Design of quadrature mirror filter banks with canonical signed digit coefficients using genetic algorithms.

This thesis is about the use of a genetic algorithm to design QMF bank with canonical signed digit coefficients. A filter bank has applications in areas like video and audio coding, data communication, etc. Filter bank design is a multiobjective optimization problem. The performance depends on the reconstruction error of the overall filter bank and the individual performance of the composing lowpass filter. In this thesis we have used reconstruction error of the overall filter bank as our main objective and passband error, stopband error, stopband and passband ripples and transition width of the individual lowpass filter as constraints. Therefore filter bank design can be formulated as single objective multiple constraint optimization problem. A unique genetic algorithm is developed to optimize filer bank coefficients such that the corresponding system\u27s response matches that of an ideal system with an additional constraint that all coefficients are in canonical signed digit (CSD) format. A special restoration technique is used to restore the CSD format of the coefficients after crossover and mutation operators in Genetic algorithm. The proposed restoration technique maintains the specified word length and the maximum number of nonzero digits in filter banks coefficients. Experimental results are presented at the end. It is demonstrated that the designed genetic algorithm is reliable, and efficient for designing QMF banks.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .U67. Source: Masters Abstracts International, Volume: 43-05, page: 1785. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

In this paper, a new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. Such structurally PR filterbanks are parameterized by two functions (β(z) and α(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical β(z) and α(z) was considered by Phoong et al. with the delay parameter M chosen as 2N - 1. In this paper, the more general case of using different nonlinear-phase FIR functions for β(z) and α(z) is studied. As the linear-phase constraint is relaxed, the lengths of β(z) and α(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.published_or_final_versio

Wavelet Filter Banks in Perceptual Audio Coding

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research

A System Approach to the Design of Multirate Filter Banks.

This dissertation studies the design of multirate filter banks by adopting a so-called system approach. The design issue of Johnston\u27s method is first investigated in which an explicit expression of the reconstruction error is derived using Lyapunov stability theory, and new convergent iterative algorithms are proposed through non-linear optimization. The results are extended to the two-dimensional filter banks. The design issue of more general multirate filter banks is also investigated through model matching method. Using standard results from modern control theory, new design algorithms are developed which minimize the reconstruction error while completely eliminating the aliasing error. State-space realizations, inner-outer factorizations, and optimal Hankel norm approximation are used to reduce the complexity of computation and improve the accuracy of the proposed design algorithms