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     

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     

A new method for adaptive IIR filter design based on tabu search algorithm

Adaptive digital filters have proven their worth in a wide range of applications such as channel equalisation, noise reduction, echo cancelling, and system identification. These filters can be broadly classified into two groups: finite impulse–response (FIR) and infinite impulse–response (IIR) filters. IIR filters have become the target of increasing interest because these filters can reduce the filter order significantly as compared to FIR filters. Tabu search is a heuristic optimisation algorithm which has been originally developed for combinatorial optimisation problems. It simulates the general rules of intelligent problem solving and has the ability of discovering the global minima in a multi-modal search space. In this work, a novel method based on tabu search is described for the design of adaptive IIR filters.     

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.     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

Weighted least-squares approximation of FIR by IIR digital filters

This paper presents a method for the weighted least-squares approximation of finite impulse response (FIR) filters by infinite impulse response (IIR) filters. It is shown, how a solution to this approximation problem can be obtained by solving a related pure least-squares approximation problem. For the latter, we utilize a generalized version of a previously published technique with low computational complexity and guaranteed stability of the IIR filters. Unlike the well-established model-reduction approaches that are carried out in the state space, our method works directly with the numerator and denominator coefficients of the transfer functions. Thus, the influence of finite-precision arithmetic on the results is small. This makes our approach applicable for the approximation of large-order FIR filters and allows the usage of arbitrarily shaped weighting functions. It is shown that our method can successfully be employed to achieve a uniform approximation     

Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L/sub /spl infin// error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.     

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     

Intelligent learning algorithms for adaptive digital filters

It is wellknown that gradient search fails in adaptive IIR filters, since their mean-square error surfaces may be multi-modal. In the letter a new approach based on learning algorithms is shown to be capable of performing global optimisation. The new algorithms are suitable for both adaptive FIR and IIR filters.<>     

Design and Factorization of Two-Channel Perfect Reconstruction Filter Banks with Causal-Stable IIR Filters

In this paper, new design and factorization methods of two-channel perfect reconstruction (PR) filter banks (FBs) with casual-stable IIR filters are introduced. The polyphase components of the analysis filters are assumed to have an identical denominator in order to simplify the PR condition. A modified model reduction is employed to derive a nearly PR causal-stable IIR FB as the initial guess to obtain a PR IIR FB from a PR FIR FB. To obtain high quality PR FIR FBs for carrying out model reduction, cosine-rolloff FIR filters are used as the initial guess to a nonlinear optimization software for solving to the PR solution. A factorization based on the lifting scheme is proposed to convert the IIR FB so obtained to a structurally PR system. The arithmetic complexity of this FB, after factorization, can be reduced asymptotically by a factor of two. Multiplier-less IIR FB can be obtained by replacing the lifting coefficients with the canonical signal digitals (CSD) or sum of powers of two (SOPOT) coefficients.     

Boundary implications for frequency response of interval FIR andIIR filters

It is shown that vertex implication results in parameter space apply to interval trigonometric polynomials. Subsequently, it is shown that the frequency responses of both interval FIR and IIR filters are bounded by the frequency responses of certain extreme filters. The results apply directly in the evaluation of properties of designed filters, especially because it is more realistic to bound the filter coefficients from above and below instead of determining those with infinite precision because of finite arithmetic effects. Illustrative examples are provided to show how the extreme filters might be easily derived in any specific interval FIR or IIR filter design problem     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

A direct approach to H2 optimal deconvolution ofperiodic digital channels

This paper studies the H₂ optimal deconvolution problem for periodic finite impulse response (FIR) and infinite impulse response (IIR) channels. It shows that the H₂ norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities (LMIs) without resorting to the commonly used lifting technique. The optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints. Under this framework, the optimization of both the FIR and IIR periodic deconvolution filters can be made convex, solved using the interior point method, and computed by using the Matlab LMI Toolbox. The robust deconvolution problem for periodic FIR and IIR channels with polytopic uncertainties are further formulated and solved, also by convex optimization and the LMIs. Compared with the lifting approach to the design of periodic filters, the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties, especially for IIR deconvolution filter design. The obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance     

Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks

This paper introduces two classes of cosine-modulated causal and stable filter banks (FBs) with near perfect reconstruction (NPR) and low implementation complexity. Both classes have the same infinite-length impulse response (IIR) analysis FB but different synthesis FBs utilizing IIR and finite-length impulse response (FIR) filters, respectively. The two classes are preferable for different types of specifications. The IIR/FIR FBs are preferred if small phase errors relative to the magnitude error are desired, and vice versa. The paper provides systematic design procedures so that PR can be approximated as closely as desired. It is demonstrated through several examples that the proposed FB classes, depending on the specification, can have a lower implementation complexity compared to existing FIR and IIR cosine-modulated FBs (CMFBs). The price to pay for the reduced complexity is generally an increased delay. Furthermore, two additional attractive features of the proposed FBs are that they are asymmetric in the sense that one of the analysis and synthesis banks has a lower computational complexity compared to the other, which can be beneficial in some applications, and that the number of distinct coefficients is small, which facilitates the design of FBs with large numbers of channels.     

Variable wordlengths in filters with least-squares error criterion

Variable coefficient wordlengths in combination with a multiplier reduces the computational complexity of fixed-point IIR digital filters with minimax error specification. When variable wordlengths are used for the least-squares error specification here, improved filters are achieved without resorting to discrete optimisation. Also. The wordlength allocation for the least squares criterion gives near-optimum results for filters with minimax specification     

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     

Non-symmetric lattice structure for pole zero filters

This communication generalizes the lattice structure of IIR digital filters and shows its relation with classical structures. The algorithm for computing the corresponding reflection coefficients is given. It is also shown that this algorithm computes the greatest common divisor of the numerator and the denominator of the transfer function.     

Design of 1-D Stable Variable Fractional Delay IIR Filters

In this brief, a two-stage approach for the design of 1-D stable variable fractional delay infinite-impulse response (IIR) digital filters is proposed. In the first stage, a set of fixed delay stable IIR filters are designed by minimizing a quadratic objective function, which is defined by integrating error criterion with IIR filter stability constraint condition. Then, the final design is determined by fitting each of the fixed delay filter coefficients as a 1-D polynomial. Two design examples are given to show the effectiveness of the proposed design method