Design of full band IIR digital differentiators

This paper presents an efficient method for designing full band IIR digital differentiators in the complex Chebyshev sense. The proposed method is based on the formulation of a generalized eigenvalue problem by using the Remez multiple exchange algorithm. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem to find the absolute minimum eigenvalue, and then the complex Chebyshev approximation is attained through a few iterations starting from a given initial guess. The proposed algorithm is computationally efficient because it not only retains the speed inherent in the Remez exchange algorithm, but also simplifies the interpolation step. One design example is presented and compared with the conventional methods. It can be seen that the design results obtained by using the proposed method are better than that in the conventional methods.