The Digital Signal Processing Lab @ UCSD


Thesis Title

Application of Weak Convergence Theory to Adaptive IIR Filters

Thesis Abstract

In this thesis, the tracking performance of two adaptive infinite impulse response (IIR) filters is analyzed using the weak convergence theory.

The first one is a system-identification kind of scenario where the signal is modeled as the output of a time-varying coefficient rational system driven by white noise (time-varying ARMA signal model). An adaptive IIR filter with a constant step size Gauss-Newton algorithm is used to track the time-varying coefficients of the plant, with the output of the plant being the input of the adaptive filter. Using weak convergence theory it is shown that ODEs can be associated with the adaptive algorithm. With the help of the pre-scaling, the tracking behavior of the adaptive filter can be analyzed using the ODEs greatly reducing the complexity of the analysis.

The second order statistics of the filter are studied by considering the limit of the normalized error processes using the weak convergence theory. We show that the interpolated normalized error

processes converge weakly to a certain diffusion, namely, the solution of a simple stochastic differential equation (SDE). Based on the SDE, approximate formulas for asymptotic filter coefficient covariance and some engineering insight have been obtained.

Lastly, we concentrate on the second problem, which is a signal processing problem, i.e. the use of a constrained IIR adaptive line enhancer for tracking the time-varying frequencies of sinusoids in noise. Using the same theory and method as used in the first case, it is shown that ODEs can be associated with the adaptive algorithm and can be used to analyze the tracking performance of the adaptive notch filter. In all the cases, computer simulations have been conducted and are in agreement with the theory.

Year of Graduation: 1987