Aimin Jiang

IIR Digital Filter Design With New Stability Constraint Based on Argument Principle

This paper presents a weighted least squares (WLS) method for IIR digital filter design using a new stability constraint. Utilizing the reweighting technique, an iterative second-order cone programming (SOCP) method is employed to solve the design problem, such that either linear or second-order cone constraints can be further incorporated. In order to guarantee the stability of designed IIR digital filters, a new stability constraint with a prescribed pole radius is derived from the argument principle (AP) of complex analysis. As compared with other frequency-domain stability constraints, the AP-based stability constraint is both sufficient and necessary. Since the derived stability constraint cannot be directly incorporated in the iterative SOCP method, the similar reweighting technique is deployed to approximate the stability constraint in a quadratic form, which is then combined with the WLS iterative design process. Filter design examples are presented to demonstrate the effectiveness of the proposed iterative SOCP method.

Minimax Design of IIR Digital Filters Using SDP Relaxation Technique

This paper presents a new algorithm using semidefinite programming (SDP) relaxation to design infinite impulse response digital filters in the minimax sense. Unlike traditional design algorithms that try to directly minimize the error limit, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit of the approximation error. Given a fixed error limit at each iteration, the SDP relaxation technique is adopted to formulate the design problem in a convex form. In practice, the true minimax design cannot be always obtained. Thus, a regularized feasibility problem is adopted in the bisection searching procedure. The stability of the designed filters can also be guaranteed by adjusting the regularization coefficient. Unlike other sequential design methods, the proposed algorithm tries to find a feasible solution at each iteration of the sequential design procedure within a feasible set defined by the relaxed constraints. This feasible set is not restricted within the neighborhood of a given point obtained from the previous iteration. Thus, the proposed method can avoid being trapped in the locally minimum point. Four examples are presented in this paper to demonstrate the effectiveness of the proposed method.

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.

Network localization using angle of arrival

In this paper, we propose two localization methods using angle of arrival (AoA) information. We assume that nodespsila axis orientations are unknown. Therefore, all AoA measurements are employed to calculate the angle differences of two different nodes viewed by the third one. Distance measurements between two nodes within the communication range are also utilized in the first method. For the second method, only AoA information is required. As all distance and angle measurements are accurate enough, the localization problem can be formulated as a linear program (LP). Otherwise, by introducing auxiliary variables, it can be cast as a quadratic program (QP). Simulation examples are presented to illustrate the effectiveness of the proposed methods.

Minimax Design of IIR Digital Filters Using Iterative SOCP

In this paper, a novel method for IIR digital filter design using iterative second-order cone programming (SOCP) is proposed under the minimax criterion. The convex relaxation technique is utilized to transform the original nonconvex design problem into an SOCP problem. By solving the relaxed problem, the lower and upper bounds on the optimal value of the original problem can be obtained. In order to reduce the discrepancy between the original and relaxed design problems, an iterative procedure is developed. At each iteration, a linear constraint is further incorporated to guarantee the convergence of the iterative procedure. In practice, the convergence speed can be further improved by introducing a soft threshold variable in this linear constraint. Accordingly, a regularization term is incorporated in the objective function of the design problem at each iteration. The stability of the designed filters can be ensured by a new positive realness based linear constraint. Several examples are presented to demonstrate the effectiveness of the proposed method.

IIR Digital Filter Design with Novel Stability Criterion Based on Argument Principle

A method for designing IIR digital filters with a novel stability criterion based on the argument principle is proposed in this paper. Unlike the stability criteria used in some design algorithms, this stability condition is both sufficient and necessary. In the paper, the weighted least-squares (WLS) design of IIR filters is first formulated as an iterative quadratic programming (QP) problem without any constraint. Then the stability criterion is incorporated in the quadratic form at each iteration. Two examples are presented to illustrate the effectiveness of the proposed approach.

Recent Advances in FIR Approximation by IIR Digital Filters

This paper provides a tutorial review on several recent design methods for approximating FIR by IIR digital filters with reduced order. These methods can generally be classified as time-domain method, frequency-domain method, and mixed-domain method. The numerator and denominator of IIR digital filters are obtained in different steps under some criteria. The final result of each design method cannot be ensured to be optimal or even suboptimal for such approximation problem. Also, some methods do not incorporate a stability constraint hence stability is not really ensured. In this paper the design steps of each of these methods are outlined. Through three examples, we analyze their performances and identify the strengths and weaknesses of each design method

Minimax IIR digital filter design using SOCP

An iterative second-order cone programming (SOCP) approach is proposed in this paper. The original nonconvex design problem is first relaxed into an SOCP problem, which can provide a lower bound on the optimal value of the original problem. For reducing the gap between the original and the convex problem, an iterative procedure is developed. The initial point of the iterative procedure can be chosen as the solution obtained from the relaxed SOCP problem. Unlike other iterative approaches, the convergence of the proposed iterative procedure is definitely guaranteed. Design examples demonstrate the effectiveness of the proposed method.

IIR Variable Fractional Delay Digital Filter Design

In this paper, two methods for the design of IIR variable fractional delay (VFD) digital filters are presented. The two methods differ in the approaches to design an initial set of fixed IIR digital filters with different fractional delays. The first method formulates the design as a quadratic programming (QP) problem under the weighted least-squares (WLS) criterion. The stability constraints of IIR filters are based on argument principle. The second method utilizes the model reduction technique to design a set of fixed IIR filters. After fixed IIR digital filters are obtained, IIR filter coefficients are then approximated by polynomial functions. The main design steps of these two methods are described. Through two VFD digital filter examples, we present their design and comparison results with two recent methods

Design of IIR Variable Fractional Delay Digital Filters

In this paper, a novel method for designing IIR variable fractional delay (VFD) digital filters with variable and fixed denominator is presented. First of all, a peak-constrained weighted least-squares (PCWLS) method is employed to design a set of FIR fixed fractional delay (FD) filters according to given specifications. The PCWLS FIR filters are implemented by the projected least-squares (PLS) algorithm. An iterative WLS model reduction technique is utilized to design denominators, which can guarantee the stability of designed IIR VFD filter if the iteration converges. The numerator of IIR fixed FD filters can be designed by two approaches: The Approach 1 solves linear equations based on the orthogonality principle; and the Approach 2 formulates the numerator design problem as a standard quadratic programming (QP) problem. The coefficients of IIR fixed FD filters are finally approximated by polynomial functions of FD. Three sets of examples are given to demonstrate the effectiveness of the proposed method.