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

Using integer coefficient filters, which can be efficiently implemented using primitive operator directed graphs, a multi-objective optimisation using genetic algorithms is used to jointly optimise filter performance and complexity. Complexity is measured using a variation of the RAG-n algorithm (Dempster and MacLeod, 1995). The optimisation maintains a non-dominated set of best-compromise solutions, which allows the designer greater choice. A flexible design tool is described which allows the designer to interactively vary many of the optimisation parameters. The proposed techniques are demonstrated for the design of both one- and two-dimensional linear phase FIR filters with both low-pass and band-pass characteristics. The method is shown to provide significantly better results than previous methods. Also considered is the design of perfect reconstruction filter pairs, which are the main building block within discrete wavelet transforms. To achieve this the use of a combination of transformation and factorisation approaches is proposed. 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.