An improved approach for the synthesis of multiplication-free highly-selective FIR half-band decimators and interpolators

A substantial improvement is provided in comparison with the systematic approach recently presented by the authors of this paper to generate multiplication-free decimators and interpolators. As the earlier one, the proposed approach is founded, first, on expressing the transfer function of a linear-phase finite-impulse response (FIR) half-band filters as a sum of the terms (1/2)z^-M and G(z²), where the odd integer M is the order of G(z), and, then, on constructing G(z) as a special tapped cascaded interconnection of identical subfilters. The essential improvement is in a quite optimized way of generating multiplication-free tap coefficients such that the resulting passband alteration of the subfilter required by meeting the overall filter criterion becomes significantly larger than in the earlier approach, where this variation is already huge against what is required by the overall filter. This increased passband alteration results in a considerably lowered subfilter order, which, in turn, even further eases finding multiplication-free representations for its coefficient values and decreases the overall filter order. Examples are included illustrating the superiority of the resulting multiplication-free filters compared with those achievable by the earlier approach and their direct-form FIR equivalents.