Narrowband linear-phase FIR filters requiring a small number of multipliers

This paper presents a new approach for synthesizing and implementing narrowband linear phase nonrecursive digital filters requiring a small number of arithmetic operations. The approach is based on transformations implemented by replacing subnetworks with transfer function (1+z^-2)/2 in a prototype network by a subnetwork whose transfer function is a polynomial of (1+z^-2)/2 but can be expressed in a form containing no multipliers. By appropriately designing the prototype network and selecting the subnetwork, the resulting filter implementations require significantly less multiplications and additions per sample than conventional nonrecursive designs, at the expense of an increased filter order. Examples show that even a reduction from 1017 to 17 multipliers is possible. The new filters present also considerable advantages over nonrecursive filters composed of cascaded decimators and interpolators.