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}`

where a conjugation now appears acting on `$F(\omega)$`.

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##Convolution vs. Cross-Correlation

The convolution theorem:

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