Mean convergence behavioural analysis of IIR adaptive filters

Abstract

In spite of having several advantages, IIR adaptive filters have not been getting their due share in applications because of the need for stability monitoring during adaptation and uncertainty in convergence time for stochastic inputs which can be mainly attributed to the involved nonquadratic criterion function. Because of this type of criterion function, it has been very difficult to estimate the nature of convergence in the stochastic frame work. Recently, it is shown that the ensemble mean parameter updating equations of the IIR adaptive algorithms can be represented by the associated ordinary differential equations (ODES). In this paper a method of solving the ODES in order to analyse the mean convergence behaviour of these filters, given the mean description of the input in the form of power spectral density is presented. Further, this procedure is applied to study the convergence behaviour of general IIR adaptive filters. Effectiveness of this method is shown through several analytical and simulation results obtained from two adaptive filtering examples.