{"id":"https://openalex.org/W2028911956","doi":"https://doi.org/10.1109/tassp.1985.1164687","title":"On computing the discrete Hartley transform","display_name":"On computing the discrete Hartley transform","publication_year":1985,"publication_date":"1985-10-01","ids":{"openalex":"https://openalex.org/W2028911956","doi":"https://doi.org/10.1109/tassp.1985.1164687","mag":"2028911956"},"language":"en","primary_location":{"id":"doi:10.1109/tassp.1985.1164687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164687","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and 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/A5059355730","display_name":"H.V. Sorensen","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Sorensen","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","Rice University (Houston, TX)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Rice University (Houston, TX)","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5105462806","display_name":"Douglas L. Jones","orcid":"https://orcid.org/0000-0002-7817-7629"},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Jones","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020160495","display_name":"C.S. Burrus","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Burrus","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021877117","display_name":"Michael T. Heideman","orcid":null},"institutions":[{"id":"https://openalex.org/I74775410","display_name":"Rice University","ror":"https://ror.org/008zs3103","country_code":"US","type":"education","lineage":["https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Heideman","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]},{"raw_affiliation_string":"Dept. of Electrical & Computer Eng., Rice University, Houston, TX, USA","institution_ids":["https://openalex.org/I74775410"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74775410"],"apc_list":null,"apc_paid":null,"fwci":12.8214,"has_fulltext":false,"cited_by_count":279,"citation_normalized_percentile":{"value":0.99140893,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"33","issue":"5","first_page":"1231","last_page":"1238"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9976999759674072,"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/T13292","display_name":"Embedded Systems and FPGA Applications","score":0.9825000166893005,"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/discrete-hartley-transform","display_name":"Discrete Hartley transform","score":0.9135736227035522},{"id":"https://openalex.org/keywords/split-radix-fft-algorithm","display_name":"Split-radix FFT algorithm","score":0.8375293016433716},{"id":"https://openalex.org/keywords/hartley-transform","display_name":"Hartley transform","score":0.8273175954818726},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.8102777004241943},{"id":"https://openalex.org/keywords/prime-factor-fft-algorithm","display_name":"Prime-factor FFT algorithm","score":0.7857117056846619},{"id":"https://openalex.org/keywords/raders-fft-algorithm","display_name":"Rader's FFT algorithm","score":0.7410466074943542},{"id":"https://openalex.org/keywords/twiddle-factor","display_name":"Twiddle factor","score":0.6666339039802551},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.6433439254760742},{"id":"https://openalex.org/keywords/decimation","display_name":"Decimation","score":0.6021639108657837},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5807582139968872},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.49662619829177856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47877418994903564},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.45336583256721497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4319833517074585},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.21243461966514587},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.16879621148109436},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.10267183184623718},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07795482873916626},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.0676892101764679},{"id":"https://openalex.org/keywords/short-time-fourier-transform","display_name":"Short-time Fourier transform","score":0.06297245621681213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06289985775947571}],"concepts":[{"id":"https://openalex.org/C192853989","wikidata":"https://www.wikidata.org/wiki/Q1006531","display_name":"Discrete Hartley transform","level":5,"score":0.9135736227035522},{"id":"https://openalex.org/C103755468","wikidata":"https://www.wikidata.org/wiki/Q17103599","display_name":"Split-radix FFT algorithm","level":5,"score":0.8375293016433716},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.8273175954818726},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.8102777004241943},{"id":"https://openalex.org/C77928272","wikidata":"https://www.wikidata.org/wiki/Q7243214","display_name":"Prime-factor FFT algorithm","level":5,"score":0.7857117056846619},{"id":"https://openalex.org/C69598009","wikidata":"https://www.wikidata.org/wiki/Q7280126","display_name":"Rader's FFT algorithm","level":5,"score":0.7410466074943542},{"id":"https://openalex.org/C4697666","wikidata":"https://www.wikidata.org/wiki/Q7857913","display_name":"Twiddle factor","level":5,"score":0.6666339039802551},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.6433439254760742},{"id":"https://openalex.org/C173642442","wikidata":"https://www.wikidata.org/wiki/Q1253346","display_name":"Decimation","level":3,"score":0.6021639108657837},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5807582139968872},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.49662619829177856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47877418994903564},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45336583256721497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4319833517074585},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.21243461966514587},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.16879621148109436},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.10267183184623718},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07795482873916626},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0676892101764679},{"id":"https://openalex.org/C166386157","wikidata":"https://www.wikidata.org/wiki/Q1477735","display_name":"Short-time Fourier transform","level":4,"score":0.06297245621681213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06289985775947571}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tassp.1985.1164687","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tassp.1985.1164687","pdf_url":null,"source":{"id":"https://openalex.org/S98930721","display_name":"IEEE Transactions on Acoustics Speech and Signal Processing","issn_l":"0096-3518","issn":["0096-3518"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Acoustics, Speech, and Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1965666210","https://openalex.org/W1975754844","https://openalex.org/W1997654368","https://openalex.org/W2006724675","https://openalex.org/W2061171222","https://openalex.org/W2073373260","https://openalex.org/W2106805276","https://openalex.org/W2111235403","https://openalex.org/W2137279816","https://openalex.org/W2141302248","https://openalex.org/W2162611351","https://openalex.org/W4249058433","https://openalex.org/W4254389654","https://openalex.org/W4296980820"],"related_works":["https://openalex.org/W2028911956","https://openalex.org/W1952542430","https://openalex.org/W2134128809","https://openalex.org/W2031515099","https://openalex.org/W1974963296","https://openalex.org/W2161738160","https://openalex.org/W2034310980","https://openalex.org/W2107529204","https://openalex.org/W2058765580","https://openalex.org/W2105168374"],"abstract_inverted_index":{"The":[0,56,84,103],"discrete":[1,147],"Hartley":[2,26,148],"transform":[3,8,27,54,149],"(DHT)":[4],"is":[5,43],"a":[6,15,22,33,120],"real-valued":[7,16,100,126,143],"closely":[9,79],"related":[10],"to":[11,65,69,95,108],"the":[12,41,70,73,76,88,96,111,116,125,133,141,146],"DFT":[13],"of":[14,36,58,72,114,132,145],"sequence.":[17],"Bracewell":[18],"has":[19],"recently":[20],"demonstrated":[21],"radix-2":[23],"decimation-in-time":[24],"fast":[25,37],"(FHT)":[28],"algorithm.":[29],"In":[30],"this":[31,152],"paper":[32],"complete":[34],"set":[35],"algorithms":[38,62,78,90,105],"for":[39,87,98],"computing":[40],"DHT":[42],"developed,":[44],"including":[45],"decimation-in-frequency,":[46],"radix-4,":[47],"split":[48],"radix,":[49],"prime":[50],"factor,":[51],"and":[52,75,93,119],"Winograd":[53],"algorithms.":[55,102,128],"philosophies":[57],"all":[59],"common":[60],"FFT":[61,82,101,127],"are":[63,91,106],"shown":[64,107],"be":[66],"equally":[67],"applicable":[68],"computation":[71,131],"DHT,":[74],"FHT":[77,89,104,134],"resemble":[80],"their":[81],"counterparts.":[83],"operation":[85],"counts":[86,97],"determined":[92],"compared":[94],"corresponding":[99],"always":[109],"require":[110],"same":[112,117],"number":[113],"multiplications,":[115],"storage,":[118],"few":[121],"more":[122,136],"additions":[123],"than":[124],"Even":[129],"though":[130],"takes":[135],"operations,":[137],"in":[138],"some":[139],"situations":[140],"inherently":[142],"nature":[144],"may":[150],"justify":[151],"extra":[153],"cost.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":12},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
