### Autocorrelation

The cross-correlation of a signal with itself gives its *autocorrelation*:

*real*and

*even*(symmetric about lag zero).

The unbiased cross-correlation similarly reduces to an unbiased autocorrelation when :

The DFT of the true autocorrelation function
is the (sampled)
*power spectral density* (PSD), or *power spectrum*, and may
be denoted

*estimate*of the PSD:

^{8.10}

At lag zero, the autocorrelation function reduces to the *average
power* (mean square) which we defined in §5.8:

Replacing ``correlation'' with ``covariance'' in the above definitions
gives corresponding zero-mean versions. For example, we may define
the *sample circular cross-covariance* as

*variance*of the signal :

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Unbiased Cross-Correlation