Autocorrelation

The cross-correlation of a signal with itself gives the autocorrelation function of that signal:

$$r_{x}(l) \isdef r_{xx}(l) = E\{\overline{x(n)}x(n+l)\}$$ (C.25)

Note that the autocorrelation function is Hermitian:

$$r_x(-l) = \overline{r_x(l)}$$

When $x$ is real, its autocorrelation is symmetric. More specifically, it is real and even.