to a single matrix multiply. This is much easier to reason about than worrying about how an FFT works which is just a speed optimization (which can be derived from dynamic programming applied to the DFT). For someone doing signal processing the results are the same. Introducing the FFT without making reference to the DFT is wrapping the subject up in an air of mystery.