DESIGN OF HIGH-ORDER DIGITAL DIFFERENTIATORS USING L(1) ERROR CRITERIA

This paper considers the optimal design of high order digital differentiators in the L(1) sense. Conventionally, using L(1) error criterion for this design problem results in a nonlinear optimization problem since the corresponding objective function contains an absolute error function. We first reformulate the design problem as a linear programming problem in the frequency domain. To avoid the requirement of huge computation load and storage space when using linear programming based algorithms, we present a method based on a modification of Karmarkar's algorithm to solve the design problem so that an analytical weighted least-squares (WLS) solution formula can be obtained. This leads to a very efficient procedure for the considered design problem. Computer simulations show that the designed differentiators can achieve more accurate wideband differentiation than those designed by using L(2) and Chebyshev (minimax) error criteria.