On the efficient realization and design of multiplier-less two-channel perfect reconstruction FIR filter banks

Abstract

This paper proposes two methods for the design and implementation of multiplier-less two-channel perfect reconstruction (PR) FIR filter banks (FB). The first method is based on the structure by Phoong which can be used to realize linear-phase and nonlinear-phase FIR FBs. A new design method is proposed to search for the sum of powers-of-two (SOPOT) coefficients so that the FB can be realized without multipliers. This method requires much less design time than using genetic algorithm and produces a number of solutions with different performance/complexity tradeoff. A new technique, called multiplier block, is proposed to further reduce the number of adders for their realization. Design results show that significant number of adders can be saved using the new technique. In the second method, we employ the lifting scheme to factor a general PR FB designed by constrained optimization. The lifting scheme not only allows us to reduce the arithmetic complexity asymptotically by a factor of two, but also allows us to approximate the lifting coefficients by SOPOT coefficients yielding multiplier-less realization. Design results, using again the random search technique, suggest that low complexity FB with good frequency characteristic can be obtained. A low-delay PR FB and a SOPOT approximation to the 9/7 wavelet filters are given as examples.