Perfect reconstruction QMF banks for two-dimensional applications

A theory is outlined whereby it is possible to design a M x N channel two-dimensional quadrature mirror filter bank which has perfect reconstruction property. Such a property ensures freedom from aliasing, amplitude distortion, and phase distortion. The method is based on a simple property of certain transfer matrices, namely the losslessness property

Alias-free, real coefficient m-band QMF banks for arbitrary m

Based on a generalized framework for alias free QMF banks, a theory is developed for the design of uniform QMF banks with real-coefficient analysis filters, such that aliasing can be completely canceled by appropriate choice of real-coefficient synthesis filters. These results are then applied for the derivation of closed-form expressions for the synthesis filters (both FIR and IIR), that ensure cancelation of aliasing for a given set of analysis filters. The results do not involve the inversion of the alias-component (AC) matrix

A Spectral Factorization Approach to Pseudo-QMF Design

A new approach to the design of M-channel pseudoquadrature-mirror-filter (QMF) banks is presented. In this approach, the prototype filter is obtained as a spectral factor of a 2Mth band filter. This completely eliminates the need for optimization whereas in conventional pseudo-QMF designs, the main computational effort is in optimization of the prototype. As in the conventional approach, the aliasing cancellation (AC) constraint ensures that all the significant aliasing terms are canceled. The overall transfer function T(z) of the analysis/synthesis system has a linear phase and an approximately “flat” magnitude response in the frequency region ε ≤ ω ≤ (π - ε), where ε depends on the transition bandwidth of the prototype and 0 < ε < (π/2M). Three design examples are included

Bidimensional PR QMF with FIR Filters

Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed

Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices

A technique is developed for the design of analysis filters in an M-channel maximally decimated, perfect reconstruction, finite-impulse-response quadrature mirror filter (FIR QMF) bank that has a lossless polyphase-component matrix E(z). The aim is to optimize the parameters characterizing E(z) until the sum of the stopband energies of the analysis filters is minimized. There are four novel elements in the procedure reported here. The first is a technique for efficient initialization of one of the M analysis filters, as a spectral factor of an Mth band filter. The factorization itself is done in an efficient manner using the eigenfilters approach, without the need for root-finding techniques. The second element is the initialization of the internal parameters which characterize E(z), based on the above spectral factor. The third element is a modified characterization, mostly free from rotation angles, of the FIR E(z). The fourth is the incorporation of symmetry among the analysis filters, so as to minimize the number of unknown parameters being optimized. The resulting design procedure always gives better filter responses than earlier ones (for a given filter length) and converges much faste

Quadrature-Mirror Filter Design for the sub-band coding of Digital Video Signals

The paper firstly reviews the basic two-channel subband coding system and its implementation using both quadrature mirror filter (QMF) and conjugate quadrature filter (CQF) designs. Their features and performance characteristics for the one-dimensional case are examined and then using the principle of separability, 2-D QMF-CQF implementations are constructed, as the product of two l-D transfer functions. Examples of 2-D QMF-CQFs in band-splitting configurations for video applications are explored and discusse

A novel fast and reduced redundancy structure for multiscale directional filter banks

2007-2008 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

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

Compaction Filter as an Optimum Solution for Multirate Subband Coder of Cyclostationary Signals

A consistent theory of optimum subband coding of zero mean wide-sense cyclostationary signals with N-periodic statistics is presented in this paper. Blocked polyphase representation of the analysis and synthesis filter banks is introduced as an effective way of multirate subband coder description. Optimum energy compaction using Nyquist-M process is presented as a solution for maximizing the coding gain of the coder. In two definitions and four theorems the author proves that Nyquist-M filters fulfill necessary and sufficient conditions imposed on subband signals. Results from Matlab simulations are presented to support theoretical conclusions

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