A NEW CLASS OF SHIFT-VARYING OPERATORS, THEIR SHIFT-INVARIANT EQUIVALENTS, AND MULTIRATE DIGITAL-SYSTEMS

We define a new class of linear, shift-varying operators that generalizes the notion of N-periodicity. It is shown that shift-invariant equivalents for these new operators exist, and that the equivalence is in a strong sense- preserving both algebraic and analytic systems properties. We show that multirate sampled-data systems, although not generally periodic, fall into this new 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 is the way to extend them both to multiinput, multioutput systems. © 1990 IEEE