{"id":"https://openalex.org/W1990535777","doi":"https://doi.org/10.1109/tpami.1979.4766945","title":"Asymptotic Properties of Discrete Unitary Transforms","display_name":"Asymptotic Properties of Discrete Unitary Transforms","publication_year":1979,"publication_date":"1979-10-01","ids":{"openalex":"https://openalex.org/W1990535777","doi":"https://doi.org/10.1109/tpami.1979.4766945","mag":"1990535777","pmid":"https://pubmed.ncbi.nlm.nih.gov/21868871"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.1979.4766945","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1979.4766945","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5110276638","display_name":"Yechiam Yemini","orcid":null},"institutions":[{"id":"https://openalex.org/I2801204180","display_name":"Marina Del Rey Hospital","ror":"https://ror.org/05wqyfz02","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2801204180"]},{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yechiam Yemini","raw_affiliation_strings":["MEMBER, IEEE, Engineering and Applied Science, University of California, Los Angeles, CA 90024; Information Science Institute, Marina Del Rey, CA","School of Engineering and Applied Science, University of California, Los Angeles, CA, USA","Information Science Institute, Marina Del Rey, CA, USA"],"affiliations":[{"raw_affiliation_string":"MEMBER, IEEE, Engineering and Applied Science, University of California, Los Angeles, CA 90024; Information Science Institute, Marina Del Rey, CA","institution_ids":[]},{"raw_affiliation_string":"School of Engineering and Applied Science, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Information Science Institute, Marina Del Rey, CA, USA","institution_ids":["https://openalex.org/I2801204180"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108208924","display_name":"Judea Pearl","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Judea Pearl","raw_affiliation_strings":["School of Engineering and Applied Science, University of California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"School of Engineering and Applied Science, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110276638"],"corresponding_institution_ids":["https://openalex.org/I161318765","https://openalex.org/I2801204180"],"apc_list":null,"apc_paid":null,"fwci":0.6137,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.61590585,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"PAMI-1","issue":"4","first_page":"366","last_page":"371"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9904000163078308,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9872000217437744,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/mathematics","display_name":"Mathematics","score":0.6100188493728638},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.6000416278839111},{"id":"https://openalex.org/keywords/discrete-cosine-transform","display_name":"Discrete cosine transform","score":0.5733522772789001},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5407220721244812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49554288387298584},{"id":"https://openalex.org/keywords/discrete-sine-transform","display_name":"Discrete sine transform","score":0.4151294529438019},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.41484352946281433},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4122558534145355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3006477355957031},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26144707202911377},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16737264394760132},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.13769745826721191},{"id":"https://openalex.org/keywords/fractional-fourier-transform","display_name":"Fractional Fourier transform","score":0.12859714031219482},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.09397530555725098},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08958926796913147},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.08700099587440491},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07502609491348267}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6100188493728638},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.6000416278839111},{"id":"https://openalex.org/C2221639","wikidata":"https://www.wikidata.org/wiki/Q2877","display_name":"Discrete cosine transform","level":3,"score":0.5733522772789001},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5407220721244812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49554288387298584},{"id":"https://openalex.org/C167058841","wikidata":"https://www.wikidata.org/wiki/Q971039","display_name":"Discrete sine transform","level":5,"score":0.4151294529438019},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.41484352946281433},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4122558534145355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3006477355957031},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26144707202911377},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16737264394760132},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.13769745826721191},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.12859714031219482},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.09397530555725098},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08958926796913147},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.08700099587440491},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07502609491348267},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.1979.4766945","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.1979.4766945","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:21868871","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21868871","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W139689721","https://openalex.org/W1601314568","https://openalex.org/W2014512781","https://openalex.org/W2028788342","https://openalex.org/W2031614119","https://openalex.org/W2045463928","https://openalex.org/W2059790158","https://openalex.org/W2116838368","https://openalex.org/W2145341540","https://openalex.org/W2151614491","https://openalex.org/W2160050411","https://openalex.org/W2330381107","https://openalex.org/W4307370599"],"related_works":["https://openalex.org/W2124172827","https://openalex.org/W2963134360","https://openalex.org/W2024146866","https://openalex.org/W2132418619","https://openalex.org/W1553874498","https://openalex.org/W2354377491","https://openalex.org/W2186032231","https://openalex.org/W2086323236","https://openalex.org/W1976370567","https://openalex.org/W4309177872"],"abstract_inverted_index":{"A":[0],"method":[1,17,41],"for":[2,31,53],"studying":[3],"the":[4,24,46],"asymptotic":[5],"behavior":[6],"of":[7,23,27,39],"discrete":[8,47],"transformations":[9],"is":[10,43,50],"developed":[11],"using":[12],"numerical":[13],"quadrature":[14],"theory.":[15],"This":[16],"allows":[18],"a":[19,36],"more":[20],"convenient":[21],"examination":[22],"correlation":[25],"properties":[26],"common":[28],"unitary":[29],"transforms":[30],"large":[32],"block":[33],"sizes.":[34],"As":[35],"practical":[37],"result":[38],"this":[40],"it":[42],"shown":[44],"that":[45],"cosine":[48],"transform":[49],"asymptotically":[51],"optimal":[52],"all":[54],"finite-order":[55],"Markov":[56],"signals.":[57]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}