4.10 Multirate Processing of Discrete-Time Jointly SC Processes
In multirate digital signal processing, systems constituted by complicate interconnections of interpolators, decimators, and linear time-invariant (LTI) filters acts on input stochastic processes (Crochiere and Rabiner 1981), (Vaidyanathan 1990). Since interpolators and decimators are linear time-variant systems, the stationarity or nonstationarity properties of the input processes turn out to be modified at the output. For example, the expanded version of a WSS process is cyclostationary with period of cyclostationarity equal to the expansion factor (Sathe and Vaidyanathan 1993).
The effects of multirate systems on second-order WSS and cyclostationary processes are analyzed in (Sathe and Vaidyanathan 1993). In (Akkarakaran and Vaidyanathan 2000), conditions that preserve at the output of an interpolation filter the wide-sense stationarity of the input sequence are derived. Moreover, conditions for the joint wide-sense stationarity of the outputs of interpolation filters are also obtained. Higher-order statistics of ACS processes are considered in (Izzo and Napolitano 1998b).
In (Sathe and Vaidyanathan 1993), (Izzo and Napolitano 1998b), and (Akkarakaran and Vaidyanathan 2000), multirate operations on a single process are addressed and no cross-statistics of a process and its expanded or decimated version are considered. Moreover, no cross-statistics are considered between processes obtained by multirate elaborations ...