Design of a Nonlinear Adaptive Infinite Impulse Response Filter

This study introduces a wavelet network based adaptive IIR filtering system satisfying asymptotic stability in the sense of Lyapunov. The proposed system is also integrated with the advantages of the time-frequency specific properties of wavelet networks in its dynamics. Two well known experiments are proposed. The results are verified that the proposed filtering system not only performs better than conventional gradient descent based algorithms but also performs as good as other stability theory based optimization algorithms.