Showing papers on "Quadrature mirror filter published in 1998"

Oversampled filter banks

Abstract: Perfect reconstruction oversampled filter banks are equivalent to a particular class of frames in l/sup 2/(Z). These frames are the subject of this paper. First, the necessary and sufficient conditions of a filter bank for implementing a frame or a tight frame expansion are established, as well as a necessary and sufficient condition for perfect reconstruction using FIR filters after an FIR analysis. Complete parameterizations of oversampled filter banks satisfying these conditions are given. Further, we study the condition under which the frame dual to the frame associated with an FIR filter bank is also FIR and give a parameterization of a class of filter banks satisfying this property. Then, we focus on non-subsampled filter banks. Non-subsampled filter banks implement transforms similar to continuous-time transforms and allow for very flexible design. We investigate the relations of these filter banks to continuous-time filtering and illustrate the design flexibility by giving a procedure for designing maximally flat two-channel filter banks that yield highly regular wavelets with a given number of vanishing moments.

Orthogonal transmultiplexers in communication: a review

Abstract: This paper presents conventional and emerging applications of orthogonal synthesis/analysis transform configurations (transmultiplexer) in communications. It emphasizes that orthogonality is the underlying concept in the design of many communication systems. It is shown that orthogonal filter banks (subband transforms) with proper time-frequency features can play a more important role in the design of new systems. The general concepts of filter bank theory are tied together with the application-specific requirements of several different communication systems. Therefore, this paper is an attempt to increase the visibility of emerging communication applications of orthogonal filter banks and to generate more research activity in the signal processing community on these topics.

Discrete frequency warped wavelets: theory and applications

Abstract: We extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discrete-time by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that the discrete-time warped wavelets lead to well-defined continuous-time wavelet bases, satisfying a warped form of the two-scale equation. The shape of the wavelets is not invariant by translation. Rather, the "wavelet translates" are obtained from one another by allpass filtering. We show that the phase of the delay element is asymptotically a fractal. A feature of the warped wavelet transform is that the cut-off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the time-frequency plane, which can be designed by selecting as little as a single parameter. This feature is particularly desirable in cochlear and perceptual models of speech and music, where accurate bandwidth selection is an issue. As our examples show, by defining pitch-synchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudo-periodic signals is greatly enhanced.

Oversampled cosine-modulated filter banks with arbitrary system delay

Abstract: Design methods for perfect reconstruction (PR) oversampled cosine-modulated filter banks with integer oversampling factors and arbitrary delay are presented. The system delay, which is an important parameter in real-time applications, can be chosen independently of the prototype lengths. Oversampling gives us additional freedom in the filter design process, which can be exploited to find FIR PR prototypes for oversampled filter banks with much higher stopband attenuations than for critically subsampled filter banks. It is shown that for a given analysis prototype, the PR synthesis prototype is not unique. The complete set of solutions is discussed in terms of the nullspace of a matrix operator. For example, oversampling allows the design of PR filter banks having unidentical prototypes (of equal and unequal lengths) for the analysis and synthesis stage. Examples demonstrate the increased design freedom due to oversampling. Finally, it is shown that PR prototypes being designed for the oversampled case can also serve as almost-PR prototypes for critically subsampled cosine-modulated pseudo QMF banks.

On the space of orthonormal wavelets

Abstract: The space of orthonormal wavelets is described by a set of parameters for which a simple recurrence generates the coefficients for all orthonormal perfect-reconstruction FIR filters of arbitrary length. The space splits into two halves, each containing the time reverse of the other's filters. A MATLAB implementation is given. This paper considers the generation of two-channel perfect reconstruction quadrature mirror filter banks corresponding to compactly supported orthonormal wavelets.

An improved method for the design of FIR quadrature mirror-image filter banks

Abstract: A new method for the design of general finite-duration impulse response (FIR) quadrature mirror-image filter (QMF) banks that eliminates the computation of large matrices is proposed. The design problem is formulated to include low-delay QMF banks, which are highly desirable in some applications. The paper concludes with design results and comparisons that show that conventional QMF banks can be designed with only a fraction of the computational effort required by a method due to Chen and Lee (1992). On the other hand, in the case of low-delay QMF banks, the proposed method can increase the stopband attenuation substantially compared with what can be achieved by existing methods.

Two-dimensional orthogonal filter banks and wavelets with linear phase

Abstract: Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of order-factorable wavelets imposes a simple constraint on each of its polynomial order-1 factors. We thus obtain a simple and complete method of constructing orthogonal order-factorable wavelets with linear phase. This method is exemplified by design in the case of four-band separable sampling. An interesting result that is similar to the one well-known in the one-dimensional (1-D) case is obtained: orthogonal order-factorable wavelets cannot be both continuous and have four-fold symmetry.

Method and apparatus for detecting voice activity

Abstract: A voice activity detector that implements a fast wavelet transformation using filter pairs. A quadrature high pass filter provides an output signal corresponding to the upper half of the Nyquist frequency and a quadrature low pass filter provides an output signal corresponding to the lower half of the Nyquist frequency. The quadrature high pass filter is useful for catching and isolating transients in the input signal and the quadrature low pass filter is useful for fine frequency analysis. The voice activity detector can utilize multiple decomposition levels that are arranged in a pyramid or tree formation to increase the reliability of the voice activity decision. For example, the output of the quadrature low pass filter can be further decomposed using a second pair of filters. The voice activity decision can be generated by comparing a signal power estimate for the output of the filter pairs to threshold levels that are specific for each filter or frequency range. The reliability of the voice activity decision is maximized by training the system to determine the optimum threshold levels and by basing the decision on a combination of the signal outputs. While increasing the number of decomposition levels increases the reliability of the voice activity decision, three decomposition levels is usually sufficient for detecting speech activity.

Time-Frequency and Time-Scale Signal Analysis by Harmonic Wavelets

Abstract: New details of the theory of harmonic wavelets are described and provide the basis for computational algorithms designed to compute high-definition time-frequency maps. Examples of the computation of phase using the complex harmonic wavelet and methods of signal segmentation based on amplitude and phase are described.

Generalized coiflets with nonzero-centered vanishing moments

Abstract: We show that imposing a certain number of vanishing moments on a scaling function (e.g., coiflets) leads to fairly small phase distortion on its associated filter bank in the neighborhood of DC. However, the phase distortion at the other frequencies can be much larger. We design a new class of real-valued, compactly supported, orthonormal, and nearly symmetric wavelets (we call them generalized coiflets) with a number of nonzero-centered vanishing moments equally distributed on scaling function and wavelet. Such a generalization of the original coiflets offers one more free parameter, the mean of the scaling function, in designing filter banks. Since this parameter uniquely characterizes the first several moments of the scaling function, it is related to the phase response of the lowpass filter at low frequencies. We search for the optimal parameter to minimize the maximum phase distortion of the filter bank over the lowpass half-band. Also, we are able to construct nearly odd-symmetric generalized coiflets, whose associated lowpass filters are surprisingly similar to those of some biorthogonal spline wavelets. These new wavelets can be useful in a broad range of signal and image processing applications because they provide a better tradeoff between the two desirable but conflicting properties of the compactly supported and real-valued wavelets, i.e., orthonormality versus symmetry, than the original coiflets.

Estimation of fractal signals using wavelets and filter banks

Abstract: A filter bank design based on orthonormal wavelets and equipped with a multiscale Wiener filter was recently proposed for signal restoration and for signal smoothing of 1/f family of fractal signals corrupted by external noise. The conclusions obtained in these papers are based on the following simplificative hypotheses: (1) The wavelet transformation is a whitening filter, and (2) the approximation term of the wavelet expansion can be avoided when the number of octaves in the multiresolution analysis is large enough. In this paper, we show that the estimation of 1/f processes in noise can be improved avoiding these two hypotheses. Explicit expressions of the mean-square error are given, and numerical comparisons with previous results are shown.

Synthesis subband filter in MPEG-II audio decoding

Abstract: An MPEG-II audio decoder with a synthesis subband filter includes a fast IMDCT (Inverse Modified Discrete Cosine Transform) module and an IPQMF (Inverse Pseudo Quadrature Mirror Filter) module. The fast IMDCT module involves a butterfly stage of input subband samples which requires only about ¼ the amount of multiplier-accumulate computation of the ISO suggested method. The IPQMF module involves an efficient memory configuration which requires only half size of the standard synthesis subband filter bank.

A direct approach to the design of QMF banks via frequency domain optimization

Abstract: This paper studies the design of quadrature mirror filter (QMF) banks via frequency domain optimization. A direct approach is adopted that gives the necessary and sufficient condition for perfect reconstruction (PR). While analysis filter banks are designed to achieve frequency domain specifications required for subband coding, synthesis filter banks are designed to minimize the reconstruction error in frequency domain. The criterion used to measure the reconstruction error is H/sub /spl infin// or Chebyshev norm (sup-norm). State-space solutions are derived for the H/sub /spl infin// optimization, and numerical algorithms are developed to obtain the optimal synthesis filter bank. Moreover, the asymptotic PR property is established for optimal H/sub /spl infin// solution of the synthesis filter bank.

Scalable VLSI architectures for lattice structure-based discrete wavelet transform

Abstract: In this paper, we develop a scalable VLSI architecture employing a two-channel quadrature mirror filter (QMF) lattice for the one-dimensional (1-D) discrete wavelet transform (DWT). We begin with the development of systematic scheduling, which determines the filtering instants of each resolution level, on the basis of a binary tree. Then input-output relation between lattices of the QMF bank is derived, and a new structure for the data format converter (DFC) which controls the data transfer between resolution levels is proposed. In addition, implementation of a delay control unit (DCU) that controls the delay between lattices of the QMF is proposed. The structures for the DFC and DCU are regular, scalable, and require a minimum number of registers, and thereby lead to an efficient and scalable architecture for the DWT. A scalable architecture for the inverse DWT is also developed in a similar manner. Finally, pipelining of the proposed architecture is considered.

Asymptotically perfect reconstruction in hybrid filter banks

Abstract: A procedure to derive a hybrid filter bank from a digital filter bank is presented. Perfect reconstruction is shown to be possible only asymptotically. The stability of the analog filters is ensured if FIR or IIR stable filters are used in the digital prototype.

Music Signal Segmentation Using Tree-Structured Filter Banks

Abstract: For music signal segmentation, an 11-stage tree-structured filter bank that leads to wavelet packet analysis was designed and implemented. The tree-structured filter bank has sufficient frequency resolution over a wide range of frequencies, while the time resolution at high frequencies satisfies the minimum time resolution for the human ear. To improve selectivity, a new family of quadrature mirror filters (QMFs) with a narrow transition region and a low reconstruction error was implemented.

An efficient approach for the design of nearly perfect-reconstruction QMF banks

Abstract: In this work, an approach for the design of a class of quadrature mirror filter (QMF) banks is presented based on a combination of IIR analysis filters and FIR synthesis filters. By examining the phase property of the all-pass based analysis filter, a condition on the synthesis part for a perfect reconstruction is established, making it possible to realize a nearly perfect-reconstruction (PR) filter bank by using a nonlinear-phase FIR synthesis filter. The distinct feature of the proposed mixed IIR/FIR filter bank is that it enjoys both a small reconstruction error and a low design and implementation complexity.

Digital filter and modulator

Abstract: A digital filter and modulator provides programmable distinctive modulation on a programmable frequency selective basis with channelization. The digital channelization processor includes a plurality of channels. Each channel includes a filter and transform circuit that convert a real input signal to a quadrature signal that has a magnitude signal and a phase signal. The quadrature signal is offset and converted back to a real signal that is temporarily held and phase shifted. The digital filter and modulator minimize throughput delay and eliminate analog tolerance and inflexibility problems while eliminating digital processing overflow difficulties.

Iterative design of two-channel IIR perfect construction QMG filters

Abstract: A simple rapidly convergent method is described for the design of two-channel IIR perfect reconstruction quadrature mirror filters For any prescribed characteristic, it has been shown how one can construct a stable two-channel IIR banks, starting from any random transmission zero locations A simple rapidly convergent search algorithm is also described for the determination of the exact locations of these transmission zeros, such that the filter has equiripple pass and stop responses as well as almost constant group delay Illustrative examples are also given to show that the proposed design method competes very well with the existing design methods © 1998 John Wiley & Sons, Ltd

Multidimensional Two-channel Linear Phase FIR Filter Banksand Wavelet Bases with Vanishing Moments

Abstract: In the paper new design methods for multidimensional two-channel perfect reconstruction (PR) FIR filter banks are described. The filters have linear phase, achieve an arbitrarily high number of vanishing moments and can be used to obtain biorthogonal wavelet bases. Two-dimensional wavelet bases with square, rectangular, and hexagonal support are constructed. A design method that trades off vanishing moments and frequency selectivity is described. These two properties are both important in subband coding, but they each require a share of the degrees of freedom available from the total number of filter coefficients. Novel analytic formulae are derived and are applied to provide illustrative examples.

Efficient finite impulse response filter implementation for CDMA waveform generation

Abstract: A finite impulse response filter including a first circuit for providing plural delayed signals in response to an input signal. A second circuit is included for multiplying respective ones of the delayed signals by a corresponding coefficient and providing a respective intermediate signal in response thereto. A third circuit selectively changes the sign of respective ones of a first set of the intermediate output signals to provide a set of component in-phase signals. A fourth circuit selectively changes the sign of respective ones of a second set of the intermediate output signals to provide a set of component quadrature signals. The component in-phase signals are combined to provide an in-phase output signal and the component quadrature signals are combined to provide a quadrature output signal. In the illustrative implementation, the coefficients are generated in accordance with an industry standard via a storage device such as a register bank. The third and fourth circuits are controlled by a pseudo-noise sequence generator. The inventive implementation affords a considerable degree of efficiency in design in that in-phase and quadrature filter outputs are generated from a single filter thereby obviating the need for a second filter required by conventional teachings.

Convergence results on the design of QMF banks

Abstract: This correspondence considers the design of quadrature mirror filter (QMF) banks whose analysis and synthesis filters are FIR and have linear phase. The design criterion is of least-squares type. An iterative computation algorithm is proposed, and its convergence is proven that offers new insight to the design of QMF banks and relates it to a more general nonlinear optimization problem.

Design and VLSI implementation of multirate filter banks based on approximately linear phase allpass sections

Abstract: The design of multirate filterbanks for applications such as subband coding with IIR QMF (quadrature mirror filter) pairs is explored. These offer reduced complexity and low latency at the expense of the loss of exact linear phase. In particular we consider the use of allpass sections where linear phase is approximately achieved by being part of the objective in numerical optimisation. The results for phase distortion in reconstruction experiments compare favourably with previous IIR based approaches. Finite wordlength design using simulated annealing shows that low coefficient wordlengths may be used. This leads to efficient realisations with 3-port adaptors. Using pipelined implementation, a flexible VLSI architecture is designed that can be used for a variety of subband decompositions. Layout and simulation of the design has been performed.

Optimization of filter banks based on properties of the input signal

Abstract: Filter banks and wavelets have found applications in signal compression, noise removal, and in many other signal processing contexts. In this tutorial we review a number of recent results on the optimization of filter banks based on the knowledge of the input. The main emphasis will be the minimization of error due to subband quantization, and its connection to principal component reconstruction. Both uniform and nonuniform filter banks are considered.

Low-complexity, perfect reconstruction FIR QMF bank

Abstract: A low-complexity, perfect reconstruction quadrature mirror filter (QMF) bank is proposed, which requires only 50% of the multiplications and additions of the existing QMF banks per output sample. In addition, the new QMF bank only needs to solve a set of linear equations instead of the commonly required nonlinear optimisation technique for the prototype filter.

Effects of finite word length in two-channel QMF banks

Abstract: Finite word-length effects in multirate two-channel quadrature mirror filter (QMF) banks are presented. Aliasing cancellation, amplitude and/or phase distortions, and the perfect-reconstruction property due to finite-precision effects are investigated. A finite-precision model is applied to several types of QMF banks and the results are reported.

Iterative design method for pseudo QMF banks

Abstract: An iterative algorithm for the design of M channel maximally decimated cosine-modulated pseudo quadrature mirror-image filter (QMF) banks is proposed. The objective function is minimized applying a practical implementation of the modified Newton method which has high design efficiency for a near perfect reconstruction and reduces the reconstruction error. Several design examples are included, and some comparisons are made with other existing design methods, to demonstrate the proposed algorithm.