### Autocorrelation

The*autocorrelation*of a signal is simply the cross-correlation of with itself:

(3.24) |

From the

*correlation theorem*, we have

*sample autocorrelation*to include a normalization suitable for this case (see Chapter 6 and Appendix C). From the autocorrelation theorem we have that a digital-filter impulse-response is that of a

*lossless allpass filter*[263] if and only if . In other words, the autocorrelation of the impulse-response of every allpass filter is impulsive.

**Next Section:**

Power Theorem for the DTFT

**Previous Section:**

Correlation Theorem for the DTFT