### Differentiation Theorem Dual

Theorem: Let denote a signal with DTFT , and let

 (3.40)

denote the derivative of with respect to . Then we have

where denotes the DTFT of .

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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