{"id":"https://openalex.org/W2033924124","doi":"https://doi.org/10.1080/0020772031000115597","title":"Schur Decomposition and Model Reduction in the Design of Two-Dimensional Separable-Denominator Digital Filters","display_name":"Schur Decomposition and Model Reduction in the Design of Two-Dimensional Separable-Denominator Digital Filters","publication_year":2003,"publication_date":"2003-02-01","ids":{"openalex":"https://openalex.org/W2033924124","doi":"https://doi.org/10.1080/0020772031000115597","mag":"2033924124"},"language":"en","primary_location":{"id":"doi:10.1080/0020772031000115597","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020772031000115597","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054145468","display_name":"Rabah W. Aldhaheri","orcid":"https://orcid.org/0000-0003-3087-131X"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"R. W. Aldhaheri","raw_affiliation_strings":["Department of Electrical and Computer Engineering , King Abdulaziz University , PO Box 80204, Jeddah, 21589, Saudi Arabia E-mail: raldhaheri@hotmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering , King Abdulaziz University , PO Box 80204, Jeddah, 21589, Saudi Arabia E-mail: raldhaheri@hotmail.com","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054145468"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.13866149,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"34","issue":"2","first_page":"83","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.972000002861023,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9451000094413757,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9000999927520752,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/digital-filter","display_name":"Digital filter","score":0.8012771606445312},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6648991107940674},{"id":"https://openalex.org/keywords/impulse-response","display_name":"Impulse response","score":0.631233811378479},{"id":"https://openalex.org/keywords/infinite-impulse-response","display_name":"Infinite impulse response","score":0.5750802755355835},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5332220792770386},{"id":"https://openalex.org/keywords/finite-impulse-response","display_name":"Finite impulse response","score":0.5308616757392883},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.521432101726532},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5184721350669861},{"id":"https://openalex.org/keywords/linear-filter","display_name":"Linear filter","score":0.5091256499290466},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.5078383088111877},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.44450944662094116},{"id":"https://openalex.org/keywords/transpose","display_name":"Transpose","score":0.44383275508880615},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.43459439277648926},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.40536874532699585},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.377037912607193},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.3635718822479248},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2480233907699585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2288563847541809},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.21432536840438843},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10232821106910706},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07245060801506042}],"concepts":[{"id":"https://openalex.org/C36390408","wikidata":"https://www.wikidata.org/wiki/Q1163067","display_name":"Digital filter","level":3,"score":0.8012771606445312},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6648991107940674},{"id":"https://openalex.org/C72279823","wikidata":"https://www.wikidata.org/wiki/Q1139726","display_name":"Impulse response","level":2,"score":0.631233811378479},{"id":"https://openalex.org/C183816354","wikidata":"https://www.wikidata.org/wiki/Q665617","display_name":"Infinite impulse response","level":4,"score":0.5750802755355835},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5332220792770386},{"id":"https://openalex.org/C198386975","wikidata":"https://www.wikidata.org/wiki/Q117785","display_name":"Finite impulse response","level":2,"score":0.5308616757392883},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.521432101726532},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5184721350669861},{"id":"https://openalex.org/C139722471","wikidata":"https://www.wikidata.org/wiki/Q2619517","display_name":"Linear filter","level":3,"score":0.5091256499290466},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.5078383088111877},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.44450944662094116},{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.44383275508880615},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.43459439277648926},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.40536874532699585},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.377037912607193},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.3635718822479248},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2480233907699585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2288563847541809},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.21432536840438843},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10232821106910706},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07245060801506042},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/0020772031000115597","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020772031000115597","pdf_url":null,"source":{"id":"https://openalex.org/S129640837","display_name":"International Journal of Systems Science","issn_l":"0020-7721","issn":["0020-7721","1464-5319"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Systems Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4312785053","https://openalex.org/W2077525098","https://openalex.org/W1928658312","https://openalex.org/W1988104711","https://openalex.org/W2060171282","https://openalex.org/W2008697969","https://openalex.org/W2093992245","https://openalex.org/W2092980391","https://openalex.org/W2107185874","https://openalex.org/W2033924124"],"abstract_inverted_index":{"A":[0],"new":[1],"and":[2,17,48,64,68,133],"numerically":[3],"efficient":[4],"technique":[5,28],"for":[6],"designing":[7],"two-dimensional":[8],"(2-D)":[9],"separable-denominator":[10],"digital":[11,51,87,99],"filters":[12,88,142],"using":[13,54],"Schur":[14],"decomposition":[15,148],"(SD)":[16],"the":[18,22,35,55,59,66,80,84,92,102,117,123,128,135,139,147,150,157,172,177,184,187],"diagonal":[19],"symmetry":[20,56,136],"of":[21,58,77,83,95,122,138,141,149,186],"2-D":[23,36,60,124],"impulse":[24,37,61,125,151],"response":[25,38,62,126,152],"specifications.":[26],"This":[27],"is":[29,89,105,113,154,164],"based":[30],"on":[31],"two":[32,43,85],"steps:":[33],"first,":[34],"specifications":[39,174],"are":[40,74,144],"decomposed":[41],"into":[42],"cascaded":[44],"specifications,":[45],"representing":[46],"SIMO":[47],"MISO":[49],"1-D":[50,86,98,173],"filters.":[52],"By":[53],"property":[57,137],"matrix":[63,153],"that":[65,143,170],"left":[67],"right":[69],"eigenspaces":[70],"obtained":[71,114,175],"by":[72,107,115],"SD":[73,118],"a":[75,160,168],"transpose":[76],"each":[78],"other,":[79],"design":[81,93,167,181],"problem":[82,94],"reduced":[90,106],"to":[91,119,166],"only":[96,120],"one":[97],"filter.":[100],"Thus,":[101],"computational":[103,111],"effort":[104],"approximately":[108],"half.":[109],"Further":[110],"reduction":[112,162],"applying":[116],"part":[121],"matrix,":[127],"leading":[129],"principal":[130],"minor":[131],"submatrix,":[132],"from":[134,176],"class":[140],"considered":[145],"here,":[146],"obtained.":[155],"In":[156],"second":[158],"step,":[159],"model":[161],"algorithm":[163],"used":[165],"filter":[169],"approximates":[171],"first":[178],"step.":[179],"Two":[180],"examples":[182],"illustrate":[183],"advantages":[185],"proposed":[188],"technique.":[189]},"counts_by_year":[{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}