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

Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property

Based on the concept of losslessness in digital filter structures, this paper derives a general class of maximally decimated M-channel quadrature mirror filter banks that lead to perfect reconstruction. The perfect-reconstruction property guarantees that the reconstructed signalhat{x} (n)is a delayed version of the input signal x (n), i.e.,hat{x} (n) = x (n - n_{0}). It is shown that such a property can be satisfied if the alias component matrix (AC matrix for short) is unitary on the unit circle of the z plane. The number of channels M is arbitrary, and when M is two, the results reduce to certain recently reported 2-channel perfect-reconstruction QMF structures. A procedure, based on recently reported FIR cascaded-lattice structures, is presented for optimal design of such FIR M-channel filter banks. Design examples are included

Design of Two-Channel Low-Delay FIR Filter Banks using Constrained Optimization

This paper shows the efficiency of using constrained optimization for designing two-channel low-delay finite impulse response filter banks. The filter banks under consideration are quadrature mirror filter (QMF) banks and perfect reconstruction (PR) biorthogonal filter banks. The design problems for both types of banks are stated as constrained minimization problems in forms that enable us to minimize the maximum of the stopband energies of the analysis filter(s) subject to the given passband and transition band constraints of the filter(s) as well as subject to the given allowable reconstruction error for QMF banks or the PR property for biorthogonal filter banks. For solving the given optimization problems a modified Dutta-Vidyasagar optimization technique has been used. The efficiency of the proposed design methods is illustrated by means of some examples

Improved approach for design of perfect reconstruction FIR QMF banks, with lossless lattice structures

A property of FIR (finite-impulse response) lossless systems is introduced, leading to substantial improvement in the sign procedure for perfect-reconstruction QMF (quadrature mirror filter) banks. The property enables the designer to initialize the coefficients of a lattice structure (which characterizes the analysis bank), in such a way as to speed up to the convergence. A design example is provided. Compared to other methods, the proposed method is shown to converge faster, and always leads to much improved attenuation characteristics for a given filter length

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

Fixed-analysis adaptive-synthesis filter banks

Subband/Wavelet filter analysis-synthesis filters are a major component in many compression algorithms. Such compression algorithms have been applied to images, voice, and video. These algorithms have achieved high performance. Typically, the configuration for such compression algorithms involves a bank of analysis filters whose coefficients have been designed in advance to enable high quality reconstruction. The analysis system is then followed by subband quantization and decoding on the synthesis side. Decoding is performed using a corresponding set of synthesis filters and the subbands are merged together. For many years, there has been interest in improving the analysis-synthesis filters in order to achieve better coding quality. Adaptive filter banks have been explored by a number of authors where by the analysis filters and synthesis filters coefficients are changed dynamically in response to the input. A degree of performance improvement has been reported but this approach does require that the analysis system dynamically maintain synchronization with the synthesis system in order to perform reconstruction. In this thesis, we explore a variant of the adaptive filter bank idea. We will refer to this approach as fixed-analysis adaptive-synthesis filter banks. Unlike the adaptive filter banks proposed previously, there is no analysis synthesis synchronization issue involved. This implies less coder complexity and more coder flexibility. Such an approach can be compatible with existing subband wavelet encoders. The design methodology and a performance analysis are presented.Ph.D.Committee Chair: Smith, Mark J. T.; Committee Co-Chair: Mersereau, Russell M.; Committee Member: Anderson, David; Committee Member: Lanterman, Aaron; Committee Member: Rosen, Gail; Committee Member: Wardi, Yora

Applications of Lattice Filters to Quadrature Mirror Filter Banks

Presented is a method for designing and implementing lattice filters to be used in Quadrature Mirror Filter (QMF) Banks. Quadrature Mirror Filter Banks find use in applications where a signal must be spilt into subbands operated on then reconstructed in the output. Because of their structure, lattice filters do this very well and allow perfect reconstruction, even when the lattice coefficients must be quantized. In this paper QMF\u27s and Lattice Filters are derived and analyzed. Application of the lattice filter is presented along with a design program and example of its use to implement a QMF. The computer aided design procedure allows the user to input the stop-band frequency, normalized to the sampling frequency, and the desired attenuation. The resulting outputs are the lattice coefficients, and the Finite Impulse Response (FIR) coefficients of an FIR filter having the same characteristics. The program selects a set of coefficients based on optimal coefficients that are within the desired tolerance. The filter design program was written in FORTRAN, with the filter coefficients stored in a data file on disk. Programs were written in MATHCAD© to show the lattice filter response and to simulate the QMF using these coefficients

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