Optimum Design of Discrete-Time Differentiators via Semi-Infinite Programming Approach

• Published in: IEEE transactions on instrumentation and measurement Vol. 57; no. 10; pp. 2226 - 2230
• Main Authors: Ho, C.Y.-F., Ling, B.W.-K., Yan-Qun Liu, Tam, P.K.-S., Kok-Lay Teo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Computational efficiency; Constraint optimization; Councils; Design optimization; Differentiators; Discrete-time differentiators; dual parameterization algorithm; eigen approach; Heating; Least squares methods; Mathematical models; Mathematics; Optimization; Parametrization; peak-constrained least squares approach; Physics; Programming; Remez approach; Ripples; semi-infinite programming; semidefinite programming approach; Signal processing algorithms; Statistics; Studies; Remez approach; semidefinite programming approach; peak-constrained least squares approach; Discrete-time differentiators; semi-infinite programming; dual parameterization algorithm; eigen approach
• ISSN: 0018-9456; 1557-9662
• DOI: 10.1109/TIM.2008.922090

In this paper, a general optimum full-band, high-order discrete-time differentiator design problem is formulated as a peak-constrained least squares optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parameterization algorithm is applied to solve the problem. The main advantages of employing the dual parameterization algorithm to solve the problem are as follows: (1) the guarantee of the convergence of the algorithm and (2) the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms that are implementing the semidefinite programming approach.