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DFT ( Discrete Fourier Transform )

Definition

DFT

  • $ X(k) = \sum_{n=0}^{N-1}{x[n]e^{-j2{\pi}kn/N}} k = 0, 1, 2, ..., N-1 $

Inverse DFT (IDFT)

  • $ x[n] = \frac{1}{N}\sum_{k=0}^{N-1}{X(k)e^{j2{\pi}kn/N}} n = 0, 1, 2, ..., N-1 $

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett