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Fourier Theorems for the DTFT

This section states and proves selected Fourier theorems for the DTFT. A more complete list for the DFT case is given in [263].3.4Since this material was originally part of an appendix, it is relatively dry reading. Feel free to skip to the next chapter and refer back as desired when a theorem is invoked.

As introduced in §2.1 above, the Discrete-Time Fourier Transform (DTFT) may be defined as

$\displaystyle X(\omega) \isdef \sum_{n=-\infty}^\infty x(n) e^{-j\omega n}.$ (3.8)

We say that $ X$ is the spectrum of $ x$ .



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