No abstract

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. Index Terms-Orthonormal subband coders, paraunitary matrix, principal component filter banks, polynomial matrix eigenvalue decomposition, sequential best rotation. I. INTRODUCTION P ARAUNITARY filter banks have been extensively studied for subband coding and applied to an increasing number of applications, including noise reduction [1], audio and image coding [2] and digital communications [3], [4]. For the case where the order of the filters is unconstrained, it is known that a principal component filter bank (PCFB) [5], [6] exists and is an orthonormal or paraunitary (PU) filter bank that is simultaneously optimal for a number of objectives [7], including mean-squared error and coding gain for subband coding in data compression applications [8]. This is also true when the filter orders are constrained to be not greater

No abstract

This version is available at https://strathprints.strath.ac.uk/32647/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL. 46, NO. 8, AUGUST 1999 1081 Design of Near Perfect Reconstruction Oversampled Filter Banks for Subband Adaptive FiltersMoritz Harteneck, Stephan Weiss, and Robert W. StewartAbstract-In this brief, a design algorithm for real-valued and complexvalued oversampled filter banks which yield a low level of inband alias and enable simple subband adaptive structures is presented. The filter banks are either based on complex modulation of a real-valued low-pass prototype or on the direct or modulated setups of real-valued filter banks. If real-valued filter banks are required, then the different channels will have different subsampling ratios so that the bandpass sampling theorem is not violated. This brief also presents design examples of real-valued and complex-valued filter banks.Index Terms-Adaptive filtering, filter bank design, oversampled nearperfect reconstruction filter banks.

Abstract-A polynomial eigenvalue decomposition of parahermitian matrices can be calculated approximately using iterative approaches such as the sequential matrix diagonalisation (SMD) algorithm. In this paper, we present an improved SMD algorithm which, compared to existing SMD approaches, eliminates more off-diagonal energy per step. This leads to faster convergence while incurring only a marginal increase in complexity. We motivate the approach, prove its convergence, and demonstrate some results that underline the algorithm's performance.