Genetic synthesis of reduced complexity filters and filter banks using primitive operator directed graphs

Using integer coefficient filters, which can be efficiently implemented usi ng primitive operator directed graphs, a multi-objective optimisation using genetic algorithms is used to jointly optimise filter performance and comp lexity. Complexity is measured using a variation of the RAG-n algorithm (De mpster and MacLeod, 1995). The optimisation maintains a non-dominated set o f best-compromise solutions, which allows the designer greater choice. A fl exible design tool is described which allows the designer to interactively vary many of the optimisation parameters. The proposed techniques are demon strated for the design of both one- and two-dimensional linear phase FIR fi lters with both low-pass and band-pass characteristics. The method is shown to provide significantly better results than previous methods. Also consid ered is the design of perfect reconstruction filter pairs, which are the ma in building block within discrete wavelet transforms. To achieve this the u se of a combination of transformation and factorisation approaches is propo sed. In this way, the problem is significantly simplified, allowing a GA to successfully find high performance filter banks with significantly better results than previous methods.