A Fast O(n) Algorithm For Adaptive Filter Bank Design

Designing optimal filer banks for subband coding applications has recently attracted considerable attention [1]-[5]. In particular, the authors have developed an adaptive algorithm based on stochastic gradient descent (SGD) that enables one to optimize two channel paraunitary filter banks in an on-line fashion [3]. The idea has also been extended to the case of tree-structured filter banks [4]. The computational complexity of the algorithm proposed in [3] is proportional to N 2 where N is the number of stages in the paraunitary lattice. In this paper we derive a fast algorithm which reduces the amount of computation to O(N). We also show that the new algorithm can be implemented using an IIR lattice. Some issues regarding numerical stability of the IIR implementation are also discussed. 1. INTRODUCTION A two channel paraunitary filter bank can be implemented using QMF lattices that insure perfect reconstruction irrespective of the specific choice of lattice coefficients [7]. For su..