Difference-operator-based models in statistical signal processing

Difference-operator-based models are an alternative to conventional shift-operator-based models for modeling stationary discrete-time random processes obtained by sampling continuous-time processes, when the sampling rate is rapid relative to the dynamics of the continuous-time process. In this regime, statistical signal processing procedures derived from the difference-operator-based models tend to be better-conditioned than their conventional analogues, resulting in better numerical performance when implemented using finite-precision arithmetic. Unlike the situation for shift-operator models, estimating the parameters of a difference-operator-based model involves solving a non-Toeplitz system of linear equations. We derive an algorithm for efficiently estimating these parameters, analogous to the Levinson algorithm for conventional models. Numerical results have been obtained that indicate that, in the presence of roundoff errors, the new algorithm gives better results than the Levinson algorithm. We also present a class of algorithms that solve for the model parameters by obtaining triangular factorizations of the covariance matrix of differenced data. These algorithms have the added advantage of not requiring the computation of any n-dimensional inner products, thus rendering them suitable for parallelization. They also suggest a lattice implementation of the modeling filter, in which the basic block is a discrete-time integrator, rather than a delay.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Engineering, Electronics and Electrical

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Vijayan, Rajiv

Contributors dc:contributor

• Poor, H.V.

• Engineering, Electronics and Electrical

Statement dc:rights

• Copyright 1991 Vijayan, Rajiv

Language dc:language

eng

Identifier

AAI9211022
(UMI)AAI9211022

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23611