The paper deals with the time-frequency analysis of a Gaussian random process on \(\mathbb{R}^d\) (random fields). It is proved that if the covariance function belongs to the Feichtinger algebra \(S_0(\mathbb{R}^{2d})\), then the Wigner distribution (Wigner spectrum) of the process exists as finite stochastic integral and the Cohen’s class (i.e. convolution of the Wigner process by a deterministic function) gives a finite variance process.