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A new expression of evaluating l 2 -sensitivity for generalized direct-form II structure of two-dimensional (2-D) separable-denominator digital filters is derived and analyzed. Unlike the previous work, l 2 -sensitivity is analyzed for the filter structure instead of its state-space realization. Then the resulting l 2 -sensitivity measure is compared with that deduced in a recent study of generalized direct-form II state-space realization of 2-D separable in denominator digital filters. In a numerical example, the new l 2 -sensitivity measure is minimized with respect to free parameters subject to l 2 -scaling constraints by an exhaustive search over a set of discrete values of finite cardinality, and the results are compared with those obtained by existing techniques.

The design of perfect-reconstruction cosine-modulated filter banks is revisited by applying new linearization techniques for the time-domain quadratic perfect reconstruction constraints. The new techniques are analyzed to explain why they can provide improved approximation accuracy hence improved performance with insignificant increase in complexity. A design example is presented for performance demonstration and comparison.

We study a class of composite FIR filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problems of designing C-filters that are optimal in least-squares, equiripple passband and lease-squares stopband, and minimax sense are formulated, and three algorithms for designing such linear-phase FIR C-filters are proposed. The algorithms are based on an alternating optimization strategy in that the prototype and shaping filters are optimized in separate steps, which are coupled and carried out in a sequential manner to yield a satisfactory design. Design examples are presented to illustrate the algorithms and demonstrate the performance of the C-filters relative to their conventional FIR counterparts.

In this paper, l 2 -sensitivity for the generalized direct-form II state-space realization of two-dimensional (2-D) separable-denominator digital filters is analyzed and minimized with respect to free parameters subject to l 2 -scaling constraints. Improved l 2 -sensitivity for 2-D separable-denominator digital filters is investigated by taking 0 and ±1 elements into account. An l 2 -sensitivity measure for the generalized direct-form II state-space realization of 2-D separable-denominator digital filters is deduced by applying improved l 2 -sensitivity. The l 2 -sensitivity measure is then minimized with respect to free parameters subject to l 2 -scaling constraints by employing an exhaustive search over a set of discrete values of finite cardinality. A numerical example is included to illustrate the validity and effectiveness of the proposed technique.

The paper is the first of a series of research investigations on robust digital filters which refer to filters that offer optimal performance under variations of filter parameters. We begin with quantitative characterization of performance robustness of a digital filter against parameter uncertainties. This is followed by several properties of the proposed robust performance measures and design formulations of robust FIR filters in L 2 (least-squares) and L ∞ (minimax) sense as nonsmooth convex problems. We present an accelerated subgradient algorithm for the design of L ∞ -robust FIR filters with technical details involved in implementing the proposed algorithm. A numerical example is included for illustration of the proposed design method and performance evaluation in comparison with conventional minimax FIR filters.

Based on the concept of polynomial operators, generalized direct-form II structure of two-dimensional (2-D) separable-denominator (SD) digital filters is explored. It is shown that 2-D SD digital filters can be modeled by a generalized SIMO direct- form II and a generalized MISO transposed direct-form II that are connected in cascade. Then an expression for the roundoff noise gain in the resulting structure is derived and investigated. Moreover, the roundoff noise gain is compared with that deduced in a recent study of generalized direct-form II realization of 2-D SD digital filters.

This paper presents an enhanced Steiglitz-McBride (SM) procedure for the design of stable minimax IIR digital filters. It is well known that minimax design of IIR filters is typically initiated with a nonconvex formulation, followed by a procedure to relax the original design problem to a sequence of convex sub-problems to be solved iteratively. We proposed an enhanced SM procedure that leads to improved convex relaxation relative to the conventional SM techniques, hence to improved designs. In addition, we make an observation that the state-of-the-art convex stability constraint based on strictly positive realness is equivalent to that deduced from an enhanced version of Rouche theorem from complex analysis. Design examples are presented to evaluate the new design algorithm.

In this paper, we explore generalized direct-form II realization of two-dimensional separable-denominator digital filters of order (m,n) based on the concept of polynomial operators, where we deal with a model with 3(m + n) + mn + 1 fixed parameters plus m + n free parameters. An l2-scaling method is introduced by utilizing different coupling coefficients at different branch nodes to avoid overflow. An expression for the roundoff noise gain in the realization is also examined. It is shown that the roundoff noise gain can be minimized with respect to the m + n free parameters by means of exhaustive search in a finite element space.

This paper presents a systematic study of pole and zero sensitivity minimization for state-space digital filters in several different yet related settings. First, a new weighted measure for pole and zero sensitivity for state-space digital filters is proposed and the problem of minimizing this measure is investigated. To this end, two efficient iterative techniques for minimizing this measure are developed by employing a quasi-Newton algorithm and relying on a recursive matrix equation, respectively. Furthermore, minimization of the proposed sensitivity measure subject to $l_{2}$ -scaling constraints is examined by extending the two aforementioned solution methods—one converts the constrained optimization problem at hand into an unconstrained problem and solves it using a quasi-Newton algorithm, while the other relaxes the constraints into a single constraint on matrix trace and solves the relaxed problem with an effective matrix iteration scheme. In addition, a simple yet novel method for the minimization of a zero sensitivity measure subject to minimal pole sensitivity is explored by pursuing an optimal coordinate transformation matrix. Simulation studies are presented to demonstrate the validity and effectiveness of the proposed techniques.

In this paper, a technique for estimating frequency and amplitude of noncircular complex sinusoid has been presented. A cascade scheme of first-order complex notch filters has been introduced where complex sequence with negative frequency is rejected in the first section and sequence with positive frequency is removed in the second section. Closed-form expressions for bias and mean square error (MSE) for frequency estimation have been presented. By using band-pass outputs of first-order notch filters, amplitudes of sinusoidal sequences with positive and negative frequencies have been also estimated. Computer simulations show the effectiveness of the proposed analyses.

We study a class of composite filters (C-filters), each is composed of a prototype filter and a shaping filter in cascade, where the shaping filter is constructed by cascading several complementary comb filters. In particular, the problem of designing a C-filter with equiripple passband and least-squares stopband subject to peak stopband gain is formulated and an algorithm for designing such a class of linear-phase FIR C-filters is proposed. The algorithm is based on an alternating convex optimization strategy in that the prototype and shaping filters are optimized in separate steps which are coupled and carried out in a sequential manner to yield a satisfactory design. Design example is presented to illustrate the algorithm and demonstrate the performance of the C-filter relative to its conventional FIR counterparts.

The joint optimization problem of high-order error feedback and realization for minimizing roundoff noise at the filter output subject to-scaling constraints for two-dimensional (2-D) separable-denominator digital filters is investigated. Linear algebraic techniques that convert the problem at hand into an unconstrained optimization problem are explored, and an efficient quasi-Newton algorithm is then applied to solve the unconstrained optimization problem iteratively. Closed-form formulas for fast and accurate gradient evaluation are derived. A numerical example is presented to demonstrate the validity and effectiveness of the proposed technique.

This paper deals with the joint optimization problem of high-order error-feedback and realization for minimizing roundoff noise at the output of a closed-loop system with a full-order observer feedback system subject to l2-scaling constraints. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained optimization problem at hand is then solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. A case study is presented to demonstrate the validity and effectiveness of the proposed technique.

Joint optimization of high-order error feedback and state-space realization for minimizing roundoff noise at filter output subject to l2-scaling constraints is investigated for one- and two-dimensional state-space digital filters. Linear algebraic techniques that convert the problems at hand into an unconstrained optimization problem are explored, and an efficient quasi-Newton algorithm is then applied to solve the unconstrained optimization problem iteratively. In this connection, closed-form formulas are derived for fast and accurate gradient evaluation. Finally, case studies are presented to demonstrate that the high-order error feedback does offer much improved performance and that the proposed joint optimization is superior relative to a sequentially optimized system where the state-space coordinate transformation and high-order error feedback matrices are optimized separately.

This paper presents a steady-state analysis of first-order complex adaptive notch filters in unbalanced three-phase power systems. By using first-order difference equation with respect to steady-state estimation error, analytical expressions of estimation bias and amplitude of oscillation error in an unbalanced condition have been derived. Closed-form expressions for bias and amplitude of oscillating error due to third harmonic have been also presented. Computer simulations show the effectiveness of the proposed analyses.

In this paper, the problem of minimizing a weighted pole and zero sensitivity measure subject to 1_2-norm dynamic range scaling constraints for state-space digital filters is investigated. First, a new measure for evaluating pole and zero sensitivity is introduced, and it is shown that the constrained optimization problem is converted into an unconstrained optimization problem by using linear algebraic techniques. Then, the unconstrained optimization problem at hand is solved iteratively by employing an efficient quasi-Newton algorithm with closed-form formulas for key gradient evaluation. A numerical example is presented to demonstrate the validity and effectiveness of the proposed iterative optimization technique.

We present a unified approach to the design of two well-known classes of computationally efficient digital filters, namely the interpolated and frequency-response-masking (FRM) FIR filters, that are optimized in minimax sense. The highly nonconvex minimax designs of these filters are carried out by jointly optimizing the subfilters involved using a convex-concave procedure (CCP) that yields an iterative and converging process where each iteration involves a convex problem of minimizing a linear function subject to convex quadratic constraints. We present an analysis to explain why CCP is well-suited for the design problems at hand. We also show that the CCP-based design framework is flexible to allow extension to the design of FRM filters that simultaneously promotes sparsity of the filter coefficients to reduce implementation complexity. Design examples with comparisons are presented to demonstrate the performance of the proposed design methods.

This paper deals with the problem of minimizing weighted p ole and zero sensitivity subject to l2-scaling constraints for state-space digital filters. A measure for pole and zero sensitivity is presented and an efficient iterative technique for minimizing this measure subject to l2-scaling constraints is developed by relaxing the constraints into a single constraint on matrix trace and solving the relaxed problem with an effective matrix iteration scheme. A numerical example is included to demonstrate the validity and effectiveness of the proposed technique.

Three-dimensional (3-D) digital filters find applications in a variety of image and video signal processing problems. This paper presents a coefficient-sensitivity analysis for a wide class of 3-D digital filters with separable denominators in local state space that leads to an analytic formulation for sensitivity minimization, and to present two solution techniques for the sensitivity minimization problem at hand. To this end, a vector-matrix-vector decomposition of a given 3-D transfer function that separates the three variables and leads to a state-space realization in a form convenient for subsequent analysis. An l2-sensitivity analysis is then performed. The result is a computationally tractable formula of the overall l2-sensitivity for 3-D digital filters. The l2-sensitivity is minimized subject to l2-scaling constraints by using one of the two solution methods proposed-one relaxes the constraints into a single trace constraint and solves the relaxed problem with an effective matrix iteration scheme; while the other converts the contained optimization problem at hand into an unconstrained problem and solves it using a quasi-Newton algorithm. A case study is presented to illustrate the validity and effectiveness of the proposed techniques.

This paper treats the minimization problem for roundoff noise in two-dimensional (2-D) recursive digital filters with an error feedback (EF). The EF is known as an available scheme for the reduction of roundoff noise, and this can be achieved by extracting a roundoff error from the quantizer and feeding it back to the adder. Since the EF circuit is an additional device of the digital filter, the bit length of the coefficients should be as short as possible for the fast arithmetic and low-cost realization. In this paper, we propose an algorithm to optimize the EF coefficients in a discrete space. The proposed algorithm is based on the branch and bound method by estimating the lower bound of the optimal solution, and the optimality of the obtained solution can be guaranteed. Finally, we give a numerical example to demonstrate the effectiveness of the proposed method, and show the optimal solution can be found without using the round-robin algorithm.

Is sparsity an issue in 2-D digital filter design problems to explore and why is it important? How a 2-D filter can be designed to retain a desired coefficient sparsity for efficient implementation while achieving best possible performance subject to that sparsity constraint? These are the focus of this paper in which we present a two-phase design method for 2-D FIR digital filters in two most common design settings, namely, the least squares and minimax designs. Simulation studies are presented to illustrate each phase of the proposed design method and to evaluate the performance of the filters designed.

For systems with uncertainties, lots of PID parameter tuning methods have been proposed from the view point of the robust stability theory. However, the control performance becomes conservative using robust PID controllers. In this paper, a new two-degree-of-freedom (2DOF) controller, which can improve the tracking properties, is proposed for nonlinear systems. According to the proposed method, the prefilter is designed as the PD compensator whose control parameters are tuned by the idea of a memory-based modeling (MBM) method. Since the MBM method is a type of local modeling methods for nonlinear systems, PD parameters can be tuned adequately in an online manner corresponding to nonlinear properties. Finally, the effectiveness of the newly proposed control scheme is numerically evaluated on a simulation example. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

PID controllers have been widely used for various process control systems represented by chemical processes. Recently, from viewpoint of productivity improvement and cost reduction, it has demands to establish the PID controller retained a desirable performance over time on steady-state in spite of changes in the system property. In this paper, a design of performance-driven model predictive PID controller is proposed, which automatically adjusts the user-specified parameter within the GPC-PID controller based on the control performance assessment. According to the proposed algorithm, the PID controller is re-tuned in order to obtain desirable system performance only if the practically performance index to assess control loop exceeds a user-defined threshold. The effectiveness of the proposed control scheme is numerically evaluated by a computer simulation example.

Techniques for the separate/joint optimization of error-feedback and realization are developed to minimize the roundoff noise subject to l 2-norm dynamic-range scaling constraints for a class of 2-D state-space digital filters. In the joint optimization, the problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. The unconstrained problem obtained is then solved by applying an efficient quasi-Newton algorithm. A numerical example is presented to illustrate the utility of the proposed techniques.

In realization of recursive digital filters with fixed point arithmetic, an error caused by roundoff arises. It is known that the level of the roundoff noise of an IIR filter tends to be high when the poles are close to the unit circle. Error feedback (EF) is an effective method to reduce the roundoff noise. It is desirable to design an EF network using as few parameters as possible in order to keep computational costs low. In this paper, we propose a method for designing a 2D EF network with identical coefficient sets. That is, the EF coefficients are divided into several subsets such that all the elements within each set have the same absolute value. In order to optimize the coefficient sets, we propose an algorithm by using the genetic algorithm. In the numerical example, we demonstrate the effectiveness of the proposed method.

In industrial processes, in order to improve the productivity, it is necessary to establish the performance-driven control mechanism, which the control performance is firstly evaluated, and the controller is reconstructed. Moreover, since most processes have nonlinearities, controller design schemes to deal with such systems are required. This paper describes a design scheme of data-driven performance-adaptive PID controllers. According to the proposed control scheme, the data-driven system identification which is effective for nonlinearity works corresponding to the result of modeling performance assessment, and PID parameters are computed using the newly estimated system parameters. Finally, a simulation example is discussed.

We investigate the problem of optimizing error-feedback and realization to minimize the roundoff noise subject to l 2 -scaling constraints in a system in which full-order state observer feedback is used in place of system state feedback. In this paper, the optimal error-feedback matrix is determined in closed-form in advance. As a result, joint optimization of error-feedback and realization is no longer required. An iterative optimization technique for obtaining the optimal coordinate transformation matrix that minimizes the roundoff noise subject to l 2 -scaling constraints is explored by emplying a quasi-Newton algorithm. We also describe a separate optimization technique for comparison purposes. The results of numerical experiments demonstrate the validity and effectiveness of the proposed technique.

In this paper, a new complex adaptive notch filter using the oscillator based algorithm has been proposed. The approach presented for second-order real coefficient IIR filters has been applied to derive a coefficient-update algorithm for a first-order complex adaptive notch filter. The case where an input complex sinusoid is given by a sum of sequences with positive and negative frequencies has been considered. An analytical expression of a frequency estimation error due to sequence with negative frequency has been derived. Closed-form expression for frequency estimation mean square error dut to input noise is then derived. Analysis for frequency tracking error has been also presented for a complex linear chirp signal. Computer simulations show the effectiveness of the proposed algorithm.

We study a class of composite digital filters, each has a dominating FIR component of order N and an extremely simple IIR component of order r with r-C N that are connected in parallel. We show that a constrained optimization setting known as convex-concave procedure (CCP) is naturally suited for the design of stable composite filters where the FIR and IIR components are jointly optimized in frequency-weighted minimax sense. A design algorithm based on successive CCP is presented and numerical examples are included to demonstrate that even with r =2 composite filters offer substantial performance improvement relative to their FIR-alone counterparts.