{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23374"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23374","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Rational modeling and linear prediction of random fields","abstract":"An approach to the two-dimensional spectrum estimation problem is proposed that is based upon modeling a random field as the output of a rational linear system driven by the innovations of the field. A variety of linear prediction problems, each depending upon the definition of past, may be formulated for random fields; consequently, there are an equal number of innovations representation models. For the rational modeling application, a good innovations representation model should provide a finite parametrization of the spectrum estimation problem; therefore, the model should be a rational linear system when the spectrum of the random field is itself rational.","abstract_html":"An approach to the two-dimensional spectrum estimation problem is proposed that is based upon modeling a random field as the output of a rational linear system driven by the innovations of the field. A variety of linear prediction problems, each depending upon the definition of past, may be formulated for random fields; consequently, there are an equal number of innovations representation models. For the rational modeling application, a good innovations representation model should provide a finite parametrization of the spectrum estimation problem; therefore, the model should be a rational linear system when the spectrum of the random field is itself rational.","abstract_has_math":false,"creators":["Krogmeier, James Vincent"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Arun, K.S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"10000-01-01","date_published":"10000-01-01","updated_at":"2026-07-22T22:25:21Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1990 Krogmeier, James Vincent"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026236","(UMI)AAI9026236"],"render_values":[{"text":"AAI9026236","href":null,"code":true},{"text":"(UMI)AAI9026236","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23374","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Arun, K.S."]},{"key":"dc:creator","label":"Author","values":["Krogmeier, James Vincent"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["10000-01-01","1990","2011-05-07T14:11:54Z"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer Engineering"]},{"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 1990 Krogmeier, James Vincent"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026236","(UMI)AAI9026236","http://hdl.handle.net/2142/23374"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["An approach to the two-dimensional spectrum estimation problem is proposed that is based upon modeling a random field as the output of a rational linear system driven by the innovations of the field. A variety of linear prediction problems, each depending upon the definition of past, may be formulated for random fields; consequently, there are an equal number of innovations representation models. For the rational modeling application, a good innovations representation model should provide a finite parametrization of the spectrum estimation problem; therefore, the model should be a rational linear system when the spectrum of the random field is itself rational.","In this dissertation, a non-causal linear interpolation problem is posed and solved by generalizing some results of one-dimensional linear interpolation theory. Spectral conditions are found for the regularity and determinism of a random field with respect to two-dimensional interpolation. The form of the non-causal innovations representation filter and the spectrum of the non-causal innovations are derived. It is shown that the interpolation problem admits a unique Wold decomposition. These results are compared to earlier work on random field linear prediction using causal definitions of past. It is shown that only the interpolation problem gives rise to a rational innovations representation filter for all fields with rational spectra.","In order to develop an estimation procedure for the parameters of the non-causal innovations representation filter, a theory of generalized Hankel forms is given for non-causal two-dimensional linear systems. A Kronecker theorem is proven for these forms relating their rank and null vectors to the rationality of the non-causal system, its minimal order, and its transfer function. This theory is used in an algorithm for rational spectrum estimation.","Made available in DSpace on 2011-05-07T14:11:54Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026236.pdf: 6720671 bytes, checksum: a11331116b4e4bd9b61377c1f1eaef4b (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:34-05:00 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":["Rational modeling and linear prediction of random fields"]}]}],"canonical_facts":{"dc:contributor":["Arun, K.S."],"dc:creator":["Krogmeier, James Vincent"],"dc:date":["10000-01-01","1990","2011-05-07T14:11:54Z"],"dc:description":["An approach to the two-dimensional spectrum estimation problem is proposed that is based upon modeling a random field as the output of a rational linear system driven by the innovations of the field. A variety of linear prediction problems, each depending upon the definition of past, may be formulated for random fields; consequently, there are an equal number of innovations representation models. For the rational modeling application, a good innovations representation model should provide a finite parametrization of the spectrum estimation problem; therefore, the model should be a rational linear system when the spectrum of the random field is itself rational.","In this dissertation, a non-causal linear interpolation problem is posed and solved by generalizing some results of one-dimensional linear interpolation theory. Spectral conditions are found for the regularity and determinism of a random field with respect to two-dimensional interpolation. The form of the non-causal innovations representation filter and the spectrum of the non-causal innovations are derived. It is shown that the interpolation problem admits a unique Wold decomposition. These results are compared to earlier work on random field linear prediction using causal definitions of past. It is shown that only the interpolation problem gives rise to a rational innovations representation filter for all fields with rational spectra.","In order to develop an estimation procedure for the parameters of the non-causal innovations representation filter, a theory of generalized Hankel forms is given for non-causal two-dimensional linear systems. A Kronecker theorem is proven for these forms relating their rank and null vectors to the rationality of the non-causal system, its minimal order, and its transfer function. This theory is used in an algorithm for rational spectrum estimation.","Made available in DSpace on 2011-05-07T14:11:54Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026236.pdf: 6720671 bytes, checksum: a11331116b4e4bd9b61377c1f1eaef4b (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:04:02Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:30:34-05:00 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"],"dc:identifier":["AAI9026236","(UMI)AAI9026236","http://hdl.handle.net/2142/23374"],"dc:language":["eng"],"dc:rights":["Copyright 1990 Krogmeier, James Vincent"],"dc:subject":["Engineering, Electronics and Electrical"],"dc:title":["Rational modeling and linear prediction of random fields"],"dc:type":["text"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:21Z"}