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Discrete-Time Fourier Transform (DTFT)

Module by: Richard Baraniuk

Summary: Details the discrete-time fourier transform.

Discrete-Time Fourier Transform Xω=n=-xn-ωn X ω n x n ω n (1)
Inverse Discrete-Time Fourier Transform xn=12π02πXωωndω x n 1 2 ω 0 2 X ω ω n (2)

Relevant Spaces

The Discrete-Time Fourier Transform maps infinite-length, discrete-time signals in l 2 l 2 to finite-length (or 2π 2 -periodic), continuous-frequency signals in L 2 L 2 .
DTFT1.png
Figure 1: Mapping l 2 l 2 in the time domain to L 2 02π L 2 0 2 in the frequency domain.

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