Cyclic Autocorrelation

For sequences of length
, the *cyclic* autocorrelation operator is defined by

(7.19) |

where and the index is interpreted

By using *zero padding* by a factor of 2 or more, cyclic
autocorrelation also implements *acyclic* autocorrelation as
defined in (6.16).

An *unbiased* cyclic autocorrelation is obtained, in the
zero-mean case, by simply normalizing
by the number
of terms in the sum:

(7.20) |

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