{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/101243"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/101243","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The closed form error expression with Parseval's theorem","abstract":"The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters. It is understood that the main reason to fail in the extension can be summarized as: (1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system. (2) The derivation procedure depends too much on cancellation among terms. To compensate the above two points, an alternative method utilizing Parseval's theorem was presented. The major problems in the extension of Yovit-Jackson's form are summarized as: (1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression. (2) To find mathematical relations between the original spectrum and factorized component spectra. (3) To find the closed form expression of generalized transfer function of optimum operator.","abstract_html":"The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters. It is understood that the main reason to fail in the extension can be summarized as: (1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system. (2) The derivation procedure depends too much on cancellation among terms. To compensate the above two points, an alternative method utilizing Parseval's theorem was presented. The major problems in the extension of Yovit-Jackson's form are summarized as: (1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression. (2) To find mathematical relations between the original spectrum and factorized component spectra. (3) To find the closed form expression of generalized transfer function of optimum operator.","abstract_has_math":false,"creators":["Yang, Seungtaik"],"institution":"Virginia Polytechnic Institute","degree_name":"M.S.","degree_level":"masters","degree_discipline":"Electrical Engineering","degree_department":"Electrical Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1968,"date_issued":"1968","date_published":"1968","updated_at":"2026-07-22T22:19:01Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10919/101243","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.department","label":"Department","values":["Electrical Engineering"]},{"key":"dc:creator","label":"Author","values":["Yang, Seungtaik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-12-14T16:34:59Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-12-14T16:34:59Z"]},{"key":"dc:date.issued","label":"Date","values":["1968"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Polytechnic Institute"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/101243"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters. It is understood that the main reason to fail in the extension can be summarized as: (1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system. (2) The derivation procedure depends too much on cancellation among terms. To compensate the above two points, an alternative method utilizing Parseval's theorem was presented. The major problems in the extension of Yovit-Jackson's form are summarized as: (1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression. (2) To find mathematical relations between the original spectrum and factorized component spectra. (3) To find the closed form expression of generalized transfer function of optimum operator."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.S."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The closed form error expression with Parseval's theorem"]}]}],"canonical_facts":{"dc:contributor.department":["Electrical Engineering"],"dc:creator":["Yang, Seungtaik"],"dc:date.accessioned":["2020-12-14T16:34:59Z"],"dc:date.available":["2020-12-14T16:34:59Z"],"dc:date.issued":["1968"],"dc:description.abstract":["The closed form error expression of optimum Wiener filter was first introduced by M. C. Yovit and J. L. Jackson in 1955. Since then, a number of people have proved the validity of this form using almost similar technique but no one has succeeded to extend the Yovit-Jackson's original formula for the other cases such as prediction and delay filters. It is understood that the main reason to fail in the extension can be summarized as: (1) The starting point that most of other authors have chosen is for the special case that confines itself to the zero delay filtering system. (2) The derivation procedure depends too much on cancellation among terms. To compensate the above two points, an alternative method utilizing Parseval's theorem was presented. The major problems in the extension of Yovit-Jackson's form are summarized as: (1) To find a new method of derivation from generalized starting point such as Y. W. Lee's error expression. (2) To find mathematical relations between the original spectrum and factorized component spectra. (3) To find the closed form expression of generalized transfer function of optimum operator."],"dc:description.degree":["M.S."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10919/101243"],"dc:language.iso":["en"],"dc:publisher":["Virginia Polytechnic Institute"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["The closed form error expression with Parseval's theorem"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["masters"],"thesis:degree_name":["M.S."],"thesis:institution_name":["Virginia Polytechnic Institute"]},"updated_at":"2026-07-22T22:19:01Z"}