An IIR adaptive filter based on estimation of all-pass system

In this paper, an IIR adaptive filter based on the estimation of the all-pass system is proposed. First, the unknown system is represented as a cascade of an all-pass system and a minimum phase system. The structure of the IIR adaptive filter is also a cascade of the all-pass and the transversal adaptive filter. Next, the adaptive algorithm that has an updating value which is the correlation of the input signal to the weights and the estimation error is derived. When the input signal to the adaptive filter is a white signal and the order of the synthesis of the all-pass section of the adaptive filter is smaller than that of the all-pass section of the unknown system, it is proven that the poles of the adaptive filter converge to a part of the poles of the all-pass section of the unknown system. Finally, the convergence performance and the convergence value of the weights are verified by computer simulations.