{"id":"https://openalex.org/W1979675760","doi":"https://doi.org/10.1109/itw.2011.6089486","title":"Widely linear SIMO filtering for hypercomplex numbers","display_name":"Widely linear SIMO filtering for hypercomplex numbers","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W1979675760","doi":"https://doi.org/10.1109/itw.2011.6089486","mag":"1979675760"},"language":"en","primary_location":{"id":"doi:10.1109/itw.2011.6089486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2011.6089486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Information Theory Workshop","raw_type":"proceedings-article"},"type":"conference-paper","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/A5049999453","display_name":"Dominik Schulz","orcid":"https://orcid.org/0000-0002-1117-5469"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Dominik Schulz","raw_affiliation_strings":["Communication Networks Research Laboratory, Ilmenau University of Technology, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communication Networks Research Laboratory, Ilmenau University of Technology, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078837557","display_name":"Jochen Seitz","orcid":"https://orcid.org/0000-0001-7867-9680"},"institutions":[{"id":"https://openalex.org/I119449181","display_name":"Technische Universit\u00e4t Ilmenau","ror":"https://ror.org/01weqhp73","country_code":"DE","type":"education","lineage":["https://openalex.org/I119449181"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jochen Seitz","raw_affiliation_strings":["Communication Networks Research Laboratory, Ilmenau University of Technology, Ilmenau, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communication Networks Research Laboratory, Ilmenau University of Technology, Ilmenau, Germany","institution_ids":["https://openalex.org/I119449181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069416979","display_name":"Jo\u00e3o Paulo C. L. da Costa","orcid":"https://orcid.org/0000-0002-8616-4924"},"institutions":[{"id":"https://openalex.org/I150729083","display_name":"Universidade de Bras\u00edlia","ror":"https://ror.org/02xfp8v59","country_code":"BR","type":"education","lineage":["https://openalex.org/I150729083"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Joao Paulo C. Lustosa da Costa","raw_affiliation_strings":["Department of Electrical Engineering, University of Bras\u00edlia, Brasilia, Brazil","Department of Electrical Engineering, University of Bras\u00edlia Bras\u00edlia, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Bras\u00edlia, Brasilia, Brazil","institution_ids":["https://openalex.org/I150729083"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Bras\u00edlia Bras\u00edlia, Brazil","institution_ids":["https://openalex.org/I150729083"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9975000023841858,"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"}},"topics":[{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9975000023841858,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hypercomplex-number","display_name":"Hypercomplex number","score":0.9930206537246704},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6404827833175659},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6249679327011108},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5692770481109619},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4949492812156677},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.4801154136657715},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4313703775405884},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3128778338432312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2926223874092102},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.13993540406227112},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08420377969741821}],"concepts":[{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.9930206537246704},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6404827833175659},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6249679327011108},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5692770481109619},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4949492812156677},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.4801154136657715},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4313703775405884},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3128778338432312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2926223874092102},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.13993540406227112},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08420377969741821},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/itw.2011.6089486","is_oa":false,"landing_page_url":"https://doi.org/10.1109/itw.2011.6089486","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2011 IEEE Information Theory Workshop","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.709.8787","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.709.8787","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.redes.unb.br/lasp/files/papers/p390-schulz.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W603092746","https://openalex.org/W639989723","https://openalex.org/W1568977570","https://openalex.org/W2078055097","https://openalex.org/W2114765937","https://openalex.org/W2118949037","https://openalex.org/W2123071279","https://openalex.org/W2132518575","https://openalex.org/W2135882834","https://openalex.org/W2170232782","https://openalex.org/W2170400088","https://openalex.org/W4211251910","https://openalex.org/W6633959220","https://openalex.org/W6678345141","https://openalex.org/W6679816651"],"related_works":["https://openalex.org/W3125691543","https://openalex.org/W2044767466","https://openalex.org/W2800395957","https://openalex.org/W2026218351","https://openalex.org/W3185621658","https://openalex.org/W14147894","https://openalex.org/W2507833514","https://openalex.org/W4388067726","https://openalex.org/W4224325206","https://openalex.org/W2916518000"],"abstract_inverted_index":{"The":[0,115,137,152],"starting":[1],"point":[2],"of":[3,10,52,67,81,105,108,124,141,172],"any":[4],"derivation":[5],"is":[6,48,60,73],"a":[7,18,26,49,168],"suitable":[8],"representation":[9,21],"the":[11,30,33,79,92,95,106,125,133,149,159,162],"given":[12],"model.":[13],"Hypercomplex":[14],"numbers":[15,43,55,83],"sometimes":[16],"provide":[17],"more":[19,23,169],"compact":[20],"and":[22,84],"insight":[24,90],"into":[25,91],"problem's":[27],"structure":[28],"than":[29,161],"reals":[31],"or":[32],"complex":[34],"numbers.":[35,114],"Hence,":[36,70],"efficient":[37],"filters":[38,111,144],"are":[39],"needed":[40],"for":[41,65,112],"hypercomplex":[42,54,82,113,135],"as":[44],"well.":[45],"As":[46],"there":[47],"large":[50],"zoo":[51],"different":[53,57],"obeying":[56],"algebras":[58],"it":[59],"cumbersome":[61],"to":[62,74,77,167],"do":[63],"derivations":[64],"each":[66],"them":[68],"individually.":[69],"our":[71],"contribution":[72],"show":[75],"how":[76,94],"abstract":[78,139],"concept":[80,107],"their":[85],"algebras.":[86],"We":[87],"give":[88],"an":[89],"questions":[93],"algebra":[96,160],"works":[97],"in":[98,132,148],"general.":[99],"Furthermore,":[100],"we":[101],"propose":[102],"two":[103],"extensions":[104],"widely":[109,117,142,173],"linear":[110,118,143,174],"first":[116,163],"filter":[119],"abstraction":[120],"presumes":[121],"several":[122],"properties":[123],"algebra,":[126],"but":[127],"can":[128],"be":[129],"computed":[130],"directly":[131],"respective":[134],"domain.":[136,151],"second":[138],"solution":[140],"does":[145],"all":[146],"calculations":[147],"real":[150],"latter":[153],"imposes":[154],"much":[155],"less":[156],"restrictions":[157],"on":[158],"one":[164],"which":[165],"leads":[166],"generic":[170],"type":[171],"filters.":[175]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}