Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

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

Classical sampling theorems in the context of multirate and polyphase digital filter bank structures

The recovery of a signal from so-called generalized samples is a problem of designing appropriate linear filters called reconstruction (or synthesis) filters. This relationship is reviewed and explored. Novel theorems for the subsampling of sequences are derived by direct use of the digital-filter-bank framework. These results are related to the theory of perfect reconstruction in maximally decimated digital-filter-bank systems. One of the theorems pertains to the subsampling of a sequence and its first few differences and its subsequent stable reconstruction at finite cost with no error. The reconstruction filters turn out to be multiplierless and of the FIR (finite impulse response) type. These ideas are extended to the case of two-dimensional signals by use of a Kronecker formalism. The subsampling of bandlimited sequences is also considered. A sequence x(n ) with a Fourier transform vanishes for |ω|&ges;Lπ/M, where L and M are integers with L<M, can in principle be represented by reducing the data rate by the amount M/L. The digital polyphase framework is used as a convenient tool for the derivation as well as mechanization of the sampling theorem

The perfect-reconstruction QMF bank: New architectures, solutions, and optimization strategies

n this paper, a scheme for perfect reconstruction in M channel, maximally decimated QMF banks is first presented, for arbitrary M. The solutions are such that the analysis and synthesis filters are FIR and of the same length. Based on the theory, lattice structures for the two-channel case are derived, which offer an efficient design as well as implementation procedure for two-channel perfect reconstruction systems. Such lattice implementations are robust in the sense that the perfect-reconstruction property is preserved in spite of coefficient quantization

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

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

Multiband Analog-to-Digital Conversion

The current trend in the world of digital communications is the design of versatile devices that may operate using several different communication standards in order to increase the number of locations for which a particular device may be used. The signal is quantized early on in the reciever path by Analog-to-Digital Converters (ADCs), which allows the rest of the signal processing to be done by low complexity, low power digital circuits. For this reason, it is advantageous to create an architecture that can quantize different bandwidths at different frequencies to suit several different communication protocols. This thesis outlines the design of an architecture that uses multiple ADCs in parallel to quantize several different bandwidths of a wideband signal. A multirate filter bank is then applied to approximate perfect reconstruction of the wideband signal from its subband parts. This highly flexible architecture is able to quantize signals of varying bandwidths at a wide range of frequencies by using identical hardware in every channel, which also makes for a simple design. A prototype for the quantizer used in each channel, a frequency-selective fourth-order sigma-delta (CA ) ADC, was designed and fabricated in a 0.5 pm CMOS process. This device uses a switched-capacitor technique to implement the frequency selection in the front-end of the CA ADC in each channel. Running at a 5MHz sample rate, the device can select any of the first sixteen 156.25kHz wide bands for conversion. Testing results for this fabricated part are also presented