Shift -variance of linear periodically shift-variant systems and non-stationarity of wide-sense cyclostationary random processes

ABSTRACT: We study shift-variance of linear periodically shift-variant (LPSV) systems and non-stationarity of wide-sense cyclostationary (WSCS) random processes (with continuous-time input and output). We determine how far an LPSV system is away from the space of linear shift-invariant systems. We consider the average of commutator’s norm as a shift-variance level, and the normalized version of it is then defined to be a shift-variance measure (SVM). Extending these ideas to random processes, we then consider non-stationarity of WSCS random processes based on the SVM of the autocorrelation operator of the process. We also introduce the expected shift-variance (which is a kind of SVM) for LPSV systems when the input is wide-sense stationary (WSS) random process, allowing us to investigate properties of output of an LPSV system when its input is a WSS random process. Finally, we analyze shift-variance and non-stationarity of generalized sampling-reconstruction processes, discrete wavelet transforms, double sideband amplitude modulated signals and double sideband amplitude modulation systems. Keywords: Linear periodically shift-variant system, Shift-variance, Generalized sampling-reconstruction process, Non-stationarity. …………………………………………………………………………………………………………………………