{"id":"https://openalex.org/W1503228241","doi":"https://doi.org/10.1109/iscas.2003.1205115","title":"A split-radix algorithm for 2-D DFT","display_name":"A split-radix algorithm for 2-D DFT","publication_year":2003,"publication_date":"2003-11-21","ids":{"openalex":"https://openalex.org/W1503228241","doi":"https://doi.org/10.1109/iscas.2003.1205115","mag":"1503228241"},"language":"en","primary_location":{"id":"doi:10.1109/iscas.2003.1205115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2003.1205115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03.","raw_type":"proceedings-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/A5072026856","display_name":"Saad Bouguezel","orcid":"https://orcid.org/0000-0001-5041-7961"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"S. Bouguezel","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068820891","display_name":"M. Omair Ahmad","orcid":"https://orcid.org/0000-0002-2924-6659"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M.O. Ahmad","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#","institution_ids":["https://openalex.org/I60158472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013967994","display_name":"M.N.S. Swamy","orcid":"https://orcid.org/0000-0002-3989-5476"},"institutions":[{"id":"https://openalex.org/I60158472","display_name":"Concordia University","ror":"https://ror.org/0420zvk78","country_code":"CA","type":"education","lineage":["https://openalex.org/I60158472"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M.N.S. Swamy","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Concordia University, Montreal, QUE, Canada","institution_ids":["https://openalex.org/I60158472"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng. Concordia Univ., Montreal, Que., Canada#TAB#","institution_ids":["https://openalex.org/I60158472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5072026856"],"corresponding_institution_ids":["https://openalex.org/I60158472"],"apc_list":null,"apc_paid":null,"fwci":0.5856,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64420123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":null,"first_page":"III","last_page":"698"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9987999796867371,"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":0.9987999796867371,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9754999876022339,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9660000205039978,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/twiddle-factor","display_name":"Twiddle factor","score":0.9423238635063171},{"id":"https://openalex.org/keywords/split-radix-fft-algorithm","display_name":"Split-radix FFT algorithm","score":0.8310854434967041},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.8259567618370056},{"id":"https://openalex.org/keywords/prime-factor-fft-algorithm","display_name":"Prime-factor FFT algorithm","score":0.7928289771080017},{"id":"https://openalex.org/keywords/radix","display_name":"Radix (gastropod)","score":0.7908133268356323},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5566076636314392},{"id":"https://openalex.org/keywords/raders-fft-algorithm","display_name":"Rader's FFT algorithm","score":0.5312696695327759},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.5179023742675781},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.5133158564567566},{"id":"https://openalex.org/keywords/cooley\u2013tukey-fft-algorithm","display_name":"Cooley\u2013Tukey FFT algorithm","score":0.4858419597148895},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4770645201206207},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4334750771522522},{"id":"https://openalex.org/keywords/lookup-table","display_name":"Lookup table","score":0.41412097215652466},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3885357975959778},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.27814725041389465},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.24870234727859497},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.15453243255615234},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.11183464527130127}],"concepts":[{"id":"https://openalex.org/C4697666","wikidata":"https://www.wikidata.org/wiki/Q7857913","display_name":"Twiddle factor","level":5,"score":0.9423238635063171},{"id":"https://openalex.org/C103755468","wikidata":"https://www.wikidata.org/wiki/Q17103599","display_name":"Split-radix FFT algorithm","level":5,"score":0.8310854434967041},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.8259567618370056},{"id":"https://openalex.org/C77928272","wikidata":"https://www.wikidata.org/wiki/Q7243214","display_name":"Prime-factor FFT algorithm","level":5,"score":0.7928289771080017},{"id":"https://openalex.org/C2779091547","wikidata":"https://www.wikidata.org/wiki/Q287565","display_name":"Radix (gastropod)","level":2,"score":0.7908133268356323},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5566076636314392},{"id":"https://openalex.org/C69598009","wikidata":"https://www.wikidata.org/wiki/Q7280126","display_name":"Rader's FFT algorithm","level":5,"score":0.5312696695327759},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.5179023742675781},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.5133158564567566},{"id":"https://openalex.org/C1370844","wikidata":"https://www.wikidata.org/wiki/Q5167446","display_name":"Cooley\u2013Tukey FFT algorithm","level":3,"score":0.4858419597148895},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4770645201206207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4334750771522522},{"id":"https://openalex.org/C134835016","wikidata":"https://www.wikidata.org/wiki/Q690265","display_name":"Lookup table","level":2,"score":0.41412097215652466},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3885357975959778},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.27814725041389465},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.24870234727859497},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.15453243255615234},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.11183464527130127},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iscas.2003.1205115","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscas.2003.1205115","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2106805276","https://openalex.org/W2131706490"],"related_works":["https://openalex.org/W1984254719","https://openalex.org/W2149121524","https://openalex.org/W2031343199","https://openalex.org/W2144412928","https://openalex.org/W2047042807","https://openalex.org/W2371538653","https://openalex.org/W4255785774","https://openalex.org/W2977460836","https://openalex.org/W2061302196","https://openalex.org/W2042527476"],"abstract_inverted_index":{"In":[0,120],"this":[1],"paper,":[2],"the":[3,8,18,26,63,81,86,94,103,117,123,133,142,150],"split-radix":[4],"approach":[5],"for":[6,17,79,146],"computing":[7],"one-dimensional":[9],"(1-D)":[10],"discrete":[11],"Fourier":[12,21],"transform":[13,22],"(DFT)":[14],"is":[15,60,125],"extended":[16],"vector-radix":[19],"fast":[20],"(FFT)":[23],"to":[24,93,116,149],"compute":[25],"two-dimensional":[27],"(2-D)":[28],"DFT":[29],"of":[30,48,102,141],"size":[31],"2(r/sub":[32],"1/)/spl":[33],"times/2(r/sub":[34],"2/),":[35],"using":[36,132],"a":[37,43,49,55,71,77,128],"radix-2/spl":[38,50],"times/2":[39,51],"index":[40,52,74,108],"map":[41,46,53,58,75],"and":[42,54,76,110,144],"radix-8/spl":[44,72],"times/8":[45,73],"instead":[47],"radix-4/spl":[56],"times/4":[57],"as":[59],"done":[61],"in":[62,100,127],"classical":[64],"split":[65],"vector":[66],"radix":[67],"FFT":[68,96],"algorithms.":[69],"Since":[70],"method":[78],"combining":[80],"twiddle":[82,111],"factors":[83],"are":[84],"used,":[85],"new":[87],"algorithm":[88,124],"provides":[89],"significant":[90],"savings":[91],"compared":[92],"2-D":[95],"algorithms":[97],"previously":[98],"reported":[99],"terms":[101],"arithmetic":[104],"complexity,":[105],"data":[106],"transfer,":[107],"generation":[109],"factor":[112],"evaluation":[113],"or":[114],"access":[115],"lookup":[118],"table.":[119],"addition,":[121],"since":[122],"expressed":[126],"simple":[129],"matrix":[130],"form":[131],"Kronecker":[134],"product,":[135],"it":[136],"facilitates":[137],"an":[138,147],"easy":[139],"implementation":[140],"algorithm,":[143],"allows":[145],"extension":[148],"multidimensional":[151],"case.":[152]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
