Some novel multirate architectures for filter realization with reduced multiplicative complexity

In this correspondence, we present some novel multirate architectures based on multirate subsystems in feedback configuration for the realization of recursive (AR) filters with reduced multiplicative complexity. Included in this are composite architectures in which there are multiple multirate subsystems with different multirate factors. This can be extended to ARMA transfer functions in which multirate subsystems occur both in feedback and feedforward configuration. The tradeoffs between additive and multiplicative complexity in such architectures are discussed. A summary of results on the effects of coefficient perturbations in such architectures due to finite word length is presented. For exact analysis of such perturbed composite multirate systems, it is shown that these systems can be equivalently represented by a MIMO multirate system.