Stretch Theorem (Repeat Theorem)
Theorem: For all
,

Proof:
Recall the stretch operator:
![$\displaystyle \hbox{\sc Stretch}_{L,m}(x) \isdef
\left\{\begin{array}{ll}
x(...
...=\mbox{integer} \\ [5pt]
0, & m/L\neq \mbox{integer} \\
\end{array} \right.
$](http://www.dsprelated.com/josimages_new/mdft/img1430.png)















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Downsampling Theorem (Aliasing Theorem)
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Rayleigh Energy Theorem (Parseval's Theorem)
Theorem: For all
,
Proof:
Recall the stretch operator: