{"id":"https://openalex.org/W2546883973","doi":"https://doi.org/10.1007/s00034-016-0447-8","title":"Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions","display_name":"Fractional Fourier, Hartley, Cosine and Sine Number-Theoretic Transforms Based on Matrix Functions","publication_year":2016,"publication_date":"2016-11-01","ids":{"openalex":"https://openalex.org/W2546883973","doi":"https://doi.org/10.1007/s00034-016-0447-8","mag":"2546883973"},"language":"en","primary_location":{"id":"doi:10.1007/s00034-016-0447-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00034-016-0447-8","pdf_url":null,"source":{"id":"https://openalex.org/S20109229","display_name":"Circuits Systems and Signal Processing","issn_l":"0278-081X","issn":["0278-081X","1531-5878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Circuits, Systems, and Signal Processing","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/A5110533743","display_name":"Paulo Hugo Esp\u00edrito Santo Lima","orcid":"https://orcid.org/0000-0002-9162-1667"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Paulo Hugo E.\u00a0S. Lima","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030282439","display_name":"Juliano B. Lima","orcid":"https://orcid.org/0000-0002-1474-1147"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Juliano B. Lima","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103560321","display_name":"Ricardo M. Campello de Souza","orcid":"https://orcid.org/0009-0008-3262-6282"},"institutions":[{"id":"https://openalex.org/I25112270","display_name":"Universidade Federal de Pernambuco","ror":"https://ror.org/047908t24","country_code":"BR","type":"education","lineage":["https://openalex.org/I25112270"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Ricardo M. Campello de Souza","raw_affiliation_strings":["Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil"],"affiliations":[{"raw_affiliation_string":"Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil","institution_ids":["https://openalex.org/I25112270"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5110533743"],"corresponding_institution_ids":["https://openalex.org/I25112270"],"apc_list":null,"apc_paid":null,"fwci":2.6836,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.89356993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"36","issue":"7","first_page":"2893","last_page":"2916"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9983999729156494,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/sine-and-cosine-transforms","display_name":"Sine and cosine transforms","score":0.7860302925109863},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.7330614328384399},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6861899495124817},{"id":"https://openalex.org/keywords/fourier-sine-and-cosine-series","display_name":"Fourier sine and cosine series","score":0.669256329536438},{"id":"https://openalex.org/keywords/dft-matrix","display_name":"DFT matrix","score":0.5209680795669556},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.4785635769367218},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.4594385027885437},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4528149962425232},{"id":"https://openalex.org/keywords/hartley-transform","display_name":"Hartley transform","score":0.43010666966438293},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.3840242922306061},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36905211210250854},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.33465975522994995},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.3042445182800293},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.2759746313095093},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16329553723335266},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.14976739883422852},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11805769801139832},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.09662139415740967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06370547413825989},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06289201974868774}],"concepts":[{"id":"https://openalex.org/C47615080","wikidata":"https://www.wikidata.org/wiki/Q1328722","display_name":"Sine and cosine transforms","level":5,"score":0.7860302925109863},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.7330614328384399},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6861899495124817},{"id":"https://openalex.org/C56552780","wikidata":"https://www.wikidata.org/wiki/Q5475798","display_name":"Fourier sine and cosine series","level":5,"score":0.669256329536438},{"id":"https://openalex.org/C103945485","wikidata":"https://www.wikidata.org/wiki/Q5204933","display_name":"DFT matrix","level":5,"score":0.5209680795669556},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4785635769367218},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.4594385027885437},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4528149962425232},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.43010666966438293},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.3840242922306061},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36905211210250854},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.33465975522994995},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.3042445182800293},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.2759746313095093},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16329553723335266},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.14976739883422852},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11805769801139832},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.09662139415740967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06370547413825989},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06289201974868774},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00034-016-0447-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00034-016-0447-8","pdf_url":null,"source":{"id":"https://openalex.org/S20109229","display_name":"Circuits Systems and Signal Processing","issn_l":"0278-081X","issn":["0278-081X","1531-5878"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Circuits, Systems, and Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4973518218","display_name":null,"funder_award_id":"456744/2014-2","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G6082855687","display_name":null,"funder_award_id":"307686/2014-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W171922849","https://openalex.org/W565312106","https://openalex.org/W606473257","https://openalex.org/W1483804921","https://openalex.org/W1966477666","https://openalex.org/W1969397475","https://openalex.org/W1982610373","https://openalex.org/W1983343479","https://openalex.org/W1995008769","https://openalex.org/W1996519494","https://openalex.org/W2018654957","https://openalex.org/W2019388666","https://openalex.org/W2020296150","https://openalex.org/W2023683339","https://openalex.org/W2026713334","https://openalex.org/W2049835395","https://openalex.org/W2059477017","https://openalex.org/W2066730489","https://openalex.org/W2069448237","https://openalex.org/W2088199355","https://openalex.org/W2090697566","https://openalex.org/W2090778219","https://openalex.org/W2092245645","https://openalex.org/W2092449709","https://openalex.org/W2099006587","https://openalex.org/W2100912680","https://openalex.org/W2110063971","https://openalex.org/W2113075022","https://openalex.org/W2121185552","https://openalex.org/W2126432053","https://openalex.org/W2129697067","https://openalex.org/W2131161908","https://openalex.org/W2137326966","https://openalex.org/W2138692623","https://openalex.org/W2145576488","https://openalex.org/W2157722058","https://openalex.org/W2166143222","https://openalex.org/W2313770498","https://openalex.org/W2732251371","https://openalex.org/W2986001730"],"related_works":["https://openalex.org/W2004950706","https://openalex.org/W2012013472","https://openalex.org/W2953981603","https://openalex.org/W1922999178","https://openalex.org/W2091527532","https://openalex.org/W2047407753","https://openalex.org/W4312337410","https://openalex.org/W2546883973","https://openalex.org/W2795868098","https://openalex.org/W4311538568"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
