**Definition: **The *circular cross-correlation* of two signals and
in may be defined by

The term ``cross-correlation'' comes from
*statistics*, and what we have defined here is more properly
called a ``sample cross-correlation.''
That is,
is an
*estimator*^{8.4} of the true
cross-correlation which is an assumed statistical property
of the signal itself. This definition of a sample cross-correlation is only valid for
*stationary* stochastic processes, *e.g.*, ``steady noises'' that
sound unchanged over time. The statistics of a stationary stochastic
process are by definition *time invariant*, thereby allowing
*time-averages* to be used for estimating statistics such
as cross-correlations.

The DFT of the cross-correlation may be called the *cross-spectral
density*, or ``cross-power spectrum,'' or even simply ``cross-spectrum'':

Recall that the cross-correlation operator is *cyclic* (circular)
since is interpreted modulo . In practice, we are normally
interested in estimating the *acyclic* cross-correlation
between two signals. For this (more realistic) case, we may define
instead the *unbiased sample cross-correlation*

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