I understand the Fourier transform of a signal f(t). It is an integral of f(t) times the Fourier basis. However, if f is a random function of t and $\omega$, what would be the fourier transform of f(t, $\omega$) represent? ($\omega$ is an element from the sample space $\Omega$)
Blindly applying the integral generates a random function which I could not quite wrap my mind around.