A neural networks approach for the design of 2-d zero-phase FIR filters

A back-propagation neural networks (BPNN) approach was presented to design general two-dimensional (2-D) zero-phase finite-impulse response (FIR) digital filters. By minimizing the frequency-domain error function, the BPNN design method was obtained. The solution was presented as a parallel algorithm to approximate the desired frequency response specification. Thus, the method avoids matrix inversion, and makes a fast calculation of the filter's coefficients possible. It is also shown that when this solution is used to design a class of zerophase filters with quadrantally symmetric or anti-symmetric frequency response specification, some further computational savings can be achieved. The implementation of the approach was described together with some design guidelines, and two optimal design examples were given to demonstrate the effectiveness of the proposed approach.