Analysis of a 'switched' implementation of the adaptive stochastic filter

A representation of the stochastic filter in which the probabilities are used to select the output of a specific fixed filter at any instant of time is studied. Thus, instead of the output being represented by a convex sum of the outputs of fixed filter components, the output is represented by the output of a single filter. This single filter is selected in a probabilistic manner which can be viewed as an implementation using logical switches, and the probabilities of the associated switches determine which one is closed at any instant in time. The initial analysis of this filter representation is presented. It is shown that the switched implementation of the stochastic filter does closely match the average filter. Since the average filter is also represented by the convex sum implementation of the stochastic filter, it appears that the switched implementation has some advantages over the convex sum in that it does not perform multiplications for each output. However, there may be some disadvantages due to the need to make a probabilistic choice of fixed filter outputs.<>