A genetic algorithm for the design of finite word length arbitrary response cascaded IIR digital filters

This paper describes a genetic algorithm (GA) for the design of optimal finite word length (FWL) infinite impulse response filters with arbitrary response functions using a cascade of second order sections. Such structures could be used for the implementation of filters for an unrestricted range of responses and are usually characterised by having low sensitivity to variations in word length and simple stability tests. A distinct feature of the GA is that it allows the single-step-design from a specified filter template hence avoiding additional errors being introduced as is the case with the two-stage-design approach. Depending on the specified template, the GA could be used to design filters with arbitrary response functions including those of the main classical filters with considerably reduced coefficient wordlengths. The paper commences by highlighting FWL effects in digital filters and reviewing existing attempts in using GAs in digital filter design. Next, the paper describes the implementation technique adopted here and reports on the results obtained using examples of 8th and 10th order filters.