### Stretch Theorem (Repeat Theorem)

**Theorem: **For all
,

*Proof: *
Recall the stretch operator:

**Next Section:**

Downsampling Theorem (Aliasing Theorem)

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Rayleigh Energy Theorem (Parseval's Theorem)

**Theorem: **For all
,

*Proof: *
Recall the stretch operator:

Downsampling Theorem (Aliasing Theorem)

Rayleigh Energy Theorem (Parseval's Theorem)