Difference-operator-based models in statistical signal processing
Vijayan, Rajiv
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Permalink
https://hdl.handle.net/2142/23611
Description
Title
Difference-operator-based models in statistical signal processing
Author(s)
Vijayan, Rajiv
Issue Date
1991
Doctoral Committee Chair(s)
Poor, H.V.
Department of Study
Engineering, Electronics and Electrical
Discipline
Engineering, Electronics and Electrical
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
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.
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