In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem.\ud 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\ud error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator.\ud The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and 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 implementing the semi-definite programming approach
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