Computationally efficient narrowband linear-phase FIR filters

A new approach is presented for synthesising 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 in (1+ Z¿2)/2 but can be expressed in a form containing no multipliers. By appropriately designing the prototype network and selecting the sub-network, 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.