An Iterated Hybrid Fast Parallel FIR Filter
Keshab K. Parhi
TL;DR
The paper addresses efficient parallel FIR filtering by revisiting polyphase-based designs and iterated fast FIR algorithms (FFAs). It introduces a novel fast hybrid parallel FIR filter that nests a transposed 2-parallel FFA in the inner iterations and a direct-form 2-parallel FFA in the outer layer, reducing hardware additions. Through explicit count analyses, the hybrid structure demonstrates lower addition requirements than traditional fast convolution and pure iterated FFA approaches, particularly for power-of-2 parallelism ($2^n$). The work points to practical hardware benefits and suggests further study on word-length effects, hardware realization, and applications in post-quantum cryptography and fast matrix/pointwise operations.
Abstract
This paper revisits the design and optimization of parallel fast finite impulse response (FIR) filters using polyphase decomposition and iterated fast FIR algorithms (FFAs). Parallel FIR filtering enhances computational efficiency and throughput in digital signal processing (DSP) applications by enabling the simultaneous processing of multiple input samples. We revisit a prior approach to design of fast parallel filter architectures by using the iterated FFA approach where the same primitive filter, such as 2-parallel, is iterated to design the fast parallel filter. In this paper, we present yet another novel iterated fast parallel FIR filter, referred to as the fast hybrid filter. The hybrid filter iterates a transposed 2-parallel fast FIR filter in all the inner layers and a direct-form 2-parallel fast FIR filter in the outermost layer, resulting in reduced hardware complexity. Such an iterated hybrid approach has not been presented before. We show that the hybrid fast parallel filters require less number of additions compared to prior approaches.