Unified view on filter banks
Andreas Klappenecker, M. Holschneider · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
An impressive variety of multirate filter banks evolved during the past twenty years. We presents an algebraic approach that subsumes many concepts developed so far (e.g. multifilters, nonseparable multidimensional filter banks, cyclic filter banks, filter banks with values in finite fields, etc.). In our approach the signals and filters are viewed as elements of a group ring. We give necessary and sufficient conditions for perfect reconstruction and derive complete parameterization in terms of ladder (or lifting) structures.