Kinematics in iterated correlations of a passive acoustic experiment

Fourier Transformations

The temporal Fourier transformation pairs of a time-domain function $F(t)$ and frequency-domain function $F(\omega)$ are defined as

$$F(\omega) = \hspace{.7cm} \int_{\infty}^{-\infty}F(t) \mathrm{exp}\left(-i\omega t\right)\mathrm{d}t,$$ (63)

$$F(t) = \frac{1}{2\pi}\int_{\infty}^{-\infty}F(\omega) \mathrm{exp}\left( i\omega t\right)\mathrm{d}\omega,$$ (64)

the particular Fourier-domain of the function $F$ is specified by the argument only.