{"id":"https://openalex.org/W2003173774","doi":"https://doi.org/10.1007/s11075-014-9862-8","title":"Fast algorithm for discrete fractional Hadamard transform","display_name":"Fast algorithm for discrete fractional Hadamard transform","publication_year":2014,"publication_date":"2014-08-13","ids":{"openalex":"https://openalex.org/W2003173774","doi":"https://doi.org/10.1007/s11075-014-9862-8","mag":"2003173774"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-014-9862-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9862-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9862-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9862-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019629900","display_name":"Aleksandr Cariow","orcid":"https://orcid.org/0000-0002-4513-4593"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology in Szczecin","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Aleksandr Cariow","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","Faculty of Computer Science and Information Technology, West Pomeranian University of Technology Szczecin, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]},{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036530734","display_name":"Dorota Majorkowska-Mech","orcid":"https://orcid.org/0000-0002-2123-0521"},"institutions":[{"id":"https://openalex.org/I155313962","display_name":"West Pomeranian University of Technology in Szczecin","ror":"https://ror.org/0596m7f19","country_code":"PL","type":"education","lineage":["https://openalex.org/I155313962"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Dorota Majorkowska-Mech","raw_affiliation_strings":["Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","Faculty of Computer Science and Information Technology, West Pomeranian University of Technology Szczecin, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]},{"raw_affiliation_string":"Faculty of Computer Science and Information Technology, West Pomeranian University of Technology Szczecin, Poland","institution_ids":["https://openalex.org/I155313962"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019629900"],"corresponding_institution_ids":["https://openalex.org/I155313962"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.5223,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.70986444,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"3","first_page":"585","last_page":"600"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9944000244140625,"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/T11130","display_name":"Coding theory and cryptography","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/hadamard-transform","display_name":"Hadamard transform","score":0.9414283633232117},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7281129360198975},{"id":"https://openalex.org/keywords/discrete-hartley-transform","display_name":"Discrete Hartley transform","score":0.6129750609397888},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6017581224441528},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.563164234161377},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5145782828330994},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.30423301458358765},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1632240116596222},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.10809436440467834}],"concepts":[{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.9414283633232117},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7281129360198975},{"id":"https://openalex.org/C192853989","wikidata":"https://www.wikidata.org/wiki/Q1006531","display_name":"Discrete Hartley transform","level":5,"score":0.6129750609397888},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6017581224441528},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.563164234161377},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5145782828330994},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.30423301458358765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1632240116596222},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.10809436440467834},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-014-9862-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9862-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9862-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s11075-014-9862-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-014-9862-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11075-014-9862-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2003173774.pdf","grobid_xml":"https://content.openalex.org/works/W2003173774.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W133257549","https://openalex.org/W401986301","https://openalex.org/W761890699","https://openalex.org/W984332474","https://openalex.org/W1576481659","https://openalex.org/W1606480398","https://openalex.org/W1630120088","https://openalex.org/W1884852932","https://openalex.org/W1996519494","https://openalex.org/W2008632147","https://openalex.org/W2013823030","https://openalex.org/W2047011378","https://openalex.org/W2067135250","https://openalex.org/W2084980870","https://openalex.org/W2090697566","https://openalex.org/W2094181097","https://openalex.org/W2100912680","https://openalex.org/W2166143222","https://openalex.org/W2484231070"],"related_works":["https://openalex.org/W4379386706","https://openalex.org/W3040110456","https://openalex.org/W1884852932","https://openalex.org/W2036171710","https://openalex.org/W2356259437","https://openalex.org/W3197029778","https://openalex.org/W2128992369","https://openalex.org/W2090697566","https://openalex.org/W2118155316","https://openalex.org/W2142891205"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,21],"fast":[4],"algorithm":[5,42],"for":[6,13],"computing":[7],"the":[8,14,29,43],"discrete":[9,30],"fractional":[10,31],"Hadamard":[11,32],"transform":[12,33],"input":[15],"vector":[16],"of":[17,23,28,45],"length":[18],"N,":[19],"being":[20],"power":[22],"two.":[24],"A":[25],"direct":[26],"calculation":[27],"requires":[34],"N":[35,51],"2":[36,53],"real":[37,46],"multiplications,":[38],"while":[39],"in":[40],"our":[41],"number":[44],"multiplications":[47],"is":[48],"reduced":[49],"to":[50],"log":[52],"N.":[54]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}