Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters

Two perfect-reconstruction structures for the two-channel quadrature mirror filter (QMF) bank, free of aliasing and distortions of any kind, in which the analysis filters have linear phase, are described. The structure in the first case is related to the linear prediction lattice structure. For the second case, new structures are developed by propagating the perfect-reconstruction and linear-phase properties. Design examples, based on optimization of the parameters in the lattice structures, are presented for both cases

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

Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks

A lattice structure and an algorithm are presented for the design of two-channel QMF (quadrature mirror filter) banks, satisfying a sufficient condition for perfect reconstruction. The structure inherently has the perfect-reconstruction property, while the algorithm ensures a good stopband attenuation for each of the analysis filters. Implementations of such lattice structures are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization. The lattice structure has the hierarchical property that a higher order perfect-reconstruction QMF bank can be obtained from a lower order perfect-reconstruction QMF bank, simply by adding more lattice sections. Several numerical examples are provided in the form of design tables

Polyphase networks, block digital filtering, LPTV systems, and alias-free QMF banks: a unified approach based on pseudocirculants

The relationship between block digital filtering and quadrature mirror filter (QMF) banks is explored. Necessary and sufficient conditions for alias cancellation in QMF banks are expressed in terms of an associated matrix, derived from the polyphase components of the analysis and synthesis filters. These conditions, called the pseudocirculant conditions, make it possible to unite QMF banks with the framework of block digital filtering directly. Absence of amplitude distortion in an alias-free QMF bank translates into the 'losslessness' property of the pseudocirculant matrix involved

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 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

Low power two-channel PR QMF bank using CSD coefficients and FPGA implementation

Finite impulse response (FIR) filter is a fundamental component in digital signal processing. Two-channel perfect reconstruction (PR) QMF banks are widely used in many applications, such as image coding, speech processing and communications. A practical lattice realization of two-channel QMF bank is developed in this thesis for dealing with the wide dynamic range of intermediate results in lattice structure. To achieve low complexity and low power consumption of two-channel perfect reconstruction QMF bank, canonical signed digit (CSD) number system is used for representing lattice coefficients in FPGA implementation. Utilization of CSD number system in lattice structures leads to more efficient hardware implementation. Many fixed-point simulations were done in Matlab in order to obtain the proper fixed-point word-length for different signals. Finally, FPGA implementation results show that perfect reconstruction signal is obtained by using the proposed method. Furthermore, the power consumption using CSD number system for representing lattice coefficients is less than that obtained by using two\u27s complement number system in two-channel QMF bank. A low complexity and low power two-channel PR QMF bank using CSD coefficients was realized

Optimum Design of Linear Phase Paraunitary Filter Bank & its Applications in Signal Processing

Filter Banks plays crucial role in signal processing and image processing as subband processing gives dominant results in time critical applications. In formal years, various Para unitary Linear Phase Filter Banks are proposed by following conventional and computational complex factorization and lattice approaches consisting of complex nonlinear optimization problems. One of the recent methods to design Filter Bank having properties of Linear Phase and Paraunitary is via Singular value decomposition technique which leads to optimum results compared to existing methods as most of the time it deals with matrix operations. In this paper, design benchmark is evaluated as two dominant optimization queries and reasonable key of each optimization query is solved by performing Singular Value Decomposition. Proposed Paper discusses linear phase condition of filter banks satisfying mirror image symmetry at analysis side and perfect reconstruction property at synthesis side. Singular Value Decomposition approach leads to fast and efficient simulation results compared to existing filter banks designs. Proposed method of filter bank design deals with any arbitrary channels and every length of the filters

Tree-structured complementary filter banks using all-pass sections

Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined