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Search Mathematics of the DFT
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The cross-correlation of a signal with itself gives its autocorrelation:
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
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