{"id":"https://openalex.org/W2123288809","doi":"https://doi.org/10.1109/jproc.2002.1015001","title":"Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications","display_name":"Statistical modeling of discrete-time chaotic processes-basic finite-dimensional tools and applications","publication_year":2002,"publication_date":"2002-05-01","ids":{"openalex":"https://openalex.org/W2123288809","doi":"https://doi.org/10.1109/jproc.2002.1015001","mag":"2123288809"},"language":"en","primary_location":{"id":"doi:10.1109/jproc.2002.1015001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jproc.2002.1015001","pdf_url":null,"source":{"id":"https://openalex.org/S68686220","display_name":"Proceedings of the IEEE","issn_l":"0018-9219","issn":["0018-9219","1558-2256"],"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":"Proceedings of the IEEE","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/A5062714455","display_name":"Gianluca Setti","orcid":"https://orcid.org/0000-0002-2496-1856"},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"G. Setti","raw_affiliation_strings":["CEG-ARCES, University of Bologna, Bologna, Italy","CEG-DI, University of Ferrara, Ferrara, Italy"],"affiliations":[{"raw_affiliation_string":"CEG-ARCES, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"CEG-DI, University of Ferrara, Ferrara, Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025958450","display_name":"G. Mazzini","orcid":"https://orcid.org/0000-0003-3867-760X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]},{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Mazzini","raw_affiliation_strings":["CEG-ARCES, University of Bologna, Bologna, Italy","CEG-DI, University of Ferrara, Ferrara, Italy"],"affiliations":[{"raw_affiliation_string":"CEG-ARCES, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"CEG-DI, University of Ferrara, Ferrara, Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088876922","display_name":"Riccardo Rovatti","orcid":"https://orcid.org/0000-0002-4731-7860"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"R. Rovatti","raw_affiliation_strings":["CEG-ARCES, University of Bologna, Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"CEG-ARCES, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024452213","display_name":"Sergio Callegari","orcid":"https://orcid.org/0000-0001-6719-598X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Callegari","raw_affiliation_strings":["CEG-ARCES, University of Bologna, Bologna, Italy"],"affiliations":[{"raw_affiliation_string":"CEG-ARCES, University of Bologna, Bologna, Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5062714455"],"corresponding_institution_ids":["https://openalex.org/I201324441","https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":10.8452,"has_fulltext":false,"cited_by_count":156,"citation_normalized_percentile":{"value":0.99015776,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"90","issue":"5","first_page":"662","last_page":"690"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9980000257492065,"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/T10244","display_name":"Chaos control and synchronization","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.98580002784729,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.7365860342979431},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6684365272521973},{"id":"https://openalex.org/keywords/statistical-signal-processing","display_name":"Statistical signal processing","score":0.6583510041236877},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5542890429496765},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5326344966888428},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45417141914367676},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.41952067613601685},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.30199572443962097},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2906736433506012},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.211769700050354},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.16423824429512024}],"concepts":[{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.7365860342979431},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6684365272521973},{"id":"https://openalex.org/C105125183","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Statistical signal processing","level":4,"score":0.6583510041236877},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5542890429496765},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5326344966888428},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45417141914367676},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.41952067613601685},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.30199572443962097},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2906736433506012},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.211769700050354},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.16423824429512024},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/jproc.2002.1015001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/jproc.2002.1015001","pdf_url":null,"source":{"id":"https://openalex.org/S68686220","display_name":"Proceedings of the IEEE","issn_l":"0018-9219","issn":["0018-9219","1558-2256"],"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":"Proceedings of the IEEE","raw_type":"journal-article"},{"id":"pmh:oai:cris.unibo.it:11585/995122","is_oa":false,"landing_page_url":"https://hdl.handle.net/11585/995122","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unife.it:11392/1209717","is_oa":false,"landing_page_url":"http://hdl.handle.net/11392/1209717","pdf_url":null,"source":{"id":"https://openalex.org/S4306400369","display_name":"Institutional Research Information System University of Ferrara (University of Ferrara)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201324441","host_organization_name":"University of Ferrara","host_organization_lineage":["https://openalex.org/I201324441"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:porto.polito.it:2696582","is_oa":false,"landing_page_url":"http://porto.polito.it/2696582/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN:0018-9219","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":88,"referenced_works":["https://openalex.org/W21223778","https://openalex.org/W186186683","https://openalex.org/W567049363","https://openalex.org/W583905556","https://openalex.org/W765741110","https://openalex.org/W1488707706","https://openalex.org/W1520128606","https://openalex.org/W1561991101","https://openalex.org/W1582592707","https://openalex.org/W1674479413","https://openalex.org/W1968971721","https://openalex.org/W1969665421","https://openalex.org/W1975706805","https://openalex.org/W1978718596","https://openalex.org/W1979684610","https://openalex.org/W1980201978","https://openalex.org/W1995242373","https://openalex.org/W1995882611","https://openalex.org/W1996984927","https://openalex.org/W1997815317","https://openalex.org/W2004021828","https://openalex.org/W2005680619","https://openalex.org/W2010703195","https://openalex.org/W2017842654","https://openalex.org/W2020555549","https://openalex.org/W2027298658","https://openalex.org/W2027380725","https://openalex.org/W2029223471","https://openalex.org/W2035667853","https://openalex.org/W2036201099","https://openalex.org/W2055729437","https://openalex.org/W2068889198","https://openalex.org/W2069531097","https://openalex.org/W2070638062","https://openalex.org/W2072216721","https://openalex.org/W2098744287","https://openalex.org/W2099503269","https://openalex.org/W2103314937","https://openalex.org/W2113619583","https://openalex.org/W2116386331","https://openalex.org/W2121893094","https://openalex.org/W2124598373","https://openalex.org/W2125566231","https://openalex.org/W2126888108","https://openalex.org/W2128089417","https://openalex.org/W2131876298","https://openalex.org/W2138383709","https://openalex.org/W2140859286","https://openalex.org/W2142606351","https://openalex.org/W2152742892","https://openalex.org/W2153985037","https://openalex.org/W2158740311","https://openalex.org/W2162432583","https://openalex.org/W2165437625","https://openalex.org/W2168577777","https://openalex.org/W2171966863","https://openalex.org/W2171987742","https://openalex.org/W2215990475","https://openalex.org/W2258832169","https://openalex.org/W2285911715","https://openalex.org/W2314709889","https://openalex.org/W2325984963","https://openalex.org/W2432517183","https://openalex.org/W2482944896","https://openalex.org/W2546284236","https://openalex.org/W2574026466","https://openalex.org/W2783985063","https://openalex.org/W2796837256","https://openalex.org/W2798333393","https://openalex.org/W2904443187","https://openalex.org/W2970873286","https://openalex.org/W3097169496","https://openalex.org/W3100012960","https://openalex.org/W4229513139","https://openalex.org/W4240351219","https://openalex.org/W4243509751","https://openalex.org/W4243959868","https://openalex.org/W4249655589","https://openalex.org/W4250146611","https://openalex.org/W4254718130","https://openalex.org/W4285719527","https://openalex.org/W4301652612","https://openalex.org/W6617265099","https://openalex.org/W6629121644","https://openalex.org/W6633552471","https://openalex.org/W6695844914","https://openalex.org/W6747705209","https://openalex.org/W6757041902"],"related_works":["https://openalex.org/W2352168067","https://openalex.org/W2019933734","https://openalex.org/W2111075373","https://openalex.org/W4301444643","https://openalex.org/W4231083737","https://openalex.org/W1774046177","https://openalex.org/W4302552134","https://openalex.org/W567856160","https://openalex.org/W2188621105","https://openalex.org/W1869295411"],"abstract_inverted_index":{"The":[0],"application":[1],"of":[2,30,40,48,104,113,171,177],"chaotic":[3,65,105,114],"dynamics":[4],"to":[5,63,70,100,155],"signal":[6],"processing":[7],"tasks":[8],"stems":[9],"from":[10,21],"the":[11,28,38,46,60,81,91,101,111,141,157,169,175],"realization":[12],"that":[13,168],"its":[14,94,98],"complex":[15],"behavior":[16],"becomes":[17],"tractable":[18],"when":[19],"observed":[20],"a":[22,121],"statistical":[23,61,125,172],"perspective.":[24],"Here":[25],"we":[26,78,89,119,152],"illustrate":[27],"validity":[29],"this":[31,76],"statement":[32],"by":[33,57,108],"considering":[34],"two":[35,158],"noteworthy":[36],"problems-namely,":[37],"synthesis":[39,149],"high-electromagnetic":[41],"compatibility":[42],"clock":[43],"signals":[44],"and":[45,56,87,97,151],"generation":[47],"spreading":[49],"sequences":[50],"for":[51,137],"direct-sequence":[52],"code-division":[53],"communication":[54],"systems,":[55],"showing":[58],"how":[59],"approach":[62],"discrete-time":[64],"systems":[66,115,179],"can":[67,131,145],"be":[68,132,146],"applied":[69],"find":[71],"their":[72],"optimal":[73],"solution.":[74],"To":[75],"aim,":[77],"first":[79],"review":[80],"basic":[82],"mathematical":[83],"tools":[84,144,173],"both":[85,163],"intuitively":[86],"formally;":[88],"consider":[90],"Perron-Frobenius":[92],"operator":[93],"spectral":[95],"decomposition":[96],"tie":[99],"correlation":[102],"properties":[103],"sequences.":[106],"Then,":[107],"leveraging":[109],"on":[110],"modeling/approximation":[112],"through":[116],"Markov":[117],"chains,":[118],"introduce":[120],"matrix/tensor-based":[122],"framework":[123],"where":[124],"indicators":[126],"such":[127],"as":[128],"high-order":[129],"correlations":[130],"quantified.":[133],"We":[134],"underline":[135],"how,":[136],"many":[138],"particular":[139],"cases,":[140,164],"proposed":[142],"analysis":[143],"reversed":[147],"into":[148],"methodologies":[150],"use":[153],"them":[154],"tackle":[156],"above":[159],"mentioned":[160],"problems.":[161],"In":[162],"experimental":[165],"evidence":[166],"shows":[167],"availability":[170],"enables":[174],"design":[176],"chaos-based":[178],"which":[180],"favorably":[181],"compare":[182],"with":[183],"analogous":[184],"nonchaos-based":[185],"counterparts.":[186]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}