Analysis of the effects of multirate filters on stationary random inputs, with application in adaptive filtering

The authors study the statistical properties of the outputs of some basic multirate filtering operations when the input is a wide-sense-stationary (WSS) or a cyclo-WSS (CWSS) process. They give necessary and sufficient conditions under which the output remains WSS or CWSS. For some multirate filters, the output response to a WS input is CWSS. Expressions for the periods of cyclostationarity for such cases are given. As an application of the theory, the optimal (Wiener) solution for a new efficient multirate adaptive filtering method suitable for identification of bandlimited channels is derived. It is shown that the optimal (Wiener) filter is a linear periodically time-varying (LPTV) filter. Simulations are included which verify that an LPTV adaptive filtering structure gives better performance than a transversal adaptive filtering structure