Measure for degree of time variance and measure for degree of non-stationarity: application to discrete LPTV systems

Processing and analysis of time-varying systems and associated non-stationary signals are of great practical importance. The issue of quantifying the amount of time variance and amount of non-stationarity has gained importance recently. This work is also an effort in that direction. In particular, in this paper, we define two measures, one for the degree of time variance ( MDTV ) in the context of linear periodically time-varying systems (LPTV) and second for the degree of non-stationarity ( MDNOST ) of cyclostationary processes as they naturally arise when a wide-sense stationary (WSS) process passes through an LPTV system. While MDTV is a system property, on the other hand, MDNOST is a signal property. This paper also tries to find a relationship between the amount of time variation of a system with the amount of non-stationarity it generates. In this light, two concepts are analyzed for two different scenarios. First, we consider a system consisting of an upsampler followed by a linear time-invariant (LTI) filter and second a dual rate system (DRS). Both these systems are LPTV. We have shown that the MDTV generated by both LPTV systems is the same as the MDNOST of their output process through simulations and rigorous mathematical proofs.