An impressive variety of multirate filter banks evolved during the past twenty years. We present 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 parametrizations in terms of ladder (or lifting) structures. 1.
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