{"id":"https://openalex.org/W2006506147","doi":"https://doi.org/10.1080/00207178608933542","title":"Simple methods for the shift-transformation matrix, direct-product matrix and summation matrix of discrete Walsh series","display_name":"Simple methods for the shift-transformation matrix, direct-product matrix and summation matrix of discrete Walsh series","publication_year":1986,"publication_date":"1986-04-01","ids":{"openalex":"https://openalex.org/W2006506147","doi":"https://doi.org/10.1080/00207178608933542","mag":"2006506147"},"language":"en","primary_location":{"id":"doi:10.1080/00207178608933542","doi":"https://doi.org/10.1080/00207178608933542","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207178608933542","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"volume":null,"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/A5054686089","display_name":"Jyh\u2010Horng Chou","orcid":"https://orcid.org/0000-0001-8096-0586","observed_orcids":["https://orcid.org/0000-0001-8096-0586"]},"institutions":[{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"JYH-HORNG CHOU","raw_affiliation_strings":["Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China","Institute of Mechanical Engineering, National Sun Yat-Sen University , Kaohsiung, Taiwan, Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China","institution_ids":["https://openalex.org/I142974352"]},{"raw_affiliation_string":"Institute of Mechanical Engineering, National Sun Yat-Sen University , Kaohsiung, Taiwan, Republic of China","institution_ids":["https://openalex.org/I142974352"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111559438","display_name":"ING-RONG HORNG","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I142974352","display_name":"National Sun Yat-sen University","ror":"https://ror.org/00mjawt10","country_code":"TW","type":"education","lineage":["https://openalex.org/I142974352"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"ING-RONG HORNG","raw_affiliation_strings":["Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China","Institute of Mechanical Engineering, National Sun Yat-Sen University , Kaohsiung, Taiwan, Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, Republic of China","institution_ids":["https://openalex.org/I142974352"]},{"raw_affiliation_string":"Institute of Mechanical Engineering, National Sun Yat-Sen University , Kaohsiung, Taiwan, Republic of China","institution_ids":["https://openalex.org/I142974352"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I142974352"],"apc_list":null,"apc_paid":null,"fwci":1.5022,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.80410858,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"43","issue":"4","first_page":"1339","last_page":"1342"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.5092999935150146,"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":0.5092999935150146,"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/T11081","display_name":"Advanced Control Systems Design","score":0.24240000545978546,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.1445000022649765,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/digital-computer-implementation","display_name":"digital computer implementation","score":0.6690000295639038},{"id":"https://openalex.org/keywords/control-systems","display_name":"control systems","score":0.8399999737739563}],"concepts":[{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6878888607025146},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5958033204078674},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5954906940460205},{"id":"https://openalex.org/C103945485","wikidata":"https://www.wikidata.org/wiki/Q5204933","display_name":"DFT matrix","level":5,"score":0.5780676603317261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5322043299674988},{"id":"https://openalex.org/C165443888","wikidata":"https://www.wikidata.org/wiki/Q1482183","display_name":"Transformation matrix","level":3,"score":0.4793158769607544},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4788353741168976},{"id":"https://openalex.org/C4263655","wikidata":"https://www.wikidata.org/wiki/Q2699958","display_name":"Matrix function","level":4,"score":0.47778400778770447},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.47399723529815674},{"id":"https://openalex.org/C183357087","wikidata":"https://www.wikidata.org/wiki/Q7141739","display_name":"Pascal matrix","level":5,"score":0.45875003933906555},{"id":"https://openalex.org/C22629506","wikidata":"https://www.wikidata.org/wiki/Q7602993","display_name":"State-transition matrix","level":4,"score":0.45445704460144043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3879355490207672},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37370795011520386},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32322633266448975},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.2655302882194519},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12340247631072998},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06485149264335632},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical 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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C39920418","wikidata":"https://www.wikidata.org/wiki/Q11476","display_name":"Kinematics","level":2,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207178608933542","doi":"https://doi.org/10.1080/00207178608933542","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207178608933542","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.4300000071525574}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1996811480"],"related_works":["https://openalex.org/W2388793872","https://openalex.org/W2010774598","https://openalex.org/W2380198058","https://openalex.org/W2379782386","https://openalex.org/W2070384391","https://openalex.org/W2370302420","https://openalex.org/W1972612702","https://openalex.org/W2246259247","https://openalex.org/W2006506147","https://openalex.org/W2901491549"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"new":[3],"easy":[4],"methods":[5,23],"for":[6],"directly":[7],"obtaining":[8],"the":[9,38],"shift-transformation":[10],"matrix,":[11],"direct-product":[12],"matrix":[13,16],"and":[14],"summation":[15],"of":[17,40],"discrete":[18,44],"Walsh":[19,45],"series.":[20],"The":[21],"proposed":[22],"can":[24],"be":[25,34],"conveniently":[26],"implemented":[27],"with":[28],"a":[29],"digital":[30],"computer.":[31],"They":[32],"will":[33],"very":[35],"useful":[36],"in":[37],"study":[39],"control":[41],"systems":[42],"via":[43],"series":[46]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
