Quadrature Mirror Filter Banks Research Articles

Design of two-channel linear-phase quadrature mirror filter banks based on neural networks

An alternative weighted least-squares (WLS) implementation of a two-channel linear-phase quadrature mirror filter (QMF) banks can be efficiently solved in a parallel manner based on the Hopfield neural network (HNN). The author extends an improved structure of feedback neural network to formulate the error function in the optimization of QMF banks as a Lyapunov energy function to find the Hopfield-related parameters. Once these parameters are obtained and input to the network, the optimal filter coefficients of the QMF banks are therefore derived when the network achieves its final state. As compared to the previously developed neural-based method, the proposed framework can be easily applied to the design of QMF banks without incurring convergence problems. In additions, the architecture of the proposed technique is regular and simple with inherent parallelism and can be easily implemented by using analog VLSI technology in real-time. Simulation results are included to illustrate the proposed neural-based approach can achieve the same performance as the method of WLS.

Design of signed powers-of-two coefficient perfect reconstruction QMF Bank using CORDIC algorithms

Lattice structures have several advantages over the tapped delay line form, especially for the hardware implementation of general digital filters. It is also efficient for the implementation of quadrature mirror filter (QMF), because the perfect reconstruction is preserved under the coefficient quantization. Moreover, if lattice coefficients are implemented in signed powers-of-two (SPT), the hardware complexity can also be reduced. But the discrete coefficient space with the SPT representation is sparse when the number of nonzero bits is small. This paper proposes a structure of orthogonal QMF lattice with SPT coefficients, which has much denser discrete coefficient space than the conventional structure. While the conventional approaches directly quantize the lattice coefficients into SPT form, the proposed algorithm considers the quantization in the SPT angle space. For this, each lattice stage is implemented by the cascade of several variants of COordinate Rotation DIgital Computer. The resulting angle space and corresponding discrete coefficient space is much denser than the one generated by the conventional direct quantization approach. An efficient coefficient search algorithm for this structure is also proposed. Since the proposed architecture provides denser coefficient space, it shows less coefficient quantization error than the conventional QMF lattice

DESIGNING QUADRATURE MIRROR FILTER BANKS USING STEEPEST DESCENT METHOD

This paper proposes a new technique for the design of quadrature mirror filter (QMF) banks by exploiting steepest descent method. The design problem is formulated to minimize an objective function, which is a weighted sum of the pass band error and stop band residual energy of the low pass analysis filter of the QMF bank. The minimization has been carried out gradually by respective optimum step lengths in the corresponding steepest descent directions of a linear combination of the objective function and square of the reconstruction error of the QMF bank at the quadrature frequency by optimizing the filter tap weights. The design results show that the proposed method gives a comparable performance to the already existing methods.

Marquardt optimization method to design two-channel quadrature mirror filter banks

This paper proposes an efficient method for the design of two-channel, quadrature mirror filter (QMF) bank. The design problem is formulated to minimize an objective function, which is a linear combination of pass-band error and stop-band residual energy of the low-pass analysis filter of the filter bank, and the square error of the overall transfer function of the QMF bank at the quadrature frequency. A new algorithm has been developed to minimize the objective function by optimizing the filter tap weights by using Marquardt optimization method. Simulation results of the algorithm show that the performance of the proposed method is better than that of the already existing methods.

Time Domain Analysis of Two-Channel QMF Bank

This manuscript presents a time domain analysis of two-channel quadrature mirror filter (QMF) bank. Product terms in the system function of the QMF bank have been replaced by the respective convolution sums. The perfect reconstruction condition and an expression for ripple energy of the QMF bank have been obtained in time domain. Symmetry properties of the filters have been exploited which obviously reduces the computational complexity.

Fast decomposition of filterbanks for the state-of-the-art audio coding

This letter derives fast decomposition for the quadrature mirror filterbanks (QMFs) of the low power spectral band replication (SBR) tools in the MPEG high efficiency advanced audio coding (HE AAC) decoder. In contrast with the standard method where computation-intensive matrix operations are employed in the QMF, the proposed method decomposes the matrix operations into conventional discrete cosine transform of type II and III (DCT-II and DCT-III) and simple permutations for easy implementation. The computational complexity can be also reduced effectively by using fast algorithms for DCT.

Wideband adaptive beamforming array with improved radiation characteristics

An efficient subband adaptive beamforming array (ABA) using a quadrature mirror filter (QMF) bank is presented. For wideband beamforming, taps have to be added to the full-band ABA for efficient suppression of the interference. However, the introduction of multiple taps results in the addition of uncorrelated noise to the ABA. This results in power loss in the direction perpendicular to the ABA. In order to compensate for the loss introduced by the addition of taps, the proposed concept is investigated. This configuration shows improved signal gain and deep suppression of the interference in the direction perpendicular to the ABA.

Optimal Design of Complex Two-Channel IIR QMF Banks with Equiripple Response

The optimal design of complex infinite impulse response (IIR) two-channel quadrature mirror filter (QMF) banks with equiripple frequency response is considered. The design problem is appropriately formulated to result in a simple optimization problem. Therefore, based on a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the complex coefficients for the IIR QMFs. The effectiveness of the proposed technique is to form an appropriate Chebyshev approximation of a desired response and then find its solution from a linear subspace in several iterations. Finally, simulation results are presented for illustration and comparison.

Low-order IIR filter bank design

The advantage of infinite-impulse response (IIR) filters over finite-impulse response (FIR) ones is that the former require a much lower order (much fewer multipliers and adders) to obtain the desired response specifications. However, in contrast with well-developed FIR filter bank design theory, there is no satisfactory methodology for IIR filter bank design. The well-known IIR filters are mostly derived by rather heuristic techniques, which work in only narrow design classes. The existing deterministic techniques usually lead to too high order IIR filters and thus cannot be practically used. In this paper, we propose a new method to solve the low-order IIR filter bank design, which is based on tractable linear-matrix inequality (LMI) optimization. Our focus is the quadrature mirror filter bank design, although other IIR filter related problems can be treated and solved in a similar way. The viability of our theoretical development is confirmed by extensive simulation.

Near-perfect-reconstruction low-complexity two-band IIR/FIR QMF banks with FIR phase-compensation filters

In this paper, we present a novel approach for the design of near-perfect-reconstruction mixed allpass-/FIR-based two-band quadrature-mirror filter banks. The proposed design method is carried out in the polyphase domain, where FIR filters are employed for compensating the non-linear phase introduced by the allpass filters. In contrast to previous approaches in literature the FIR phase-compensation filters can be designed very efficiently using analytical expressions. Furthermore, starting from a generalized two-band structure, we introduce three special cases with different properties which are based on the same design principle. In all systems the remaining amplitude and phase distortions are controllable and can be made arbitrarily small at the expense of additional system delay. Simultaneously, aliasing can be minimized or completely canceled if further delay can be tolerated.

Performance Comparison of OFDM and WOFDM Based V-BLAST Wireless Systems

Wavelet based OFDM V-BLAST system design and its simulation results are briefly discussed in this article. The orthonormal wavelet bases are generated from Haar and Daubechies Quadrature Mirror Filter (QMF) bank. The BER performance of this system as compared to Fourier based OFDM V-BLAST system shows significant improvement.

DOA Estimation of Moving Target under the Clutter Environment by Applying MUSIC to the QMF Doppler Filter Bank

This paper proposes a new angular measurement system to a moving target in the presence of clutter. We apply MUSIC (MUltiple SIgnal Classification) to the outputs of a Doppler filter bank consisting of quadrature mirror filter (QMF). The comparison between QMF and the short time Fourier transform (STFT) as a preprocessor of MUSIC is also discussed. DOA estimation performance by QMF-MUSIC is nearly equal to that of STFT-MUSIC. On the other hand, QMF-MUSIC overcomes STFT-MUSIC in the aspect of computational cost. In a specific example in this paper, the proposal QMF bank by Daubechies (4th order) wavelet requires 80% fewer the number of multiplications and 25% fewer the number of additions than the FFT-based STFT filter bank.

The peak-constrained optimization of stable linear-phase IIR PRQMF bank

In this paper, we propose a new approach for optimization based stable linear-phase infinite impulse response (IIR) perfect reconstruction quadrature mirror filter (PRQMF) bank design. To this end, the design problem is formulated using stop-band energy, stability, transition-band, pass-band and stop-band ripples requirements as constraints. Lagrange multiplier method is used for the solution of optimization-based design problem. The brief conclusion with design example that illustrates the proposed design method is presented.

Design and VLSI implementation of QMF banks

The authors consider the design of multirate filterbanks for applications such as subband coding with IIR QMF (quadrature mirror filter) pairs. These offer reduced complexity and low latency at the expense of the loss of exact linear phase. In particular, consideration is given to the use of all-pass sections where linear phase is approximately achieved by being part of the objective in numerical optimisation experiments. This approach compares favourably with previous IIR based approaches. Finite wordlength design using simulated annealing shows that low coefficient wordlength may be used. This leads to efficient realisations with three-port adaptors. Using pipelining implementation, a flexible VLSI architecture is designed that can be used for a variety of subband decompositions. Layout and simulation of the design have been performed.

Discrete Wavelet Transform Basedon Cyclic Convolutions

A filterbank in which cyclic convolutions are used in place of linear convolutions will be referred to as a cyclic convolution filterbank (CCFB). A dyadic tree-structured CCFB can be used to perform a discrete wavelet transform suitable for coding based on symmetric extension methods. This paper derives two types of efficient implementation techniques for the tree-structured CCFB: one using complex arithmetic and one using only real arithmetic. In addition, the present paper analyzes in detail the perfect reconstruction (PR) condition for the two-channel CCFB and shows that this condition is much less restrictive than that of usual two-channel filterbanks. When each of the two-channel CCFBs constituting a tree-structured CCFB is designed to be PR, the whole system is PR. A quadrature mirror filter (QMF) CCFB having the PR property is demonstrated to be easily designed using a standard filter design subroutine. In contrast, designing a linear-phase PR FIR QMF bank that has good frequency response is not possible when filters are realized by linear convolutions.

Multicriterion optimized QMF bank design

The quadrature mirror filter (QMF) bank with multicriterion constraints such as minimal aliasing and/or minimal error coding is among the most important problems in filterbank design, for solving which linear algebra-based methods are still heuristic and do not always work, especially for large filter length. It is shown in this paper that this problem can be reduced either to convex linear matrix inequality (LMI) optimization (when filters are of nonlinear phase) or to semi-infinite linear (SIP) programming (when filters are of linear phase), which can be very efficiently solved either by the standard LMI solvers or our previously developed SIP solver. The proposed computationally tractable optimization formulations are confirmed by several simulations.

A solution to the wavelet transform optimization problem in multicomponent analysis

The wavelet transform has been shown to be an efficient tool for data treatment in multivariate calibration. However, previous works had the limitation of using fixed wavelets, which must be chosen a priori, because adjusting the wavelets to the data set involves a complex constrained optimization problem. This difficulty is overcome here and the mathematical background involved is described in detail. The proposed approach maximizes the compression performance of the quadrature-mirror filter bank used to process the spectra. After the optimization phase, the recently proposed successive projections algorithm is used to select subsets of wavelet coefficients in order to minimize collinearity problems in the regression. To demonstrate the efficiency of the entire strategy, a low-resolution ICP-AES was deliberately chosen to tackle a hard multivariate calibration problem involving the simultaneous multicomponent determination of Mn, Mo, Cr, Ni and Fe in steel samples. This analysis is intrinsically complex, due to strong collinearity and severe spectral overlapping, problems that are aggravated by the use of low-resolution optics. Moreover, there are also several regions in the spectra where the signal-to-noise ratio is poor. The results demonstrate that the optimization leads to models with better parsimony and prediction ability when compared to the fixed-wavelet approach adopted in previous papers.

Two-Channel FIR Filter Banks Utilizing the FRM Approach

The frequency-response masking (FRM) approach has been introduced as a means of generating narrow transition band linear-phase finite impulse response (FIR) filters with a low arithmetic complexity. This paper proposes an approach for synthesizing two-channel maximally decimated FIR filter banks utilizing the FRM technique. For this purpose, a new class of FRM filters is introduced. Filters belonging to this class are used for synthesizing nonlinear-phase analysis and synthesis filters for two types of two-channel filter banks. For the first type, there exist no phase distortion and aliasing errors, but this type suffers from a small amplitude distortion as for the well-known quadrature mirror filter (QMF) banks. Compared to conventional QMF filter banks, the proposed banks lower significantly the overall arithmetic complexity at the expense of a somewhat increased overall filter bank delay in applications demanding narrow transition bands. For the second type, there are also small aliasing errors, allowing one to reduce the arithmetic complexity even further. Efficient structures are introduced for implementing the proposed filter banks, and algorithms are described for maximizing the stopband attenuations of the analysis and synthesis filters in the minimax sense subject to the given allowable amplitude and/or aliasing errors. Examples are included illustrating the benefits provided by the proposed filter banks.

Design of two-channel linear-phase QMF banks based on real IIR all-pass filters

The design of two-channel linear-phase quadrature mirror filter (QMF) banks constructed by real infinite impulse response (IIR) digital all-pass filters is considered. The design problem is appropriately formulated to result in a simple optimisation problem. Using a variant of Karmarkar's algorithm, the optimisation problem can be efficiently solved through a frequency sampling and iterative approximation method to find the real coefficients for the IIR digital all-pass filters. The resulting two-channel QMF banks possess an approximately linear phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of the desired phase response and then finding its solution from a linear subspace in a few iterations. Finally, several simulation examples are presented for illustration and comparison.

DS/CDMA signature sequences based on PR-QMF banks

In this paper, we propose two classes of multivalued signature sequences for direct sequence code division multiple access (DS/CDMA) systems. The proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks (PR-QMF). The first and second classes are derived from the tree and lattice structure PR-QMF banks, respectively, and they both have perfect correlation properties for synchronous DS/CDMA systems. The second class, in addition, has generally better correlation properties than other well-known sequences in asynchronous DS/CDMA systems. Some numerical results for the performance of the asynchronous DS/CDMA systems with several sequences, including the second class of sequences, are obtained.