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.
Downsampling and Aliasing