Design of low complexity parallel polyphase finite impulse response filter using coefficient symmetry

In this correspondence, a mathematical model is developed for the efficient realisation of a generalised M × M polyphase parallel finite impulse response (FIR) filter structure composed of M parallel conventional decimator polyphase filters. Primarily, the proposed structure is designed in such a way that the benefit of coefficient symmetry property of linear-phase FIR filters can be availed without using the pre/post circuit blocks. A numerical example is also studied to validate the proposed structure. Furthermore, the delay-elements reduction approach is given to avoid the excessive usage of memory elements and the performance of the proposed structure is evaluated in terms of the number of delay elements $\left(D\right)$, adders $\left(A\right)$ and multipliers $\left(M\right)$. Compared to the traditional structures, our proposed structure is found to be more efficient in terms of $M$. Moreover, in contrast to the fast FIR algorithms, the proposed structure resolves the issues of additional requirements of the pre/post blocks and the absence of parallel structure with coefficient symmetry for higher prime values of M (i.e. M > 3). The synthesis result reveals that the proposed 37-tap filter (with M = 3 and 12-bit inputs) involves 30% less area-delay-product (ADP) per output and 33.05% less power per output compared to the most recent structure.