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e−2πij = 1 for any value of j. Thus, In other words, the value simply repeats itself after k = N. Thus, F(1) = F(N + 1); F(2) = F(N + 2) and so on. This is the reason, why we only compute the Fourier transform as k ranges from 0 to N — 1. The values simply keep on repeating afterward. More