Optimal design of periodically time-varying and multirate digital filters

A description of time-varrying digital filters is developed that uses a transfer function of two frequency variables. This proves to be particularly powerful for periodically time-varying systems and results in the sources and effects of aliasing and folding being explicitly shown. This method is used to allow the optimal frequency domain design of these systems using time-invariant methods. An application to a narrow-band filter design gives up to a factor of three improvement in efficiency.