{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/100295"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/100295","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Uniform FIR approximation of causal Wiener filters with applications to causal coherence","abstract":"Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation","abstract_html":"Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation","abstract_has_math":false,"creators":["Barnes, Leighton P. (Leighton Pate)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.","school":null,"contributors":[],"advisors":["George Verghese."],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015","date_published":"2015","updated_at":"2026-07-22T22:20:48Z","subjects":["Electrical Engineering and Computer Science."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/100295","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["George Verghese."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science."]},{"key":"dc:creator","label":"Author","values":["Barnes, Leighton P. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/100295"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Cataloged from student-submitted PDF version of thesis.","Includes bibliographical references (pages 35-36)."]},{"key":"dc:description.abstract","label":"Abstract","values":["Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation"]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M. Eng."]},{"key":"dc:title","label":"Title","values":["Uniform FIR approximation of causal Wiener filters with applications to causal coherence"]}]}],"canonical_facts":{"dc:contributor.advisor":["George Verghese."],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science."],"dc:contributor.other":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science."],"dc:creator":["Barnes, Leighton P. (Leighton Pate)"],"dc:date.accessioned":["2015-12-16T15:54:03Z"],"dc:date.available":["2015-12-16T15:54:03Z"],"dc:date.issued":["2015"],"dc:description":["Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.","This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.","Cataloged from student-submitted PDF version of thesis.","Includes bibliographical references (pages 35-36)."],"dc:description.abstract":["Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation"],"dc:description.degree":["M. Eng."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/100295"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Electrical Engineering and Computer Science."],"dc:title":["Uniform FIR approximation of causal Wiener filters with applications to causal coherence"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:20:48Z"}