WLS design of FIR Nyquist filter based on neural networks

In this paper, we devised an analog circuit for the weighted least-squares (WLS) design of FIR Nyquist filters by using a Hopfield neural network (HNN). The approach is based on formulating the error function in the optimization of the FIR Nyquist filter as a Lyapunov energy function to find the Hopfield related parameters. By using these parameters and input to the network, the optimal filter coefficients of the FIR Nyquist filter can be derived when the network achieves its convergence. The proposed technique is regular and simple to implement the problems of filter optimization without having the convergence problem as compared to the previous neural-based method. Additionally, the structure proposed can be implemented by using analog VLSI technology in real-time. Simulation results are offered as a suggestion for illustrating the usability of the new method.