(\omega) \, e^{i\omega t} d\omega
\end{multline}`

&ldquo;A convolution in time is a multiplication in frequency.&rdquo;


The cross-correlation theorem:

`\begin{multline}
(f\star g)(t)=\int_{-\infty}^{\infty}   f^*(\tau-t) g(\tau) d\tau= \int_{-\infty}^{\infty} f^*(\tau) g(\tau+t) d\tau
\\=\frac{1}{2\pi}\int_{-\infty}^{\infty} F^*(\omega) G(\omega) \, e^{i\omega t} d\omega
\end{multline}`

&ldquo;A cross-correlation in time is a multiplication in frequency *with the first function conjugated.*&rdquo;




