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given a sequence of N samples f(n), indexed by n=0....N-1, the discrete fourier transform (DFT) is defined as F(k), where k=...N-1.

The sequence f(n) and F(k) using the inverse discrete transform (IDFT)

Although we have stated that both n and k range over 0..N-1, the definitions above have a periodicity of N:

F(k+N)=F(k) f(n+N)=f(n)

so both f(n) and F(k) are defined for all integral n and k respectively, but we only need to calculate values in the range 0...N-1. Any other points can be obtained using the above periodicity property.

Please let me know if you need any clarification. I'm always happy to answer your questions.