Least Squares Design of 2-D FIR Notch Filters Based on the Hopfield Neural Networks

This paper presents a design paradigm for the 2-D (two-dimensional) FIR (finite impulse response) notch filter using Hopfield neural network. A Hopfield neural network is chosen and the relationship between the least squares error criterion and the Lyapunov energy function is established. The design problem is transformed into the problem of finding the minimum value of the Lyapunov energy function. When the minimum value of the Lyapunov energy function is obtained, the outputs of the Hopfield neural network are the coefficients of the 2-D FIR notch filter. The complexity of computation can be reduced by using the Hopfield neural network. The simulation results demonstrate the effectiveness of the proposed algorithm.