Requirements for the Degree of Doctor of Philosophy ADAPTATION OF GENERALIZED FEEDFORWARD FILTERS WITH APPLICATIONS TO SPEECH By

Generalized feedforward filters with first order sections are characterized by a feedback parameter that controls the region of support of the impulse response. Examples of filters that belong to this class of structures include the gamma and the Laguerre filters. Adaptation procedures for this class of structures have been restricted to the LMS algorithm which suffers from slow convergence for large eigenvalue spread. Convergence speed can be greatly improved using recursive least squares (RLS) procedures. RLS algorithms, however, are unsuitable for tracking time varying parameters in nonstationary environments. Direct application of standard RLS algorithms to generalized feedforward filters is not possible because changes in the feedback parameter lead to corresponding changes in the weight vector and this mimics a time varying environment. Block RLS with covariance resetting represents the most direct solution to the nonstationarity problem, vi but it is a wasteful solution since the state of the filter is lost. A better-suited solution exploits the relationship between the feedback parameter and the weights to develop update rules, for the covariance matrix and the weights, that compensate for the effects of changing the feedback parameter. Based on this evaluation, the primary goal of this study is to develop the necessary update equations and to incorporate them in an RLS based procedure that is capable of on-line operation. During this study and while looking at different representations for the cost function, we proved that standard RLS algorithms with the appropriate initialization reduce to the statistical method known as ridge regression. In other words, we developed a recursive procedure for adapting the ridge parameters. Another dimension of this study involves developing a new application area for the gamma filter. By virtue of its IIR nature, the gamma filter is expected to outperform the adaptive transversal filter in many applications. One area of interest is speech coding. Through an extensive experimental setup that involved every English phoneme, we showed that a gamma-based speech coder can achieve up to 20% reduction in the number of coding bits when compared to the adaptive transversal filter, the most commonly used structure in speech coding.