{"id":"https://openalex.org/W2151614491","doi":"https://doi.org/10.1109/tit.1975.1055403","title":"On the residual correlation of finite-dimensional discrete Fourier transforms of stationary signals (Corresp.)","display_name":"On the residual correlation of finite-dimensional discrete Fourier transforms of stationary signals (Corresp.)","publication_year":1975,"publication_date":"1975-07-01","ids":{"openalex":"https://openalex.org/W2151614491","doi":"https://doi.org/10.1109/tit.1975.1055403","mag":"2151614491"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1975.1055403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1975.1055403","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","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/A5077171156","display_name":"Mohammad Hamidi","orcid":"https://orcid.org/0000-0002-8686-6942"},"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":true,"raw_author_name":"M. Hamidi","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"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108226525","display_name":"J. 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":"J. 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/A5077171156"],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":1.7607,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.86800527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"4","first_page":"480","last_page":"482"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9988999962806702,"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":0.9988999962806702,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9854000210762024,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/diagonal","display_name":"Diagonal","score":0.6875594854354858},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6649753451347351},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5857598781585693},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5656371116638184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5212464928627014},{"id":"https://openalex.org/keywords/covariance-matrix","display_name":"Covariance matrix","score":0.5198302865028381},{"id":"https://openalex.org/keywords/rational-quadratic-covariance-function","display_name":"Rational quadratic covariance function","score":0.4809374213218689},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.413329154253006},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.3468543291091919},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.32717519998550415},{"id":"https://openalex.org/keywords/covariance-intersection","display_name":"Covariance intersection","score":0.17042571306228638},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06825703382492065}],"concepts":[{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6875594854354858},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6649753451347351},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5857598781585693},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5656371116638184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5212464928627014},{"id":"https://openalex.org/C185142706","wikidata":"https://www.wikidata.org/wiki/Q1134404","display_name":"Covariance matrix","level":2,"score":0.5198302865028381},{"id":"https://openalex.org/C148893098","wikidata":"https://www.wikidata.org/wiki/Q7295778","display_name":"Rational quadratic covariance function","level":5,"score":0.4809374213218689},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.413329154253006},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.3468543291091919},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32717519998550415},{"id":"https://openalex.org/C83042196","wikidata":"https://www.wikidata.org/wiki/Q5178898","display_name":"Covariance intersection","level":4,"score":0.17042571306228638},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06825703382492065},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1975.1055403","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1975.1055403","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2026517766","https://openalex.org/W2035928002","https://openalex.org/W2059790158","https://openalex.org/W2160050411"],"related_works":["https://openalex.org/W2046078371","https://openalex.org/W2048777342","https://openalex.org/W4237672998","https://openalex.org/W4315750325","https://openalex.org/W1991005374","https://openalex.org/W143964308","https://openalex.org/W2022823194","https://openalex.org/W4296295513","https://openalex.org/W2952384845","https://openalex.org/W3128703436"],"abstract_inverted_index":{"The":[0,105],"covariance":[1,25,34,49,59,79,114],"matrix":[2,89],"of":[3,7,31,57,87,107],"the":[4,24,29,48,55,58,64,78,84,88,92,113],"Fourier":[5],"coefficients":[6],"<tex":[8,40,70,99],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[9,41,71,100],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</tex>":[10],"-":[11],"sampled":[12],"stationary":[13],"random":[14],"signals":[15],"is":[16,27,51,81],"studied.":[17],"Three":[18],"theorems":[19],"are":[20,109],"established.":[21],"1)":[22],"If":[23,47,77],"sequence":[26,50,80,115],"summable,":[28,54,83],"magnitude":[30,56],"every":[32],"off-diagonal":[33,93],"element":[35],"converges":[36,66,95],"to":[37,67,96],"zero":[38,68,97],"as":[39,69,98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N":[42,72,101],"\\rightarrow":[43,73,102],"\\infty</tex>":[44,74,103],".":[45,75,104],"2)":[46],"only":[52,91],"square":[53,82],"elements":[60,94],"sufficiently":[61],"far":[62],"from":[63],"diagonal":[65],"3)":[76],"weak":[85],"norm":[86],"containing":[90],"rates":[106],"convergence":[108],"also":[110],"determined":[111],"when":[112],"satisfies":[116],"additional":[117],"conditions.":[118]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}