This paper extends the neural network based algorithm to the equiripple design of FIR digital differentiators in the weighted least-squares (WLS) sense. The error representation reformulated by the Lyapunov error function reflects the difference between the desired amplitude response and the designed response. The optimal filter coefficients are obtained when the neural network is convergent. Furthermore, the proposed method using a weighted updating-function can make a very good approximation of the minimax solution. Simulation results indicate that the proposed approach can achieve a good performance in the parallelism manner without incurring convergence problems.
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