{"id":"https://openalex.org/W1832762830","doi":"https://doi.org/10.1137/100805777","title":"Algebraic Signal Processing Theory: Cooley\u2013Tukey-Type Algorithms for Polynomial Transforms Based on Induction","display_name":"Algebraic Signal Processing Theory: Cooley\u2013Tukey-Type Algorithms for Polynomial Transforms Based on Induction","publication_year":2011,"publication_date":"2011-04-01","ids":{"openalex":"https://openalex.org/W1832762830","doi":"https://doi.org/10.1137/100805777","mag":"1832762830"},"language":"en","primary_location":{"id":"doi:10.1137/100805777","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100805777","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5023723304","display_name":"Aliaksei Sandryhaila","orcid":null},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Aliaksei Sandryhaila","raw_affiliation_strings":["Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101863660","display_name":"Jelena Kova\u010devi\u0107","orcid":"https://orcid.org/0000-0003-0139-2803"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jelena Kova\u010devi\u0107","raw_affiliation_strings":["Carnegie Mellon University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076407181","display_name":"Markus P\u00fcschel","orcid":"https://orcid.org/0000-0001-8834-8551"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Markus P\u00fcschel","raw_affiliation_strings":["Swiss Federal Institute of Technology, Zu\u0308rich"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Swiss Federal Institute of Technology, Zu\u0308rich","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023723304"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":3.43,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.92787867,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"32","issue":"2","first_page":"364","last_page":"384"},"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":0.9988999962806702,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7437765598297119},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"Discrete Fourier transform (general)","score":0.6264313459396362},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5903371572494507},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5831261277198792},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.5623236894607544},{"id":"https://openalex.org/keywords/hartley-transform","display_name":"Hartley transform","score":0.5294990539550781},{"id":"https://openalex.org/keywords/sine-and-cosine-transforms","display_name":"Sine and cosine transforms","score":0.45630592107772827},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.44954153895378113},{"id":"https://openalex.org/keywords/non-uniform-discrete-fourier-transform","display_name":"Non-uniform discrete Fourier transform","score":0.4476093053817749},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.44132286310195923},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.41987723112106323},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.38743478059768677},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3613564372062683},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.3435804545879364},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2156020700931549},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.20526760816574097},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1864258050918579},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1594703495502472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7437765598297119},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.6264313459396362},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5903371572494507},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5831261277198792},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.5623236894607544},{"id":"https://openalex.org/C67757890","wikidata":"https://www.wikidata.org/wiki/Q1567607","display_name":"Hartley transform","level":5,"score":0.5294990539550781},{"id":"https://openalex.org/C47615080","wikidata":"https://www.wikidata.org/wiki/Q1328722","display_name":"Sine and cosine transforms","level":5,"score":0.45630592107772827},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.44954153895378113},{"id":"https://openalex.org/C62058723","wikidata":"https://www.wikidata.org/wiki/Q7049066","display_name":"Non-uniform discrete Fourier transform","level":5,"score":0.4476093053817749},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.44132286310195923},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.41987723112106323},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.38743478059768677},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3613564372062683},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.3435804545879364},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2156020700931549},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.20526760816574097},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1864258050918579},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1594703495502472},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100805777","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100805777","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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":38,"referenced_works":["https://openalex.org/W1500032036","https://openalex.org/W1538005160","https://openalex.org/W1600546103","https://openalex.org/W1805381866","https://openalex.org/W1916685473","https://openalex.org/W1964153492","https://openalex.org/W1975754844","https://openalex.org/W1978798278","https://openalex.org/W1986263670","https://openalex.org/W1992283714","https://openalex.org/W1998849268","https://openalex.org/W2017928198","https://openalex.org/W2018483531","https://openalex.org/W2019764548","https://openalex.org/W2021962862","https://openalex.org/W2028911956","https://openalex.org/W2029769546","https://openalex.org/W2034469359","https://openalex.org/W2059998776","https://openalex.org/W2060231433","https://openalex.org/W2061171222","https://openalex.org/W2064988984","https://openalex.org/W2078104849","https://openalex.org/W2086393337","https://openalex.org/W2088086218","https://openalex.org/W2092378566","https://openalex.org/W2099490452","https://openalex.org/W2108603643","https://openalex.org/W2111235403","https://openalex.org/W2115755118","https://openalex.org/W2118193919","https://openalex.org/W2123222407","https://openalex.org/W2139880562","https://openalex.org/W2145246767","https://openalex.org/W2149599446","https://openalex.org/W2169691387","https://openalex.org/W2585083698","https://openalex.org/W4235934856"],"related_works":["https://openalex.org/W2112696840","https://openalex.org/W1843552549","https://openalex.org/W2945379152","https://openalex.org/W2343504300","https://openalex.org/W2142891205","https://openalex.org/W4299146998","https://openalex.org/W3021381481","https://openalex.org/W3025787786","https://openalex.org/W3197029778","https://openalex.org/W2963406743"],"abstract_inverted_index":{"A":[0],"polynomial":[1,67,75,82],"transform":[2,112,117],"is":[3,16],"the":[4,36,50,72,78,90,109,114],"multiplication":[5],"of":[6,38,81,93,118],"an":[7,101],"input":[8],"vector":[9],"by":[10,88],"a":[11,22,28,59,97],"matrix":[12],"whose":[13],"th":[14],"element":[15],"defined":[17],"as":[18,96],"for":[19,66,108],"polynomials":[20],"from":[21,27],"list":[23,29],"and":[24,43,77,113],"sample":[25],"points":[26],".":[30],"Such":[31],"transforms":[32,76],"find":[33],"applications":[34],"in":[35],"areas":[37],"signal":[39],"processing,":[40],"data":[41],"compression,":[42],"function":[44],"interpolation.":[45],"An":[46],"important":[47],"example":[48],"includes":[49],"discrete":[51,110,115],"Fourier":[52,111],"transform.":[53],"In":[54],"this":[55],"paper":[56],"we":[57,85,103],"introduce":[58],"novel":[60,105],"technique":[61,70],"to":[62],"derive":[63,86,104],"fast":[64],"algorithms":[65,87,107],"transforms.":[68],"The":[69],"uses":[71],"relationship":[73],"between":[74],"representation":[79],"theory":[80],"algebras.":[83],"Specifically,":[84],"decomposing":[89],"regular":[91],"modules":[92],"these":[94],"algebras":[95],"stepwise":[98],"induction.":[99],"As":[100],"application,":[102],"general-radix":[106],"cosine":[116],"type":[119],"4.":[120]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-28T14:05:53.105641","created_date":"2025-10-10T00:00:00"}