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On the Use of Lyapunov Function for the Design of Equiripple FIR Digital Filters

This paper is to provide an alternative approach for the equiripple design of FIR filters by using a Hopfield Neural Network (HNN). The proposed approach establishes the error function between the amplitude response of the desired FIR filter and the designed one as a Lyapunov energy function to find the HNN parameters. Using the framework of HNN, the optimal filter coefficients can be obtained from the output state of the network. With the advantages of local connectivity, regularity and modularity, the architecture of the proposed approach is capable of achieving an excellent performance for filter design.