Issues in multirate statistical signal processing

The statistical analysis of random signals and noise is traditionally carried out under the assumption of wide sense stationarity. In the processing of signals through systems at multiple data rates, even local stationarity is not always a valid assumption. While a stationary discrete-time signal that is down-sampled at a multiple of the original sampling rate retains wide sense stationarity, the same may not be true for a signal that is interpolated and processed at a higher rate. Such multirate signals however exhibit cyclostationarity and can be optimally processed by periodically time-varying systems. This paper discusses some issues in the theory of multirate random signals, and suggests some structures for optimal filtering for combinations of these signals.