{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23611"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23611","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Difference-operator-based models in statistical signal processing","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Vijayan, Rajiv"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Engineering, Electronics and Electrical","degree_department":null,"school":null,"contributors":["Poor, H.V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:20:34Z","date_published":"2011-05-07T14:20:34Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1991 Vijayan, Rajiv"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9211022","(UMI)AAI9211022"],"render_values":[{"text":"AAI9211022","href":null,"code":true},{"text":"(UMI)AAI9211022","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23611","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Poor, H.V."]},{"key":"dc:creator","label":"Author","values":["Vijayan, Rajiv"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:20:34Z","10000-01-01","1991"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Engineering, Electronics and Electrical"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1991 Vijayan, Rajiv"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9211022","(UMI)AAI9211022","http://hdl.handle.net/2142/23611"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2011-05-07T14:20:34Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9211022.pdf: 2009713 bytes, checksum: 895a0051623d0c712ab1bc1f6168c13a (MD5) Previous issue date: 1991","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:05:39Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:31:28-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Difference-operator-based models in statistical signal processing"]}]}],"canonical_facts":{"dc:contributor":["Poor, H.V."],"dc:creator":["Vijayan, Rajiv"],"dc:date":["2011-05-07T14:20:34Z","10000-01-01","1991"],"dc:description":["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.","Made available in DSpace on 2011-05-07T14:20:34Z (GMT). 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