L2(R) nonstationary processes and the sampling theorem

In [1], a sampling theorem for nonstationary random processes is developed, under the condition that the two-dimensional (2-D) power spectrum (2DPS) of the process has compact support. In this letter, it is shown that, for L-2(R) processes, only a one-dimensional (1-D) restriction on the marginal along time of the time-frequency distribution is necessary to guarantee the compactness of the 2DPS in the 2-D plane, As a direct consequence, it is observed that under mild conditions, a nonstationary autocorrelation function of a bandpass L-2(R) process is nearly stationary in small time intervals. The influence of this result in real-time detection of nonstationary stochastic signals is discussed.