The design of analogue and digital filters using genetic algorithms

The conventional approach to filter design is to select one of the standard polynomial transfer functions that satisfies the response specification, followed by the implementation of the transfer function in one of the standard circuit structures. In many cases this approach is inadequate and an optimisation approach is required. The need for this can arise in a various ways, including non-standard response specification, and the consideration of practical effects such as finite-arithmetic effects and computational complexity for digital filters, and component selection and device imperfections in analogue filters. Classical hill-climbing optimisation methods have succeeded in certain cases but are less suited to the general design task which can be mixed discrete/continuous, can have many local minima, and have high dimensionality. Recently genetic algorithm (GA) optimisation methods have emerged as a powerful approach to solving the more difficult optimisation problems. Publications are emerging in the literature on GAs applied to filter design and promise to move filter design significantly forwards to the ultimate goal of a single-step design from general specification to full practical implementation. This paper aims to: give a brief tutorial on GAs; provide a set of commented references on GAs applied to filter design; and present some new work on single-step design of finite wordlength (FWL) IIR digital filters that simultaneously satisfy magnitude and phase template specifications.