Differentiation Theorem Dual
Theorem: Let
denote a signal with DTFT
, and let
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(3.40) |
denote the derivative of



where


Proof:
Using integration by parts, we obtain

An alternate method of proof is given in §B.3.
Corollary: Perhaps a cleaner statement is as follows:

This completes our coverage of selected DTFT theorems. The next section adds some especially useful FT theorems having no precise counterpart in the DTFT (discrete-time) case.
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Scaling Theorem
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Downsampling and Aliasing