A Dichotomy of the Application of Genetic Algorithms in the Optimal Design of Multirate Filter Banks

Abstract

This paper considers theoretical issues regarding reconstruction errors and conditions for near perfect reconstruction (PR) of the input signal for a uniform and non-uniform multiband multirate filter banks. The main emphasis is on the application of genetic algorithms in the optimization process of the design of the two forms of filter banks with further consideration of a dichotomy of design issues and optimization of the uniform and non-uniform filter banks. The issues of design of uniform multiband filter banks is based on the use of a single prototype square root raised cosine low pass filter from which the multiband filters are derived using cosine modulation technique. On the other hand, non-uniform multiband filter banks are designed using multiple square root raised cosine prototype filters from which the analysis and synthesis filters are derived using the closed form approximation. The optimization process using genetic algorithms is thus based on perturbing the bandwidth and roll-off factor of the prototype filters to generate near-optimal results.