A new class of shift-varying operators, their shift-invariant equivalents, and multirate digital systems

Abstract

A class of linear, shift-varying operators that generalize the notion of N-periodicity is defined. It is shown that shift-invariant equivalents for these operators exist, and that the equivalence is in a strong sense, preserving both algebraic and analytic system properties. It is shown that multirate sampled-data systems, although not generally periodic, fall into this class. Kranc vector switch decomposition and block filter implementations for single-input, single-output multirate systems are connected under the unifying framework of shift-invariant equivalents, and this framework provides a way to extend them both to multi-input, multi-output systems.