A periodically time‐varying digital filter containing a discrete fourier transformer

Abstract

AbstractSo far, three periodically time‐varying models have been proposed in the research on periodically time‐varying digital filters. They are the coefficients time‐varying model, the output sampling polyphase model, and the input sampling polyphase model. Analyses of these models have also been completed by the authors.This paper proposes new models to solve a problem which the three conventional models cannot solve. It is known that a periodically time‐varying digital filter can be used to implement a spectrum scrambler. However, when these models are to be used to implement a spectrum scrambler, time‐invariant filters in these models are restricted to FIR filters.This paper proposes and analyzes an output sampling polyphase model and an input sampling polyphase model, both of which contain a discrete Fourier transformer. Relationships between the newly proposed models and the conventional coefficients time‐varying model are established.By making use of the newly proposed periodically time‐varying models, we can design a spectrum scrambler employing not only FIR time‐invariant filters but IIR time‐invariant filters as well. Furthermore, compared to the conventional models, the newly proposed periodically time‐varying models are shown to have an advantage of less amount of computation when they are used to implement a spectrum scrambler.