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Discrete Fourier Transform

definition

Let X[n] be a DT signal with period N

DFT

$ X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N} $

IDFT

$ x [n] = (1/N) \sum_{k=0}^{N-1} X[k].e^{J.2pi.kn/N} $


Derivation

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