Generalized Polyphase Multistep FIR Structures: Modular Realization of Polyphase Filters

Polyphase structured digital sample rate converters have proved their importance in efficiently realizing the advanced wireless communication technologies as they allow filtering operation at the lowest possible sampling rate. However, the unavailability of modular polyphase finite impulse response (FIR) structures that can avail the benefits of both software and hardware reuse restrict the overall performance gain of the systems. To bridge this gap, we propose a generalized polyphase multistep (GPM) structure. In particular, we derive the governing mathematical expression for its transfer function. We further use it for developing the modular decimator and interpolator in γ multiple steps under the condition that the order of downsampler/upsampler (i.e., J) is a positive non-prime value. Furthermore, two types of module (Module-A and Module-B) are presented, and it is shown that a Jth order FIR filter can be realized by an interconnecting a suitable number of Module-A and Module-B in a systematic manner. It is also discussed that, for sample rate alteration applications, this modular feature of GPM structures can reduce the elapsed time and the hardware complexity compared to the conventional polyphase structure.