{"id":"https://openalex.org/W4386038319","doi":"https://doi.org/10.1109/lsp.2023.3305193","title":"Pure Number Discrete Fractional Complex Hadamard Transform","display_name":"Pure Number Discrete Fractional Complex Hadamard Transform","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4386038319","doi":"https://doi.org/10.1109/lsp.2023.3305193"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2023.3305193","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3305193","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","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/A5102759368","display_name":"Zi-Chen Fan","orcid":"https://orcid.org/0009-0009-7355-8594"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zi-Chen Fan","raw_affiliation_strings":["School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101614656","display_name":"Di Li","orcid":"https://orcid.org/0000-0001-8059-8783"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Di Li","raw_affiliation_strings":["School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China"],"affiliations":[{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054558832","display_name":"Susanto Rahardja","orcid":"https://orcid.org/0000-0003-0831-6934"},"institutions":[{"id":"https://openalex.org/I168639165","display_name":"Singapore Institute of Technology","ror":"https://ror.org/01v2c2791","country_code":"SG","type":"education","lineage":["https://openalex.org/I168639165"]},{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Susanto Rahardja","raw_affiliation_strings":["School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China","Singapore Institute of Technology, Singapore"],"affiliations":[{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi&#x0027;an, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, Shaanxi, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Singapore Institute of Technology, Singapore","institution_ids":["https://openalex.org/I168639165"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102759368"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":0.5957,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65065394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"30","issue":null,"first_page":"1087","last_page":"1091"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9991999864578247,"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":0.9991999864578247,"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/T11873","display_name":"PAPR reduction in OFDM","score":0.996399998664856,"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/hadamard-transform","display_name":"Hadamard transform","score":0.8104330897331238},{"id":"https://openalex.org/keywords/kronecker-product","display_name":"Kronecker product","score":0.7882407903671265},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.6241924166679382},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5970878601074219},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.566002607345581},{"id":"https://openalex.org/keywords/hadamard-product","display_name":"Hadamard product","score":0.5550466179847717},{"id":"https://openalex.org/keywords/discrete-hartley-transform","display_name":"Discrete Hartley transform","score":0.5170651078224182},{"id":"https://openalex.org/keywords/hadamard-matrix","display_name":"Hadamard matrix","score":0.4999244213104248},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.48882147669792175},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47792893648147583},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4758971631526947},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4528995752334595},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.4330004155635834},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.43228667974472046},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4226109981536865},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.3734568953514099},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.3333185911178589},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.258245050907135},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.14735963940620422},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13154715299606323}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.8104330897331238},{"id":"https://openalex.org/C46030957","wikidata":"https://www.wikidata.org/wiki/Q1238125","display_name":"Kronecker product","level":3,"score":0.7882407903671265},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.6241924166679382},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5970878601074219},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.566002607345581},{"id":"https://openalex.org/C90230998","wikidata":"https://www.wikidata.org/wiki/Q3406746","display_name":"Hadamard product","level":3,"score":0.5550466179847717},{"id":"https://openalex.org/C192853989","wikidata":"https://www.wikidata.org/wiki/Q1006531","display_name":"Discrete Hartley transform","level":5,"score":0.5170651078224182},{"id":"https://openalex.org/C30463267","wikidata":"https://www.wikidata.org/wiki/Q1422682","display_name":"Hadamard matrix","level":3,"score":0.4999244213104248},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.48882147669792175},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47792893648147583},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4758971631526947},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4528995752334595},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.4330004155635834},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.43228667974472046},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4226109981536865},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3734568953514099},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.3333185911178589},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.258245050907135},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.14735963940620422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13154715299606323},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/lsp.2023.3305193","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3305193","pdf_url":null,"source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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 Signal Processing Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.49000000953674316,"id":"https://metadata.un.org/sdg/9","display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W984332474","https://openalex.org/W1884852932","https://openalex.org/W1978997021","https://openalex.org/W1997108546","https://openalex.org/W2001543623","https://openalex.org/W2001751266","https://openalex.org/W2003173774","https://openalex.org/W2013823030","https://openalex.org/W2026976756","https://openalex.org/W2084371999","https://openalex.org/W2090697566","https://openalex.org/W2105282081","https://openalex.org/W2133001976","https://openalex.org/W2166143222","https://openalex.org/W2314929147","https://openalex.org/W2803629055","https://openalex.org/W2963887371","https://openalex.org/W3040110456","https://openalex.org/W3112373213","https://openalex.org/W3161807206","https://openalex.org/W6639105583"],"related_works":["https://openalex.org/W2024672858","https://openalex.org/W1546716936","https://openalex.org/W2604983122","https://openalex.org/W1983543686","https://openalex.org/W1968037667","https://openalex.org/W2375071087","https://openalex.org/W2322982587","https://openalex.org/W4283588189","https://openalex.org/W2036171710","https://openalex.org/W4386038319"],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,95],"novel":[4],"discrete":[5,12,27],"fractional":[6,13,28],"transform":[7,16,30,83],"termed":[8],"as":[9],"pure":[10,67],"number":[11,68],"complex":[14],"Hadamard":[15,29],"(PN-FCHT).":[17],"The":[18],"proposed":[19],"PN-FCHT":[20,35,56,79],"offers":[21],"three":[22],"advantages":[23],"over":[24],"the":[25,33,38,45,49,78,82],"traditional":[26],"(FHT).":[31],"Firstly,":[32],"higher-order":[34],"matrix":[36],"exhibits":[37],"Self-Kronecker":[39],"product":[40],"structure,":[41],"which":[42],"allows":[43],"for":[44,64],"recursive":[46],"generation":[47],"from":[48],"<inline-formula":[50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[51],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[52],"notation=\"LaTeX\">$2\\times":[53],"2$</tex-math></inline-formula>":[54],"core":[55],"matrix.":[57],"Secondly,":[58],"it":[59],"possesses":[60],"two":[61],"important":[62],"properties":[63],"computation,":[65],"i.e.":[66],"property.":[69],"Lastly,":[70],"compared":[71],"to":[72,89],"existing":[73],"state-of-the-art":[74],"fast":[75],"FHT":[76],"algorithms,":[77],"can":[80],"reduce":[81],"multiplication":[84],"computational":[85],"complexity":[86],"by":[87],"up":[88],"80%":[90],"and":[91],"this":[92],"results":[93],"in":[94],"more":[96],"efficient":[97],"hardware":[98],"implementation.":[99]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-27T14:29:43.386196","created_date":"2025-10-10T00:00:00"}