Computationally efficient circularly symmetric two-dimensional FIR filters

An efficient technique is presented for synthesising and implementing narrowband circularly symmetric two-dimensional finite-impulse-response digital filters. The technique is based on a special case of the generalised McClellan transformations, and it uses an efficient implementation proposed by McClellan and Chan for filters designed via the transformation method. The transformation is constructed in such a way that the requirements for the prototype one-dimensional filter are much alleviated, and the subnetworks implementing the transformation require no multipliers and only a few adders. Examples show how the new filter implementations require, in narrowband applications, significantly less multiplications and additions per output sample than equivalent filters designed using the original transformation of McClellan.