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Discrete-time signals and digital filters have become increasingly important in recent years with the rapid advance of technology in integrated digital circuitry and the increasing availability of digital computers. This paper is concerned with a class of linear time-varying digital filters and the response of such filters with stochastic input signal. It is shown that these filters possess a number of useful properties; the most important of which is the preservation of wide-sense stationarity of stochastic inputs. Such properties can facilitate considerably the analysis of systems incorporating these filters. It is shown that this class is the most general class of time-varying filters that preserve the wide-sense stationarity of the inputs. A subclass of these filters is shown to be periodic and hence can be implemented simply by using parallel connection of time-invariant filters and a rotating switch. The response of these filters to periodic inputs is analyzed.