Nonstationary Processes and the Sampling Theorem
Francisco Moreno, Isabel M. G. Lourtie, Jorge Buescu · 2001
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 2 ( ) 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 2 ( ) process is nearly stationary in small time intervals. The influence of this result in real-time detection of nonstationary stochastic signals is discussed.