{"id":"https://openalex.org/W2502458799","doi":"https://doi.org/10.1109/tsp.2016.2598325","title":"New Look on &lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;$q2^r$&lt;/tex-math&gt; &lt;/inline-formula&gt;-Point Fast Fourier Transforms","display_name":"New Look on &lt;inline-formula&gt; &lt;tex-math notation=\"LaTeX\"&gt;$q2^r$&lt;/tex-math&gt; &lt;/inline-formula&gt;-Point Fast Fourier Transforms","publication_year":2016,"publication_date":"2016-08-04","ids":{"openalex":"https://openalex.org/W2502458799","doi":"https://doi.org/10.1109/tsp.2016.2598325","mag":"2502458799"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2016.2598325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2598325","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/A5030506701","display_name":"Artyom M. Grigoryan","orcid":"https://orcid.org/0000-0001-6683-0064"},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Artyom M. Grigoryan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX, USA","institution_ids":["https://openalex.org/I45438204"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048285657","display_name":"Sos \u0421. Agaian","orcid":"https://orcid.org/0000-0003-4601-4507"},"institutions":[{"id":"https://openalex.org/I45438204","display_name":"The University of Texas at San Antonio","ror":"https://ror.org/01kd65564","country_code":"US","type":"education","lineage":["https://openalex.org/I45438204"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sos S. Agaian","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, TX, USA","institution_ids":["https://openalex.org/I45438204"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I45438204"],"apc_list":null,"apc_paid":null,"fwci":0.2501,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.52047596,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"64","issue":"22","first_page":"5972","last_page":"5980"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9944999814033508,"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"}},"topics":[{"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/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5918356776237488},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5527467131614685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5468475818634033},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.48587197065353394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4683990180492401},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4670029878616333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39647817611694336},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.31454998254776},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.24023059010505676},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18201565742492676},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.10357978940010071},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10353854298591614}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5918356776237488},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5527467131614685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5468475818634033},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.48587197065353394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4683990180492401},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4670029878616333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39647817611694336},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.31454998254776},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.24023059010505676},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18201565742492676},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.10357978940010071},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10353854298591614}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2016.2598325","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2598325","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1493818369","https://openalex.org/W1908016184","https://openalex.org/W1979555829","https://openalex.org/W1986624946","https://openalex.org/W1987741783","https://openalex.org/W2005015931","https://openalex.org/W2018023989","https://openalex.org/W2023186279","https://openalex.org/W2025849754","https://openalex.org/W2026294215","https://openalex.org/W2041842719","https://openalex.org/W2056180735","https://openalex.org/W2087375257","https://openalex.org/W2131706490","https://openalex.org/W2139045269","https://openalex.org/W2164409373","https://openalex.org/W2167872248","https://openalex.org/W2512335183","https://openalex.org/W2904838066","https://openalex.org/W4237537879","https://openalex.org/W4239894305","https://openalex.org/W4253801236","https://openalex.org/W4254389654","https://openalex.org/W4299616802"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2062850566","https://openalex.org/W2516295475","https://openalex.org/W2766639751","https://openalex.org/W2390401148","https://openalex.org/W1553466895"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,11,18,27,32,63,70,81,89,94,98,110,120,128,139,158,165,169],"method":[4],"of":[5,8,10,20,29,36,67,69,88,105,116,122,127,153,157,164],"splitting":[6],"orparallelization":[7],"calculation":[9,68,87],"N-point":[12],"discrete":[13,141],"Fourier":[14],"transform":[15,90],"(DFT)":[16],"by":[17,138],"DFTs":[19],"smaller":[21],"orders":[22],"is":[23,50,55,91,100],"described.":[24,56],"For":[25],"that":[26],"concept":[28],"partitions":[30,59],"revealing":[31],"one-dimensional":[33],"(1-D)":[34],"DFT":[35,77,112,135],"order":[37],"q2":[38,71,129],"<sup":[39,72,130],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[40,73,131],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</sup>":[41,74,132],",":[42],"where":[43],"r":[44],">":[45,48],"1and":[46],"q":[47,82],"1":[49],"a":[51,103,150],"positive":[52],"odd":[53],"number,":[54],"Two":[57],"different":[58],"are":[60,78,136,176],"considered":[61],"and":[62,161,173],"corresponding":[64],"effective":[65],"algorithms":[66,167],"-point":[75,133],"1-D":[76,106,111,134,140],"described":[79],"for":[80,147,168],"=":[83,171],"3":[84],"case.":[85],"The":[86,125,155],"based":[92],"on":[93],"paired":[95,159],"representations,":[96],"when":[97],"signal":[99],"represented":[101],"as":[102],"set":[104,121],"signals":[107],"which":[108,118,145],"define":[109],"in":[113],"disjoint":[114],"subsets":[115],"frequency-points":[117],"cover":[119],"all":[123],"frequencies.":[124],"splittings":[126],"performed":[137],"2and":[142],"qpaired":[143],"transforms":[144,160],"allow":[146],"calculating":[148],"with":[149],"minimum":[151],"number":[152],"operations.":[154],"examples":[156],"computational":[162],"complexity":[163],"proposed":[166],"N":[170],"6":[172],"12":[174],"cases":[175],"given.":[177]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}