Minimax design of two-channel IIR QMF banks with arbitrary groupdelay

The paper deals with the minimax design of two-channel infinite impulse response (IIR) QMF banks with arbitrary group delay, for which the IIR analysis filters and the resulting filter bank possess the frequency response optimal in the minimax (L_∞) sense. Utilising a lattice structure for the denominators of the IIR analysis filters, a design technique is presented based on an approximation scheme and a weighted least-squares (WLS) algorithm, previously developed by one of the authors for solving the resulting design problem that is basically a nonlinear optimisation problem. During the design process, this technique finds the tap coefficients for the numerator and the reflection coefficients for the denominator of the prototype IIR analysis filter simultaneously. The stability of the designed prototype IIR analysis filter is ensured by incorporating an efficient stabilisation procedure to make all of the reflection coefficient values fall between -1 and +1. Computer simulations show the effectiveness of the proposed design technique     

Design of two-channel IIR filter banks with arbitrary group delay

The nonlinear optimisation problem that results from considering the design of a two-channel nonuniform division filter bank is solved. This is through a frequency sampling and iterative approximation technique to find the tap coefficients and the reflection coefficients for the numerator and the denominator of the IIR analysis filters. An efficient stabilisation procedure ensures that the reflection coefficients lie in (-1,1). Simulation examples are provided for illustration     

A technique for the design of 2-D recursive digital filters with guaranteed stability

In the present technique, the denominator and numerator in the filter are designed separately and recursively. First, the denominator coefficients, derived from the stable matrix of the Roesser model (the Fornasini-Marchesini second model), are found by minimizing a performance index through the alternating variable method. The numerator coefficients are then determined analytically by solving linear simultaneous equations. The above process will be repeated until there is negligible change in the objective function. Finally, a numerical example is given to illustrate the utility of the proposed technique.     

A maximally flat group delay recursive digital filter with improved passband magnitude response

A technique is proposed for the design of a recursive digital filter with maximally flat responses in both magnitude and group delay. In comparison to the previous designs [1]-[3], the magnitude and group delay always show smooth responses no matter what the difference is in the polynomial degrees of the numerator and denominator.     

Design of two-channel low-delay IIR nonuniform-division filter banks using L/sub 1/ error criteria

The design of a two-channel nonuniform-division filter (NDF) bank with infinite impulse response (IIR) analysis/synthesis filters and low group delay in the sense of L/sub 1/ error criteria is considered. The problem formulation results in a nonlinear optimisation problem. Based on a variant of Karmarkar's algorithm, the optimisation problem is solved through a frequency sampling and iterative approximation technique to find the tap coefficients and the reflection coefficients for the numerator and the denominator of the IIR analysis filters. An efficient stabilisation procedure ensures that the reflection coefficients lie in (-1, 1). Simulation results are provided for illustration and comparison.     

Efficient Recursive Digital Filters using Combined Look-Ahead Denominator Distribution and Numerator Decomposition

This paper presents a new efficient method for designing stable look-ahead pipelined recursive digital filters with reduced multipliers. The multiplier savings are obtained by generating pipelined transfer functions which combine numerator decomposition with look-ahead denominator distribution. This is achieved by not restricting the denominator to either the clustered or scattered forms while also preserving term count from the unpipelined filter transfer function. The coefficients of the pipelined transfer function are obtained by running product solved using matrices and an algorithm with two stages: pre and post distribution, each having a multiplier cost which are minimised independently. The proposed method can produce pipelined filter designs requiring fewer multipliers when compared with previously reported methods. For example, for a range of second order transfer functions and pipelining levels, an average 40% reduction in multipliers can be achieved while an 18% reduction in multipliers necessary for pipelining is obtained for a sixth order filter. Furthermore, the proposed two-stage algorithm can accommodate pipelined adders as well as pipelined multipliers in the recursive filter structure, avoiding delay penalties otherwise suffered by previously reported methods. A detailed analysis has been carried out confirming that filters designed using the proposed method do not suffer increased noise.     

Adaptive allpass filtering for nonminimum-phase systemidentification

Efficient algorithms for the recursive identification of nonminimum-phase systems using an adaptive allpass filter together with an adaptive transversal filter are introduced. Both the output and input sequences are assumed to be available, and the proposed technique basically uses a linear predictor at the output of the system to equalise its magnitude response and an allpass filter to match its phase response. The mirror image property of the numerator and denominator polynomials in an allpass transfer function reduces the number of adaptive parameters needed compared to an unconstrained recursive identification scheme. Computer simulations are used to support the claims made in the paper     

Stable IIR notch filter design with optimal pole placement

This paper presents a two-stage approach for designing an infinite impulse response (IIR) notch filter. First, the numerator of the transfer function of the IIR notch filter is obtained by placing the zeros at the prescribed notch frequencies. Then, the denominator polynomial is determined by using an iterative scheme in which the optimal pole placements are found by solving a standard quadratic programming problem. For stability, the pole radius in the single notch filter design is specified by the designer, and in the multiple notch filter design, the pole radius is constrained by using the implications of Rouche's theorem. Examples are included to illustrate the effectiveness of the proposed techniques     

Recursive digital filters with predetermined group delay andChebyshev stopband attenuation

Recently, a conformal mapping technique has been described whereby the transfer function of a recursive digital filter with prescribed group delay and Chebyshev stopband can be obtained in such a way that the numerator and denominator polynomials are different in order. It is shown here that such a transfer function can also be determined using the familiar bilinear transformation and the well known method in the s-domain. Numerical examples are included to demonstrate the technique     

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.     

Minimax design of two-dimensional parallelogram filter banks

The authors present a technique for the minimax design of two-dimensional (2-D) parallelogram filter bank (PFB) systems with linear-phase analysis/synthesis filters. To achieve perfect reconstruction, the required analysis filters must have parallelogram-shaped frequency responses. In general, the original design problem is found to be an optimisation problem with nonlinear constraints. The authors present a linearisation approach to reformulate the design problem. As a result, updating the filter coefficient vector at each iteration for the original design problem can be accomplished by searching the gradient of the linearised optimisation problem. They further present an efficient method based on a modified Karmarkar's algorithm for computing the required gradient vector and finding the required step size analytically. Therefore the filter coefficients can easily be computed by solving only linear equations at each iteration during the design process. The effectiveness of the proposed technique is shown by computer simulations     

Design of Constrained Causal Stable IIR Filters Using a New Second- Order-Cone-Programming-Based Model-Reduction Technique

This brief proposes a new method for designing infinite-impulse response (IIR) filter with peak error and prescribed flatness constraints. It is based on the model reduction of a finite-impulse response function that satisfies the specification by extending a method previously proposed by Brandenstein. The proposed model-reduction method retains the denominator of the conventional techniques and formulates the optimal design of the numerator as a second-order cone programming problem. Therefore, linear and convex quadratic inequalities such as peak error constraints and prescribed number of zeros at the stopband for IIR filters can be imposed and solved optimally. Moreover, a method is proposed to express the denominator of the model-reduced IIR filter as a polynomial in integer power of z, which efficiently facilitates its polyphase implementation in multirate applications. Design examples show that the proposed method gives better performance, and more flexibility in incorporating a wide variety of constraints than conventional methods     

Minimax design of two-channel low-delay perfect-reconstruction FIRfilter banks

The authors deal with the design problem of low-delay perfect-reconstruction filter banks for which the FIR analysis and synthesis filters have equiripple magnitude response. Based on the minimax error criterion, the design problem is formulated in such a manner that the coefficients for the FIR analysis filters can be found by minimising the weighted peak error of the designed analysis filters, subject to the perfect-reconstruction constraints. A design technique based on a modified dual-affine scaling variant of Karmarkar's (1989) algorithm, in conjunction with approximation schemes, is then developed for solving the resulting nonlinear optimisation problem. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

一种数字全通滤波器的设计方法研究

研究了一种数字全通滤波器的设计方法.对于一个平稳的全通滤波器,其分母多项式一定具有最小相位.该方法是基于最小相位滤波器的复倒谱系数和其群迟延函数以及其系统函数之间的关系,通过一个非线性的递归方程求解分母多项式的系数.由全通滤波器的特性已知,分母系数可以完全决定全通滤波器的传递函数.仿真结果表明这种方法能够使所设计滤波器的群延迟特性在整个频率范围内以近似理想的群延迟特性存在.并结合实现提出了一种用FIR逼近IIR的方法.     

电流传输器型滤波器的一种系统设计

利用电流传输器ＣＣⅡ±进行的系统设计，电路组成是规则化的；滤波特性原则上为低通；传输函数分子和分母多项式的系数能单独调节，并可用通式表示     

Finite-horizon robust Kalman filter design

We study the problem of finite-horizon Kalman filtering for systems involving a norm-bounded uncertain block. A new technique is presented for robust Kalman filter design. This technique involves using multiple scaling parameters that ran be optimized by solving a semidefinite program. The use of optimized scaling parameters leads to an improved design. A recursive design method that can be applied to real-time applications is also proposed     

Complex notch filter design using allpass filter

Complex coefficient IIR notch filter design problems are investigated. The specification of a notch filter is first transformed into that of an allpass filter. An effective approach to the design of this desired allpass filter is developed. The realisation of the proposed notch filter is equivalent to the realisation of an allpass filter. Owing to the mirror-image symmetry relation between the numerator and denominator polynomials of allpass filters, the notch filter can be realised by a computationally efficient lattice structure with very low sensitivity     

Design of IIR digital filters based on eigenvalue problem

This paper presents a new method for designing IIR digital filters with optimum magnitude response in the Chebyshev sense and different order numerator and denominator. The proposed procedure is based on the formulation of a generalized eigenvalue problem by using Remez exchange algorithm. Since there exist more than one eigenvalue in the general eigenvalue problem, we introduce a very simple selection rule for the eigenvalue to be sought for where the rational interpolation is performed if and only if the positive minimum eigenvalue is chosen. Therefore, the solution of the rational interpolation problem can be obtained by computing only one eigenvector corresponding to the positive minimum eigenvalue, and the optimal filter coefficients are easily obtained through a few iterations. The design algorithm proposed in this paper not only retains the speed inherent in the Remez exchange algorithm but also simplifies the interpolation step because it has been reduced to the computation of the positive minimum eigenvalue. Some properties of the filters such as lowpass filters, bandpass filters, and so on are discussed, and several design examples are presented to demonstrate the effectiveness of this method     

Use of a Luenberger observer to control the numerator and denominator of a transfer function

It is shown that a Luenberger observer may be used to convert a transfer function having a numerator of degree m and a denominator of degree n (with m?n?1) into one having a numerator of degree n+m?1 and a denominator of degree 2n?1, with the denominator polynomial and n?1 of the numerator coefficients assignable arbitrarily.