n a close relative of the convolution called the *cross-correlation*, defined as
`\[(f\star g)(t)=\int_{-\infty}^{\infty}  f^*(\tau-t) g(\tau) d\tau= \int_{-\infty}^{\infty} f^*(\tau) g(\tau+t) d\tau
\]`

which is just a different way to filter one time series with another.  Unlike the convolution, the cross-correlation is not symmetric.

The frequency-domain expression of this action is given by the *cross-correlation theorem*,

`\begin{multline}
(f\star g)(t)=\int_{-\infty}^{\infty}   f^*(\tau-t) g(\tau) 