{"id":"https://openalex.org/W2102182691","doi":"https://doi.org/10.1109/jproc.2004.840301","title":"The Design and Implementation of FFTW3","display_name":"The Design and Implementation of FFTW3","publication_year":2005,"publication_date":"2005-01-24","ids":{"openalex":"https://openalex.org/W2102182691","doi":"https://doi.org/10.1109/jproc.2004.840301","mag":"2102182691"},"language":"en","primary_location":{"id":"doi:10.1109/jproc.2004.840301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jproc.2004.840301","pdf_url":null,"source":{"id":"https://openalex.org/S68686220","display_name":"Proceedings of the IEEE","issn_l":"0018-9219","issn":["0018-9219","1558-2256"],"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":"Proceedings of the IEEE","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/A5080084162","display_name":"Matteo Frigo","orcid":"https://orcid.org/0000-0001-8150-1090"},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]},{"id":"https://openalex.org/I4210156936","display_name":"IBM Research - Austin","ror":"https://ror.org/05gjbbg60","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115","https://openalex.org/I4210156936"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Frigo","raw_affiliation_strings":["IBM Austin Research Laboratory, Austin, TX, USA","IBM Austin Research Lab, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Austin Research Laboratory, Austin, TX, USA","institution_ids":["https://openalex.org/I4210156936"]},{"raw_affiliation_string":"IBM Austin Research Lab, TX, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087662980","display_name":"Steven G. Johnson","orcid":"https://orcid.org/0000-0001-7327-4967"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S.G. Johnson","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA","Massachusetts Institute of Technology; ,; Cambridge MA USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology; ,; Cambridge MA USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":200.7331,"has_fulltext":false,"cited_by_count":5158,"citation_normalized_percentile":{"value":1.0,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"93","issue":"2","first_page":"216","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9997000098228455,"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":0.9997000098228455,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11417","display_name":"Advancements in PLL and VCO Technologies","score":0.9980999827384949,"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/compiler","display_name":"Compiler","score":0.8141271471977234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7921439409255981},{"id":"https://openalex.org/keywords/simd","display_name":"SIMD","score":0.7016284465789795},{"id":"https://openalex.org/keywords/implementation","display_name":"Implementation","score":0.6879615187644958},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.6314584612846375},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.5605199933052063},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5421891808509827},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.5222766399383545},{"id":"https://openalex.org/keywords/software","display_name":"Software","score":0.5198136568069458},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5112662315368652},{"id":"https://openalex.org/keywords/sine-and-cosine-transforms","display_name":"Sine and cosine transforms","score":0.4668107032775879},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4480488896369934},{"id":"https://openalex.org/keywords/software-implementation","display_name":"Software implementation","score":0.41902539134025574},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4140244722366333},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.40869638323783875},{"id":"https://openalex.org/keywords/computer-engineering","display_name":"Computer engineering","score":0.39382797479629517},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.37645411491394043},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3193630576133728},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.134611576795578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10508105158805847},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08654695749282837}],"concepts":[{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.8141271471977234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7921439409255981},{"id":"https://openalex.org/C150552126","wikidata":"https://www.wikidata.org/wiki/Q339387","display_name":"SIMD","level":2,"score":0.7016284465789795},{"id":"https://openalex.org/C26713055","wikidata":"https://www.wikidata.org/wiki/Q245962","display_name":"Implementation","level":2,"score":0.6879615187644958},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.6314584612846375},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.5605199933052063},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5421891808509827},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.5222766399383545},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.5198136568069458},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5112662315368652},{"id":"https://openalex.org/C47615080","wikidata":"https://www.wikidata.org/wiki/Q1328722","display_name":"Sine and cosine transforms","level":5,"score":0.4668107032775879},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4480488896369934},{"id":"https://openalex.org/C2983609787","wikidata":"https://www.wikidata.org/wiki/Q10534782","display_name":"Software implementation","level":3,"score":0.41902539134025574},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4140244722366333},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.40869638323783875},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.39382797479629517},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.37645411491394043},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3193630576133728},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.134611576795578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10508105158805847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08654695749282837},{"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/C166386157","wikidata":"https://www.wikidata.org/wiki/Q1477735","display_name":"Short-time Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/jproc.2004.840301","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jproc.2004.840301","pdf_url":null,"source":{"id":"https://openalex.org/S68686220","display_name":"Proceedings of the IEEE","issn_l":"0018-9219","issn":["0018-9219","1558-2256"],"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":"Proceedings of the IEEE","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.136.7045","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.136.7045","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.mit.edu/~stevenj/papers/FrigoJo05.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.66.3097","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.3097","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.fftw.org/fftw-paper-ieee.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W6645728","https://openalex.org/W123426918","https://openalex.org/W196260823","https://openalex.org/W1489894178","https://openalex.org/W1499852305","https://openalex.org/W1508951955","https://openalex.org/W1547277055","https://openalex.org/W1820775600","https://openalex.org/W1916685473","https://openalex.org/W1966904279","https://openalex.org/W1972209410","https://openalex.org/W1985426706","https://openalex.org/W1989539889","https://openalex.org/W1997654368","https://openalex.org/W2010918451","https://openalex.org/W2011191879","https://openalex.org/W2022028092","https://openalex.org/W2022281229","https://openalex.org/W2029102349","https://openalex.org/W2036812077","https://openalex.org/W2037026538","https://openalex.org/W2037221767","https://openalex.org/W2045836768","https://openalex.org/W2046630216","https://openalex.org/W2048332769","https://openalex.org/W2049835395","https://openalex.org/W2050879237","https://openalex.org/W2052977106","https://openalex.org/W2054042449","https://openalex.org/W2057638273","https://openalex.org/W2060876740","https://openalex.org/W2061171222","https://openalex.org/W2069441027","https://openalex.org/W2072277531","https://openalex.org/W2073086065","https://openalex.org/W2075924804","https://openalex.org/W2086393337","https://openalex.org/W2095875205","https://openalex.org/W2096070062","https://openalex.org/W2100413522","https://openalex.org/W2110931499","https://openalex.org/W2111235403","https://openalex.org/W2114012357","https://openalex.org/W2123119012","https://openalex.org/W2127391977","https://openalex.org/W2134128809","https://openalex.org/W2134572726","https://openalex.org/W2135653967","https://openalex.org/W2136952590","https://openalex.org/W2137367115","https://openalex.org/W2138692623","https://openalex.org/W2140215930","https://openalex.org/W2143840042","https://openalex.org/W2150654326","https://openalex.org/W2163491234","https://openalex.org/W2164197394","https://openalex.org/W2171641226","https://openalex.org/W2432517183","https://openalex.org/W2478884216","https://openalex.org/W2752885492","https://openalex.org/W2764683856","https://openalex.org/W2916086000","https://openalex.org/W3006102157","https://openalex.org/W3016647895","https://openalex.org/W3140728482","https://openalex.org/W3145042860","https://openalex.org/W3145128584","https://openalex.org/W4243796884","https://openalex.org/W4254389654","https://openalex.org/W4299616802","https://openalex.org/W6682220324"],"related_works":["https://openalex.org/W1563354830","https://openalex.org/W3197070112","https://openalex.org/W2953981603","https://openalex.org/W2944076056","https://openalex.org/W2962923203","https://openalex.org/W4231970225","https://openalex.org/W4234606700","https://openalex.org/W2002380597","https://openalex.org/W1922999178","https://openalex.org/W126348833"],"abstract_inverted_index":{"FFTW":[0],"is":[1,32],"an":[2,25,29],"implementation":[3,30],"of":[4,60,66,71,86],"the":[5,13,39,87],"discrete":[6,88],"Fourier":[7],"transform":[8],"(DFT)":[9],"that":[10,23,31,42],"adapts":[11],"to":[12,17],"hardware":[14],"in":[15],"order":[16],"maximize":[18],"performance.":[19],"This":[20],"paper":[21],"shows":[22],"such":[24],"approach":[26],"can":[27,82],"yield":[28],"competitive":[33],"with":[34],"hand-optimized":[35],"libraries,":[36],"and":[37,49,77,90],"describes":[38],"software":[40],"structure":[41],"makes":[43],"our":[44],"current":[45],"FFTW3":[46],"version":[47],"flexible":[48],"adaptive.":[50],"We":[51],"further":[52],"discuss":[53],"a":[54,63,79,95],"new":[55,64],"algorithm":[56],"for":[57],"real-data":[58],"DFTs":[59,68],"prime":[61],"size,":[62],"way":[65],"implementing":[67],"by":[69],"means":[70],"machine-specific":[72],"single-instruction,":[73],"multiple-data":[74],"(SIMD)":[75],"instructions,":[76],"how":[78],"special-purpose":[80],"compiler":[81],"derive":[83],"optimized":[84],"implementations":[85],"cosine":[89],"sine":[91],"transforms":[92],"automatically":[93],"from":[94],"DFT":[96],"algorithm.":[97]},"counts_by_year":[{"year":2026,"cited_by_count":100},{"year":2025,"cited_by_count":177},{"year":2024,"cited_by_count":216},{"year":2023,"cited_by_count":251},{"year":2022,"cited_by_count":215},{"year":2021,"cited_by_count":288},{"year":2020,"cited_by_count":277},{"year":2019,"cited_by_count":254},{"year":2018,"cited_by_count":267},{"year":2017,"cited_by_count":229},{"year":2016,"cited_by_count":278},{"year":2015,"cited_by_count":270},{"year":2014,"cited_by_count":306},{"year":2013,"cited_by_count":308},{"year":2012,"cited_by_count":261}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}