L/sup 2/(R) nonstationary processes and the sampling theorem

Abstract

In a previous paper W. Gardner (see IEEE Trans. Inform. Theory, vol.IT-18, p.808-9, 1972) developed a sampling theorem for nonstationary random processes, 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/sup 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/sup 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.