Design of FIR paraunitary filter banks for subband coding using a polynomial eigenvalue decomposition

The problem of paraunitary filter bank design for subband coding has received considerable attention in recent years, not least because of the energy preserving property of this class of filter banks. In this paper, we consider the design of signal-adapted, finite impulse response (FIR), paraunitary filter banks using polynomial matrix EVD (PEVD) techniques. Modifications are proposed to an iterative, time-domain PEVD method, known as the sequential best rotation (SBR2) algorithm, which enables its effective application to the problem of FIR orthonormal filter bank design for efficient subband coding. By choosing an optimisation scheme that maximises the coding gain at each stage of the algorithm, it is shown that the resulting filter bank behaves more and more like the infiniteorder principle component filter bank (PCFB). The proposed method is compared to state-of-the-art techniques, namely the iterative greedy algorithm (IGA), the approximate EVD (AEVD), standard SBR2 and a fast algorithm for FIR compaction filter design, called the window method (WM). We demonstrate that for the calculation of the subband coder, the WM approach offers a low-cost alternative at lower coding gains, while at moderate to high complexity, the proposed approach outperforms the benchmarkers. In terms of run-time complexity, AEVD performs well at low orders, while the proposed algorithm offers a better coding gain than the benchmarkers at moderate to high filter order for a number of simulation scenarios

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..