Meta-heuristic evolutionary algorithms for the design of optimal multiplier-less recombination filter banks

Abstract

This paper proposes a design for multiplier-less recombination non-uniform filter banks (RNUFBs) optimized using meta-heuristic algorithms. The structure consists of an M-channel uniform filter bank, with some channels combined by the synthesis filters of a transmultiplexer (TMUX), yielding non-uniform sub-bands. When any structure is realized in hardware, it is necessary to have low power consumption and a small chip area. These can be achieved by replacing the multipliers with shifters and adders. Once the continuous coefficient recombination non-uniform filter bank is designed, the coefficients are converted to the canonic-signed-digit (CSD) space to make the design multiplier-less, so as to reduce the complexity of the hardware implementation. To reduce the number of adders and shifters in the multiplier-less implementation, the filter coefficients are rounded with a restricted number of signed power-of-two (SPT) terms, which may cause degradation in the performance of the RNUFBs. To improve the performance of the CSD rounded filters and filter bank, meta-heuristic algorithms such as the artificial bee colony (ABC) algorithm, harmony search algorithm (HSA) and gravitational search algorithm (GSA) are deployed. Of these meta-heuristic algorithms, GSA is found to give the best performance. The method proposed in this paper results in non-uniform filter banks with rational sampling factors which are multiplier-less and have linear-phase and near-perfect-reconstruction.