{"id":"https://openalex.org/W2604588876","doi":"https://doi.org/10.3233/fi-2017-1477","title":"A Comprehensive Survey on Fractional Fourier Transform","display_name":"A Comprehensive Survey on Fractional Fourier Transform","publication_year":2017,"publication_date":"2017-03-11","ids":{"openalex":"https://openalex.org/W2604588876","doi":"https://doi.org/10.3233/fi-2017-1477","mag":"2604588876"},"language":"en","primary_location":{"id":"doi:10.3233/fi-2017-1477","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1477","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","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/A5100434437","display_name":"Yudong Zhang","orcid":"https://orcid.org/0000-0002-4870-1493"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yudong Zhang","raw_affiliation_strings":["School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007987858","display_name":"Shuihua Wang\u200e","orcid":"https://orcid.org/0000-0003-4713-2791"},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuihua Wang","raw_affiliation_strings":["School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China. wangshuihua@njnu.edu.cn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China. wangshuihua@njnu.edu.cn","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005666034","display_name":"Jianfei Yang","orcid":"https://orcid.org/0000-0002-8075-0439"},"institutions":[{"id":"https://openalex.org/I4210144799","display_name":"Jiangsu Key Laboratory of 3D Printing Equipment and Manufacturing","ror":"https://ror.org/04dzj3g56","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210144799"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian-Fei Yang","raw_affiliation_strings":["Jiangsu Key Laboratory of 3D, Printing Equipment and Manufacturing, Nanjing, Jiangsu 210042, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jiangsu Key Laboratory of 3D, Printing Equipment and Manufacturing, Nanjing, Jiangsu 210042, China","institution_ids":["https://openalex.org/I4210144799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100459168","display_name":"Zheng Zhang","orcid":"https://orcid.org/0000-0003-1470-6998"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zheng Zhang","raw_affiliation_strings":["Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90089, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103007606","display_name":"Preetha Phillips","orcid":"https://orcid.org/0000-0003-1712-1178"},"institutions":[{"id":"https://openalex.org/I107118585","display_name":"Shepherd University","ror":"https://ror.org/00y93ak93","country_code":"US","type":"education","lineage":["https://openalex.org/I107118585"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Preetha Phillips","raw_affiliation_strings":["School of Natural Sciences and Mathematics, Shepherd University, Shepherdstown, WV 25443, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Natural Sciences and Mathematics, Shepherd University, Shepherdstown, WV 25443, USA","institution_ids":["https://openalex.org/I107118585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101612131","display_name":"Ping Sun","orcid":"https://orcid.org/0000-0001-6757-8032"},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ping Sun","raw_affiliation_strings":["Department of Electrical Engineering, The City College of New York, CUNY, New York, NY 10031, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, The City College of New York, CUNY, New York, NY 10031, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101437838","display_name":"Jie Yan","orcid":"https://orcid.org/0000-0002-8800-6487"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jie Yan","raw_affiliation_strings":["Department of Applied Physics, Stanford University, Stanford, CA 94305, USA","Journal:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Physics, Stanford University, Stanford, CA 94305, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Journal:","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5100434437"],"corresponding_institution_ids":["https://openalex.org/I152031979"],"apc_list":null,"apc_paid":null,"fwci":7.1261,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.97625012,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"151","issue":"1-4","first_page":"1","last_page":"48"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.996399998664856,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9890000224113464,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.9465802907943726},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5688649415969849},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5585252046585083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5441256165504456},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.48483097553253174},{"id":"https://openalex.org/keywords/non-uniform-discrete-fourier-transform","display_name":"Non-uniform discrete Fourier transform","score":0.4558615982532501},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.42122140526771545},{"id":"https://openalex.org/keywords/short-time-fourier-transform","display_name":"Short-time Fourier transform","score":0.417686402797699},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.41375380754470825},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3313356637954712},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.29099351167678833},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.27901607751846313},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.24283304810523987},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11818426847457886}],"concepts":[{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.9465802907943726},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5688649415969849},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5585252046585083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5441256165504456},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.48483097553253174},{"id":"https://openalex.org/C62058723","wikidata":"https://www.wikidata.org/wiki/Q7049066","display_name":"Non-uniform discrete Fourier transform","level":5,"score":0.4558615982532501},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.42122140526771545},{"id":"https://openalex.org/C166386157","wikidata":"https://www.wikidata.org/wiki/Q1477735","display_name":"Short-time Fourier transform","level":4,"score":0.417686402797699},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.41375380754470825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3313356637954712},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.29099351167678833},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.27901607751846313},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.24283304810523987},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11818426847457886}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/fi-2017-1477","is_oa":false,"landing_page_url":"https://doi.org/10.3233/fi-2017-1477","pdf_url":null,"source":{"id":"https://openalex.org/S39012697","display_name":"Fundamenta Informaticae","issn_l":"0169-2968","issn":["0169-2968","1875-8681"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fundamenta Informaticae","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":270,"referenced_works":["https://openalex.org/W67433252","https://openalex.org/W69906484","https://openalex.org/W188319388","https://openalex.org/W207971512","https://openalex.org/W284396425","https://openalex.org/W301752678","https://openalex.org/W596427627","https://openalex.org/W606205799","https://openalex.org/W783608400","https://openalex.org/W1475705016","https://openalex.org/W1484044435","https://openalex.org/W1495573900","https://openalex.org/W1537090536","https://openalex.org/W1546709507","https://openalex.org/W1551742371","https://openalex.org/W1581627189","https://openalex.org/W1599086055","https://openalex.org/W1606052466","https://openalex.org/W1682293995","https://openalex.org/W1760782549","https://openalex.org/W1782428036","https://openalex.org/W1912141599","https://openalex.org/W1949503316","https://openalex.org/W1963939054","https://openalex.org/W1966044033","https://openalex.org/W1966705176","https://openalex.org/W1967546992","https://openalex.org/W1969845721","https://openalex.org/W1972827834","https://openalex.org/W1974247794","https://openalex.org/W1974609466","https://openalex.org/W1975001338","https://openalex.org/W1976509963","https://openalex.org/W1976649959","https://openalex.org/W1977526674","https://openalex.org/W1977661098","https://openalex.org/W1978432871","https://openalex.org/W1978813522","https://openalex.org/W1979410400","https://openalex.org/W1979811716","https://openalex.org/W1982011857","https://openalex.org/W1982208035","https://openalex.org/W1982270967","https://openalex.org/W1982610373","https://openalex.org/W1982626236","https://openalex.org/W1983906499","https://openalex.org/W1983980729","https://openalex.org/W1984747376","https://openalex.org/W1985840387","https://openalex.org/W1987629572","https://openalex.org/W1988762128","https://openalex.org/W1989490707","https://openalex.org/W1989624704","https://openalex.org/W1991190050","https://openalex.org/W1995417480","https://openalex.org/W1996028757","https://openalex.org/W1996519494","https://openalex.org/W1997362593","https://openalex.org/W1998134205","https://openalex.org/W1998182320","https://openalex.org/W1998207089","https://openalex.org/W1999198554","https://openalex.org/W1999206877","https://openalex.org/W2000195887","https://openalex.org/W2002301998","https://openalex.org/W2003089132","https://openalex.org/W2005650597","https://openalex.org/W2005997557","https://openalex.org/W2006162762","https://openalex.org/W2007151317","https://openalex.org/W2007241134","https://openalex.org/W2007289039","https://openalex.org/W2007483085","https://openalex.org/W2007615215","https://openalex.org/W2009055754","https://openalex.org/W2009431939","https://openalex.org/W2009964255","https://openalex.org/W2010218041","https://openalex.org/W2011844723","https://openalex.org/W2011879093","https://openalex.org/W2011953277","https://openalex.org/W2014936281","https://openalex.org/W2014999390","https://openalex.org/W2015774812","https://openalex.org/W2015854950","https://openalex.org/W2016331928","https://openalex.org/W2016757911","https://openalex.org/W2018858424","https://openalex.org/W2019388666","https://openalex.org/W2019411158","https://openalex.org/W2019887363","https://openalex.org/W2023105414","https://openalex.org/W2023179925","https://openalex.org/W2025301848","https://openalex.org/W2025328969","https://openalex.org/W2025735542","https://openalex.org/W2026110406","https://openalex.org/W2027845167","https://openalex.org/W2028450740","https://openalex.org/W2029675836","https://openalex.org/W2030037063","https://openalex.org/W2032178627","https://openalex.org/W2032621498","https://openalex.org/W2033514934","https://openalex.org/W2033865676","https://openalex.org/W2034010579","https://openalex.org/W2035301540","https://openalex.org/W2035859245","https://openalex.org/W2038207995","https://openalex.org/W2040140135","https://openalex.org/W2040199575","https://openalex.org/W2041645650","https://openalex.org/W2044779774","https://openalex.org/W2045977191","https://openalex.org/W2046263013","https://openalex.org/W2048254304","https://openalex.org/W2048367757","https://openalex.org/W2048598794","https://openalex.org/W2049586412","https://openalex.org/W2050187231","https://openalex.org/W2050234274","https://openalex.org/W2050697133","https://openalex.org/W2051295016","https://openalex.org/W2052300393","https://openalex.org/W2052482900","https://openalex.org/W2052775703","https://openalex.org/W2053376112","https://openalex.org/W2054613697","https://openalex.org/W2055075659","https://openalex.org/W2055086936","https://openalex.org/W2055753092","https://openalex.org/W2056470453","https://openalex.org/W2056833498","https://openalex.org/W2057427176","https://openalex.org/W2057451158","https://openalex.org/W2058163662","https://openalex.org/W2058376449","https://openalex.org/W2058750436","https://openalex.org/W2058807357","https://openalex.org/W2059464004","https://openalex.org/W2059665122","https://openalex.org/W2059877382","https://openalex.org/W2061779639","https://openalex.org/W2063198413","https://openalex.org/W2063275842","https://openalex.org/W2063826109","https://openalex.org/W2064060101","https://openalex.org/W2065513155","https://openalex.org/W2065803566","https://openalex.org/W2068707705","https://openalex.org/W2072202056","https://openalex.org/W2073580244","https://openalex.org/W2073972347","https://openalex.org/W2074617333","https://openalex.org/W2075735090","https://openalex.org/W2076218736","https://openalex.org/W2076538124","https://openalex.org/W2079018767","https://openalex.org/W2079976945","https://openalex.org/W2081448223","https://openalex.org/W2082401884","https://openalex.org/W2082493123","https://openalex.org/W2082685661","https://openalex.org/W2082941927","https://openalex.org/W2083504715","https://openalex.org/W2084708932","https://openalex.org/W2084832863","https://openalex.org/W2084939654","https://openalex.org/W2085823609","https://openalex.org/W2086676048","https://openalex.org/W2086943289","https://openalex.org/W2090697566","https://openalex.org/W2090781792","https://openalex.org/W2091245089","https://openalex.org/W2092702594","https://openalex.org/W2093695303","https://openalex.org/W2093857038","https://openalex.org/W2096438497","https://openalex.org/W2097622836","https://openalex.org/W2098083269","https://openalex.org/W2099006587","https://openalex.org/W2101778459","https://openalex.org/W2104277451","https://openalex.org/W2104346248","https://openalex.org/W2105688293","https://openalex.org/W2107736073","https://openalex.org/W2108651312","https://openalex.org/W2108710836","https://openalex.org/W2110063971","https://openalex.org/W2110623713","https://openalex.org/W2112219864","https://openalex.org/W2113561697","https://openalex.org/W2114190816","https://openalex.org/W2114418710","https://openalex.org/W2114928250","https://openalex.org/W2115960474","https://openalex.org/W2116721035","https://openalex.org/W2116983948","https://openalex.org/W2117105584","https://openalex.org/W2118941648","https://openalex.org/W2120174293","https://openalex.org/W2121185552","https://openalex.org/W2122106254","https://openalex.org/W2124008909","https://openalex.org/W2127778721","https://openalex.org/W2128888911","https://openalex.org/W2128959946","https://openalex.org/W2129394040","https://openalex.org/W2132192698","https://openalex.org/W2132538465","https://openalex.org/W2133843397","https://openalex.org/W2133999728","https://openalex.org/W2134736029","https://openalex.org/W2135028448","https://openalex.org/W2135097420","https://openalex.org/W2136106070","https://openalex.org/W2136523858","https://openalex.org/W2137222429","https://openalex.org/W2139841744","https://openalex.org/W2139892168","https://openalex.org/W2140307704","https://openalex.org/W2141076950","https://openalex.org/W2142110716","https://openalex.org/W2142883007","https://openalex.org/W2144649139","https://openalex.org/W2145576488","https://openalex.org/W2145934012","https://openalex.org/W2149510369","https://openalex.org/W2149812146","https://openalex.org/W2152646364","https://openalex.org/W2153412006","https://openalex.org/W2155023014","https://openalex.org/W2156330710","https://openalex.org/W2156902662","https://openalex.org/W2157344677","https://openalex.org/W2162322666","https://openalex.org/W2166080323","https://openalex.org/W2166143222","https://openalex.org/W2166247258","https://openalex.org/W2166808759","https://openalex.org/W2169103119","https://openalex.org/W2169280036","https://openalex.org/W2184455905","https://openalex.org/W2199807983","https://openalex.org/W2202656477","https://openalex.org/W2253210145","https://openalex.org/W2254123896","https://openalex.org/W2255511367","https://openalex.org/W2275123641","https://openalex.org/W2296119179","https://openalex.org/W2302637280","https://openalex.org/W2310869573","https://openalex.org/W2313770498","https://openalex.org/W2317831243","https://openalex.org/W2384337057","https://openalex.org/W2400559871","https://openalex.org/W2413943978","https://openalex.org/W2509876630","https://openalex.org/W2520000989","https://openalex.org/W2534373732","https://openalex.org/W2545050591","https://openalex.org/W2550701922","https://openalex.org/W2553647727","https://openalex.org/W3095950531","https://openalex.org/W3111396974","https://openalex.org/W3139648008","https://openalex.org/W3145611588","https://openalex.org/W3151784279","https://openalex.org/W3168682951","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2118155316","https://openalex.org/W3141389362","https://openalex.org/W2382218334","https://openalex.org/W2116983948","https://openalex.org/W2090697566","https://openalex.org/W2065632335","https://openalex.org/W2057875231","https://openalex.org/W2154898175","https://openalex.org/W1967434260","https://openalex.org/W4405441726"],"abstract_inverted_index":{"The":[0],"Fractional":[1],"Fourier":[2,17],"transform":[3,18,22],"(FRFT)":[4],"is":[5,12,112],"a":[6,13,23,27,38,62,83],"relatively":[7],"novel":[8],"linear":[9],"transforms":[10],"that":[11,69,114],"generalization":[14],"of":[15,41,48,71,87],"conventional":[16],"(FT).":[19],"FRFT":[20,49,88],"can":[21],"particular":[24],"signal":[25],"to":[26,36,89],"unified":[28],"time-frequency":[29],"domain.":[30],"In":[31],"this":[32,115],"survey,":[33],"we":[34,45,60,81],"try":[35],"present":[37],"comprehensive":[39,63],"investigation":[40],"FRFT.":[42,125],"Firstl":[43],"y,":[44],"provided":[46],"definition":[47],"and":[50,57,66,76,108],"its":[51],"three":[52],"discrete":[53],"versions":[54],"(weighted-type,":[55],"sampling-type,":[56],"eigendecomposition-type).":[58],"Secondly,":[59],"offered":[61],"theoretical":[64],"research":[65],"technological":[67],"studies":[68],"consisted":[70],"hardware":[72],"implementation,":[73,75],"software":[74],"optimal":[77,94],"order":[78],"selection.":[79],"Thirdly,":[80],"presented":[82],"survey":[84,116],"on":[85,124],"applications":[86],"following":[90],"fields:":[91],"communication,":[92],"encryption,":[93],"engineering,":[95],"radiology,":[96],"remote":[97],"sensing,":[98],"fractional":[99,101],"calculus,":[100],"wavelet":[102],"transform,":[103],"pseudo-differential":[104],"operator,":[105],"pattern":[106],"recognition,":[107],"image":[109],"processing.":[110],"It":[111],"hoped":[113],"would":[117],"be":[118],"beneficial":[119],"for":[120],"the":[121],"researchers":[122],"studying":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
