This paper considers the optimal design of high order digital differentiators in the L/sub 1/ sense. Conventionally, using L/sub 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/sub 2/ and Chebyshev (minimax) error criteria.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>