{"id":"https://openalex.org/W2941724526","doi":"https://doi.org/10.1109/tsp.2019.2912878","title":"Fractional Fourier Analysis Using the M\u00f6bius Inversion Formula","display_name":"Fractional Fourier Analysis Using the M\u00f6bius Inversion Formula","publication_year":2019,"publication_date":"2019-04-27","ids":{"openalex":"https://openalex.org/W2941724526","doi":"https://doi.org/10.1109/tsp.2019.2912878","mag":"2941724526"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2019.2912878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2912878","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on 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/A5084904340","display_name":"Hongxia Miao","orcid":"https://orcid.org/0000-0003-4808-0989"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongxia Miao","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4808-0989","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100784476","display_name":"Feng Zhang","orcid":"https://orcid.org/0000-0003-2643-6446"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Zhang","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-2643-6446","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067803447","display_name":"Ran Tao","orcid":"https://orcid.org/0000-0002-5243-7189"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ran Tao","raw_affiliation_strings":["Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Fractional Signals and Systems, School of Information and Electronics, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":4.5456,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.95371421,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"67","issue":"12","first_page":"3181","last_page":"3196"},"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":0.9944999814033508,"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":0.9923999905586243,"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/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.7873786687850952},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.6433032751083374},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6280089020729065},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5809272527694702},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5679906606674194},{"id":"https://openalex.org/keywords/discrete-fourier-series","display_name":"Discrete Fourier series","score":0.5641556978225708},{"id":"https://openalex.org/keywords/discrete-time-fourier-transform","display_name":"Discrete-time Fourier transform","score":0.555099368095398},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.5308913588523865},{"id":"https://openalex.org/keywords/non-uniform-discrete-fourier-transform","display_name":"Non-uniform discrete Fourier transform","score":0.44597673416137695},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4440225064754486},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.42606014013290405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38032734394073486}],"concepts":[{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.7873786687850952},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.6433032751083374},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6280089020729065},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5809272527694702},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5679906606674194},{"id":"https://openalex.org/C175225751","wikidata":"https://www.wikidata.org/wiki/Q15927242","display_name":"Discrete Fourier series","level":5,"score":0.5641556978225708},{"id":"https://openalex.org/C122444316","wikidata":"https://www.wikidata.org/wiki/Q1440048","display_name":"Discrete-time Fourier transform","level":5,"score":0.555099368095398},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.5308913588523865},{"id":"https://openalex.org/C62058723","wikidata":"https://www.wikidata.org/wiki/Q7049066","display_name":"Non-uniform discrete Fourier transform","level":5,"score":0.44597673416137695},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4440225064754486},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.42606014013290405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38032734394073486}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2019.2912878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2019.2912878","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4639895821","display_name":null,"funder_award_id":"61421001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6952756739","display_name":null,"funder_award_id":"61331021","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7315783478","display_name":"\u57fa\u4e8e\u5206\u6570\u53d8\u6362\u7684\u91c7\u6837\u548c\u79bb\u6563\u5316\u7814\u7a76","funder_award_id":"61571042","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1483327278","https://openalex.org/W1490667383","https://openalex.org/W1847929618","https://openalex.org/W1978432871","https://openalex.org/W1989490707","https://openalex.org/W2007241134","https://openalex.org/W2018654957","https://openalex.org/W2045773285","https://openalex.org/W2048715026","https://openalex.org/W2067368921","https://openalex.org/W2082685661","https://openalex.org/W2082819064","https://openalex.org/W2083092557","https://openalex.org/W2096438497","https://openalex.org/W2108710836","https://openalex.org/W2109346866","https://openalex.org/W2110063971","https://openalex.org/W2116401656","https://openalex.org/W2116983948","https://openalex.org/W2124178020","https://openalex.org/W2125411978","https://openalex.org/W2128539777","https://openalex.org/W2137621591","https://openalex.org/W2139993747","https://openalex.org/W2149510369","https://openalex.org/W2154898175","https://openalex.org/W2155549970","https://openalex.org/W2155897647","https://openalex.org/W2162845162","https://openalex.org/W2166420781","https://openalex.org/W2166959930","https://openalex.org/W2169103119","https://openalex.org/W2170411504","https://openalex.org/W2177332526","https://openalex.org/W2289495092","https://openalex.org/W2344912857","https://openalex.org/W2372472251","https://openalex.org/W2406349259","https://openalex.org/W2522661861","https://openalex.org/W2565331392","https://openalex.org/W2604588876","https://openalex.org/W2622269493","https://openalex.org/W2741373247","https://openalex.org/W2751901877","https://openalex.org/W2753584719","https://openalex.org/W2769776396","https://openalex.org/W6684297928"],"related_works":["https://openalex.org/W2118155316","https://openalex.org/W2154898175","https://openalex.org/W198181464","https://openalex.org/W3141389362","https://openalex.org/W2382218334","https://openalex.org/W2116983948","https://openalex.org/W2170364018","https://openalex.org/W2945379152","https://openalex.org/W2101778459","https://openalex.org/W1591129816"],"abstract_inverted_index":{"Compared":[0],"with":[1,56],"the":[2,5,21,26,30,41,47,59,67,73,78,84,95,103,108,113,125,133,136,140,155,164,170,177,180,183],"Fourier":[3,7,32,43,50,129],"analysis,":[4],"fractional":[6,31,42,49,128],"analysis":[8,33],"is":[9,145,150,167],"more":[10],"suitable":[11,168],"to":[12,147],"process":[13],"linear":[14],"frequency":[15],"modulation":[16],"type":[17],"non-stationary":[18],"functions.":[19],"To":[20,54],"best":[22],"of":[23,29,77,91,112,139,154,163,182,191],"our":[24],"knowledge,":[25],"theoretical":[27],"framework":[28],"has":[34],"not":[35],"well":[36],"established":[37],"yet,":[38],"especially":[39],"for":[40,94,169],"series":[44],"(FrFS)":[45],"and":[46,62,75,110,132,188,193],"discrete":[48,127],"transform":[51,130],"(DFrFT)":[52],"algorithms.":[53,158],"tackle":[55],"these":[57],"problems,":[58],"efficient":[60,116],"FrFS":[61,79,97,109],"DFrFT":[63,117,157],"algorithms":[64,93,118,144,185],"based":[65,101],"on":[66,83,102],"M\u00f6bius":[68,85],"function":[69],"are":[70,80,98,119,122],"proposed.":[71,99],"First,":[72],"existence":[74],"applicability":[76],"analyzed":[81],"basing":[82],"inversion":[86],"formula.":[87],"Second,":[88],"two":[89,115,141],"kinds":[90],"fast":[92],"infinite/finite":[96],"Then,":[100],"amplitude":[104],"scaling":[105],"relationship":[106],"between":[107],"samples":[111],"FrFT,":[114],"obtained,":[120],"which":[121,149],"noted":[123],"as":[124],"arithmetic":[126],"(ADFrFT)-I":[131],"ADFrFT-II.":[134],"Importantly,":[135],"multiplication":[137],"complexity":[138],"proposed":[142],"ADFrFT":[143,184],"reduced":[146],"O(M),":[148],"less":[151],"than":[152],"that":[153],"state-of-the-art":[156],"The":[159],"parallel":[160],"butterfly":[161],"structure":[162],"ADFrFT-II":[165],"algorithm":[166],"very":[171],"large":[172],"scale":[173],"integration":[174],"implementation.":[175],"Finally,":[176],"simulations":[178],"justify":[179],"efficiency":[181],"in":[186],"filtering":[187],"parameter":[189],"evaluation":[190],"radar":[192],"optical":[194],"signals.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}