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The design of digital filters can be formulated as to solve a system of linear equations. This is completed by solving a system of linear equations or by using some matrix properties to simplify the optimization. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. In this paper, the neural-based methods for the design of FIR filters and filter banks are reviewed.