Invertible periodically time-varying digital filters

A class of periodically time-varying filters has been defined in which the specifications are chosen in invertible filter pairs. That is, for every filter in this class there exist an inverse time-varying filter. All of filters have an FIR structure. Consequently, straight forward optimal design procedures are available for each filter in the pair and stability problems are avoided. Initially, the bifrequency maps of the filters are constrained to a stepwise functions. The constrained configurations allow the frequency domain operation of the filter to be described by a finite dimensional matrix operator where each flat region in the bifrequency map is a coefficient in the matrix. The inverse system is found by determining the matrix inverse. And, building the corresponding time-varying filter. The class is extended by allowing each step an arbitrary delay (linear phase) term. The corresponding delays in the inverse system can not be found by a straight matrix inverse; however, a system of equations can be found to determine these delays.