{"id":"https://openalex.org/W2155534368","doi":"https://doi.org/10.1109/tit.2009.2034793","title":"Prediction by Samples From the Past With Error Estimates Covering Discontinuous Signals","display_name":"Prediction by Samples From the Past With Error Estimates Covering Discontinuous Signals","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2155534368","doi":"https://doi.org/10.1109/tit.2009.2034793","mag":"2155534368"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2034793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2034793","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/A5068793419","display_name":"Carlo Bardaro","orcid":"https://orcid.org/0000-0002-7567-4005"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Carlo Bardaro","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089022492","display_name":"P. L. Butzer","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul L. Butzer","raw_affiliation_strings":["Lehrstuhl A f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl A f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035605717","display_name":"R. L. Stens","orcid":"https://orcid.org/0000-0002-8433-9081"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Rudolf L. Stens","raw_affiliation_strings":["Lehrstuhl A f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl A f\u00fcr Mathematik, RWTH Aachen University, Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032527090","display_name":"Gianluca V\u0131nt\u0131","orcid":"https://orcid.org/0000-0002-9875-2790"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Gianluca Vinti","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Perugia, Perugia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Perugia, Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068793419"],"corresponding_institution_ids":["https://openalex.org/I27483092"],"apc_list":null,"apc_paid":null,"fwci":2.9053,"has_fulltext":false,"cited_by_count":76,"citation_normalized_percentile":{"value":0.92040391,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"56","issue":"1","first_page":"614","last_page":"633"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9986000061035156,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/emphasis","display_name":"Emphasis (telecommunications)","score":0.9498335123062134},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5875539779663086},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48786139488220215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3729736804962158},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3607940673828125},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22029954195022583},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1740676462650299}],"concepts":[{"id":"https://openalex.org/C177454536","wikidata":"https://www.wikidata.org/wiki/Q578290","display_name":"Emphasis (telecommunications)","level":2,"score":0.9498335123062134},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5875539779663086},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48786139488220215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3729736804962158},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3607940673828125},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22029954195022583},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1740676462650299},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2009.2034793","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2034793","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"},{"id":"pmh:oai:publications.rwth-aachen.de:189525","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/189525","pdf_url":null,"source":{"id":"https://openalex.org/S4306401033","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE transactions on information theory 56(1), 614-633 (2010). doi:10.1109/TIT.2009.2034793","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W15012609","https://openalex.org/W75309157","https://openalex.org/W169490768","https://openalex.org/W202287110","https://openalex.org/W612072376","https://openalex.org/W1031827536","https://openalex.org/W1506013563","https://openalex.org/W1510355813","https://openalex.org/W1511042830","https://openalex.org/W1516465313","https://openalex.org/W1523940121","https://openalex.org/W1966264494","https://openalex.org/W1970599830","https://openalex.org/W1981573954","https://openalex.org/W1990457693","https://openalex.org/W1991877147","https://openalex.org/W2004197337","https://openalex.org/W2007012640","https://openalex.org/W2007885389","https://openalex.org/W2010285609","https://openalex.org/W2014037862","https://openalex.org/W2019963663","https://openalex.org/W2022554507","https://openalex.org/W2023527294","https://openalex.org/W2045877198","https://openalex.org/W2053364263","https://openalex.org/W2060772540","https://openalex.org/W2075231798","https://openalex.org/W2084052726","https://openalex.org/W2090344516","https://openalex.org/W2102175125","https://openalex.org/W2123716859","https://openalex.org/W2161965203","https://openalex.org/W2162870748","https://openalex.org/W2164304403","https://openalex.org/W2188719066","https://openalex.org/W2205606353","https://openalex.org/W2247630043","https://openalex.org/W2289623915","https://openalex.org/W2313953460","https://openalex.org/W2492200303","https://openalex.org/W2574741566","https://openalex.org/W2579615275","https://openalex.org/W2901284532","https://openalex.org/W2970070367","https://openalex.org/W2997829126","https://openalex.org/W3003741091","https://openalex.org/W3004696454","https://openalex.org/W3133975174","https://openalex.org/W3189601352","https://openalex.org/W4205354563","https://openalex.org/W4230533591","https://openalex.org/W4249188671","https://openalex.org/W4285719527","https://openalex.org/W4388315803","https://openalex.org/W6687213796","https://openalex.org/W6688021335","https://openalex.org/W6998655374","https://openalex.org/W7038151286","https://openalex.org/W7052301953"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2055105357","https://openalex.org/W2153819599","https://openalex.org/W2255426644","https://openalex.org/W2072124641","https://openalex.org/W2167093538","https://openalex.org/W2018956713","https://openalex.org/W2081479354","https://openalex.org/W2113107605","https://openalex.org/W3204693335"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"There":[3],"are":[4,56,212,222],"several":[5],"reasons":[6],"why":[7],"the":[8,21,60,71,93,104,112,117,121,171,218],"classical":[9],"sampling":[10],"theorem":[11],"is":[12,28,98,151],"rather":[13,81],"impractical":[14],"for":[15,32,83],"real":[16],"life":[17],"signal":[18,64],"processing.":[19],"First,":[20],"<emphasis":[22,49,65,84,128,144,160,205],"emphasistype=\"italic\"><formula":[23,50,66,85,129,145,161,206],"formulatype=\"inline\"><tex":[24,51,67,130,162,207],"Notation=\"TeX\">$":[25,148],"{\\rm":[26,149],"sinc}$</tex></formula></emphasis>-kernel":[27],"not":[29,185,193],"very":[30],"suitable":[31],"fast":[33],"and":[34,108,191],"efficient":[35],"computation;":[36],"it":[37],"decays":[38],"much":[39],"too":[40],"slowly.":[41],"Second,":[42],"in":[43,201,225],"practice":[44],"only":[45,164],"a":[46,63,76,99,165],"finite":[47,72,166],"number":[48,167],"Notation=\"TeX\">$N$</tex></formula></emphasis>":[52],"of":[53,62,106,158,168,203,210],"sampled":[54],"values":[55],"available,":[57],"so":[58],"that":[59],"representation":[61],"Notation=\"TeX\">$f$</tex>":[68],"</formula></emphasis>":[69],"by":[70,153],"sum":[73],"would":[74],"entail":[75],"truncation":[77],"error":[78,199],"which":[79],"decreases":[80],"slowly":[82],"formulatype=\"inline\">":[86,146],"<tex":[87,147],"Notation=\"TeX\">$N\\to":[88],"\\infty":[89],"$</tex></formula></emphasis>,":[90],"due":[91,102],"to":[92,103,120,125,139,182],"first":[94],"drawback.":[95],"Third,":[96],"band-limitation":[97],"definite":[100],"restriction,":[101],"nonconformity":[105],"band":[107],"time-limited":[109],"signals.":[110,196],"Further,":[111],"samples":[113,169],"needed":[114],"extend":[115],"from":[116,170],"entire":[118],"past":[119,172],"full":[122],"future,":[123],"relative":[124],"some":[126],"time":[127],"Notation=\"TeX\">$t":[131],"=":[132],"t_{0}$</tex></formula></emphasis>.":[133],"This":[134,176],"paper":[135],"presents":[136],"an":[137,204],"approach":[138,178],"overcome":[140],"these":[141],"difficulties.":[142],"The":[143],"sinc}$</tex></formula></emphasis>-function":[150],"replaced":[152],"certain":[154],"simple":[155],"linear":[156],"combinations":[157],"shifted":[159],"Notation=\"TeX\">$B$</tex></formula></emphasis>-splines,":[163],"need":[173],"be":[174,180],"available.":[175],"deterministic":[177],"can":[179],"used":[181],"process":[183],"arbitrary,":[184],"necessarily":[186,194],"bandlimited":[187],"nor":[188],"differentiable":[189],"signals,":[190],"even":[192],"continuous":[195],"Best":[197],"possible":[198],"estimates":[200],"terms":[202],"Notation=\"TeX\">$L^{p}$</tex></formula></emphasis>-average":[208],"modulus":[209],"smoothness":[211],"presented.":[213],"Several":[214],"typical":[215],"examples":[216],"exhibiting":[217],"various":[219],"problems":[220],"involved":[221],"worked":[223],"out":[224],"detail.":[226],"</para>":[227]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-10T08:33:47.465468","created_date":"2025-10-10T00:00:00"}
