Correlation Theorem

**Theorem: **For all
,

where the correlation operation ` ' was defined in §7.2.5.

*Proof: *

The last step follows from the convolution theorem and the result from §7.4.2. Also, the summation range in the second line is equivalent to the range because all indexing is modulo .

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University