Neural weighted least-squares design of FIR higher-order digital differentiators

Abstract

This paper extends the neural network based algorithm for equiripple design of higher-order digital differentiators in the weighted least-squares sense. The proposed approach formulates an error representation reflecting the difference between the desired amplitude response and the designed response in a Lyapunov error function. The optimal filter coefficients are obtained when neural network achieves convergence. Furthermore, by using a weighted updating function, the proposed method can find a very good approximation of the minimax solution. Simulation results indicate that the proposed technique is able to achieve good performance in a parallelism manner.