New insights into multirate systems with stochastic inputs using bifrequency analysis

In multirate processing, it is often necessary to understand how the statistical properties of signals (such as stationarity) are altered by passage through multirate systems. Some of these issues have been addressed previously by Sathe et al. (1993). For example, it has been shown that a necessary and sufficient condition for the output of an L-fold interpolation filter to be wide sense stationary (WSS) for all WSS inputs, is that the filter have an aliasfree (L) support. However, this result was established using conventional tools such as polyphase matrices, which resulted in a convoluted derivation which does not provide much insight. It also leaves many questions unanswered, since it does not generalize easily to the case of systems with vector inputs. This paper shows that problems of this nature can be addressed in an elegant and insightful manner by using bifrequency maps, and bispectra. In particular, we give a simpler proof of the above-mentioned result of Sathe et al., and generalize it to the case of vector systems