Design and Multiplierless Implementations of 9^th order linear-Phase Bireciprocal Lattice Wave Digital Wavelet Filter Banks

In this paper, a filter bank structure for the implementation of infinite impulse response (IIR) discrete wavelet transform (DWT) is proposed. Bireciprocal lattice wave filters (BLWDFs) are utilized in a linear-phase design of 9th order IIR wavelet filter bank (FB). Each of the two branches in the structure of the BLWDF bank realizes an all-pass filter. Filters of this bank belong to the intermediate design group, maintaining linear-phase property with best roll-off characteristics in their frequency responses. The design is first simulated using Matlab7.10 programming in order to investigate the resulting wavelet filter properties and to find the suitable wordlength to represent the BLWDF’s coefficients in quantized forms for best selection of some prescribed performance measures. All adopted measures show an excellent closeness to some typical cases. Each coefficient in the resulting structure is realized in a multiplierless manner after representing it as sum-of-powers-of-two (SPT). Multiplications are then achieved by only shift and add. Multiplierless FPGA implementations of the proposed IIR wavelet filter banks are also achieved with less complexity and high operating frequency.