Formulas to generate efficient piecewise-polynomial implementations of narrowband linear-phase FIR filters

Two computationally efficient structures to design and implement linear-phase narrowband FIR filters with a symmetrical piecewise-polynomial impulse response have been proposed by Saramaki and Mitra. The efficiency of these structures is based on implementing the overall transfer function as a parallel connection of a few branches of the form G_l(z^L)F_l(z), where each F_l(z) requires no real multipliers. These structures have been generated in an ad-hoc manner. This paper introduces straightforward approaches to generate such F_l(z)s for both structures