Linear Phase Quadrature Mirror Filter Research Articles

Performance of different window functions for designing quadrature mirror filter bank using closed form method

In this paper, a closed form method for designing two-channel linear phase Quadrature Mirror Filter (QMF) bank presented by Kumar et al. is examined and improved by exploiting different window functions for designing the prototype filter for QMF bank. In this method, the optimum pass-band edge frequency is determined via empirical formula instead of using single or multivariable optimisation technique for the given stop-band attenuation and roll-off factor (RF). This method reduces the overall computational time with minimum amplitude distortion to make suitable design of QMF bank for applications, which are carried out in real or quasi-real time. Simulation results presented in this paper how enhanced performance of this algorithm over the other existing algorithms.

Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints

In this article, a novel approach for 2-channel linear phase quadrature mirror filter (QMF) bank design based on a hybrid of gradient based optimization and optimization of fractional derivative constraints is introduced. For the purpose of this work, recently proposed nature inspired optimization techniques such as cuckoo search (CS), modified cuckoo search (MCS) and wind driven optimization (WDO) are explored for the design of QMF bank. 2-Channel QMF is also designed with particle swarm optimization (PSO) and artificial bee colony (ABC) nature inspired optimization techniques. The design problem is formulated in frequency domain as sum of L2 norm of error in passband, stopband and transition band at quadrature frequency. The contribution of this work is the novel hybrid combination of gradient based optimization (Lagrange multiplier method) and nature inspired optimization (CS, MCS, WDO, PSO and ABC) and its usage for optimizing the design problem. Performance of the proposed method is evaluated by passband error (ϕp), stopband error (ϕs), transition band error (ϕt), peak reconstruction error (PRE), stopband attenuation (As) and computational time. The design examples illustrate the ingenuity of the proposed method. Results are also compared with the other existing algorithms, and it was found that the proposed method gives best result in terms of peak reconstruction error and transition band error while it is comparable in terms of passband and stopband error. Results show that the proposed method is successful for both lower and higher order 2-channel QMF bank design. A comparative study of various nature inspired optimization techniques is also presented, and the study singles out CS as a best QMF optimization technique.

Design of Alias-Free Linear Phase Quadrature Mirror Filter Banks using Eigen value-Eigen vector Approach

An eigenvalue-eigenvector approach for the design of two-channel linear phase quadrature mirror filter (QMF) bank is proposed. To reduce the computational complexity, finite-duration impulse response (FIR) low-pass prototype filter of the filter bank is represented by polyphase components. The design problem is formulated to optimize the filter tap weights of the low-pass prototype filter of the QMF bank to minimize an objective function, which is the weighted sum of the square error of the filter bank transfer function at the quadrature frequency, pass-band error and stop-band residual energy of the low-pass prototype filter and measure of reconstruction ripple. The objective function has been minimized by an iterative algorithm. As compared to the existing design techniques, the proposed algorithm gives better performance in terms of mean square error in stop-band, number of iterations required and stop-band edge attenuation. Design examples are presented to validate the effectiveness of the proposed method.

An improved particle swarm optimization method for multirate filter bank design

In this paper, a new particle swarm optimization (PSO) based method is proposed for the design of a two-channel linear phase quadrature mirror filter (QMF) bank in frequency domain. The origional particle swarm optimization technique is modified by introducing the concept of Scout Bee from Artificial Bee Colony (ABC) technique for designing a low pass prototype filter having ideal filter characteristics in the passband and stopband regions, and its magnitude response at quadrature frequency is 0.707. The design problem is formulated as a linear combination of passband error and residual stop band energy of the low pass filter, and the square error of the overall transfer function of the QMF bank at the quadrature frequency π/2, in the transition band. The design results included in the paper clearly show the improvement of the proposed PSO technique over earlier reported results.

A hybrid method for designing linear-phase quadrature mirror filter bank

In this work, a hybrid method in frequency domain for design of a linear-phase quadrature mirror filter bank is proposed. The nonlinear least square hybrid method based on Levenberg-Marquardt (LM) and Quasi-Newton (QN) is developed for the design of a low-pass prototype filter whose responses in the passband and stopband are ideal, and the filter bank response at quadrature frequency is 0.707. The proposed method is employed to optimize the quadratic measure of ideal characteristics of the prototype filter and filter bank at quadrature frequency. Performance and effectiveness of the proposed method in terms of peak reconstruction error (PRE), mean squares error in passband and stopband regions, and error in transition band at quadrature frequency are shown through numerical examples and comparison of the results with other existing method. It was found that the proposed method is very simple and easy to implement for QMF bank design problem.

An Improved Method for Designing Quadrature Mirror Filter Banks via Unconstrained Optimization

This paper proposes an algorithm to design a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is presented systematically as an unconstrained optimization that minimizes the weighted sum of error of transfer function of the filter bank at quadrature frequency, stopband energy and the passband error of a prototype filter (PF). A new method is developed for the design of a low pass prototype filter for QMF banks. For solving given optimization problem, Quasi-Newton optimization technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and effectiveness of this method. An application of the proposed method is considered in the area of subband coding of the images.

A simple method for designing quadrature mirror filter banks via quadratic constrained optimisation

This paper proposes a simple algorithm for the design of a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is formulated as a quadratic constrained least square minimisation that optimises the performance of a prototype filter (PF) and distortion transfer function of filter bank at quadrature frequency. A new method is developed for the design of a low pass prototype filter for QMF banks. For solving the given optimisation problem, a sequential quadratic programming (SQP) technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and the effectiveness of the proposed method. An application of this method is considered in the area of subband coding of the images.

A closed form design method for the two-channel quadrature mirror filter banks

This paper presents a simple and efficient closed form method for designing two-channel linear phase quadrature mirror filter (QMF) banks with prescribed stopband attenuation and channel overlap. The proposed method is based on optimum passband edge frequency, which is calculated using empirical formulas instead of using optimization algorithm. Different window functions are used to design the prototype filter for QMF banks. When compared to other existing methods, the proposed method reduces computation time (CPU time) and amplitude distortion (eam), which results in a simpler and efficient design procedure for the applications where the design must be carried out in real or quasi-real-time. Several design examples are included to illustrate the proposed method and its improved performances over other exiting methods. An application of the proposed method is considered in the area of subband coding of ultrasound image.

FFT-Based Computation of Shift Invariant Analytic Wavelet Transform

This letter introduces an analytic wavelet transform based on linear phase quadrature mirror filters (QMFs). The computation of the analytic signal and the reconstruction of the signal is carried by the fast Fourier transform (FFT)-based algorithm. The transform yields energy preserving and shift invariant decimated analytic wavelet coefficients, which are free of aliasing effects. The present method can be implemented in the microprocessor and VLSI environment using a commercial FFT chip

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 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.

Design of QMF banks based on derivative information

New L2 objective functions for the design of quadrature mirror filter (QMF) banks are proposed. They are based on the derivative information of the reconstruction error. Simple and explicit matrix-form formulas for the proposed objective functions are derived. Efficient design methods are proposed by incorporating a separability technique into the derived optimality conditions on prototype filters. The proposed design methods need only solve linear equation iteratively without nonlinear optimisation. Design examples demonstrate that good low-delay QMF banks and linear-phase QMF banks can be obtained in only a few iterations. Compared with the conventional approach, the new approach leads to QMF banks with larger stopband attenuation and smaller reconstruction errors.

Design of two-channel equiripple FIR linear-phase quadrature mirror filters using the vector space projection method

A new technique for designing finite impulse response (FIR) quadrature mirror filters (QMFs) is proposed. The approach is based on the vector space projection method (VSPM). Convex constraint sets and their projections that capture the properties of the desired QMFs are given. The proposed approach produces equiripple filters. This method is compared with the classical Johnston's (1980) method and is shown to have certain advantages.

Linear-phase quadrature mirror filters with coefficients −1, 0 and + 1

This paper considers the linear-phase quadrature mirror filters (LP-QMFs) with coefficients constrained to the values of −1, 0 and + 1. A new filter structure and a design technique based on a recently developed weighted least-squares (WLS) algorithm are presented. First, we design an LP-QMF with continuous coefficients using the WLS algorithm. This design process provides two favourable design results that the prototype LP analysis filter has least-squares stopband response and the resulting QMF bank shows quasi-equiripple reconstruction error behavior. In conjunction with the new proposed filter structure, we then present an efficient method to obtain a design solution with coefficients restricted to −1, 0 and + 1 in the minimax sense. Several design examples demonstrating the effectiveness of the proposed technique are provided.

Design of linear-phase quadrature mirror filters with powers-of-two coefficients

This paper considers the design of linear-phase quadrature mirror filters (QMF's) with powers-of-two coefficients. A design method based on a recently developed weighted least-squares (WLS) algorithm is presented. First, we design QMF's with continuous coefficients using the WLS algorithm. This design process provides two favorable design results that the prototype analysis filter has quasi-equiripple stopband response and the resulting QMF bank shows quasi-equiripple reconstruction error behavior. To avoid the effect of nonuniformly distributed coefficient grid due to discretization of the filter coefficients, a procedure is then performed for obtaining an appropriate filter gain factor. Finally, utilizing the resulting error weighting function obtained by the WLS algorithm, we propose an efficient discrete optimization process to obtain a discrete solution in the minimax optimal sense. Design examples demonstrating the effectiveness of the proposed method are included.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A filter based bit allocation scheme for subband compression of HDTV

The authors compare the subband compression capabilities of eight filter sets (consisting of linear-phase quadrature mirror filters (QMFs), perfect reconstruction filters, and nonlinear phase wavelets) at different bit rates, using-a filter-based bit allocation procedure. Using DPCM and PCM in HDTV subband coding, it is found that QMFs have an edge over the rest.