{"id":"https://openalex.org/W1986708144","doi":"https://doi.org/10.1016/s0165-1684(99)00058-4","title":"A natural vector space of two-sided discrete-time signals","display_name":"A natural vector space of two-sided discrete-time signals","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W1986708144","doi":"https://doi.org/10.1016/s0165-1684(99)00058-4","mag":"1986708144"},"language":"en","primary_location":{"id":"doi:10.1016/s0165-1684(99)00058-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0165-1684(99)00058-4","pdf_url":null,"source":{"id":"https://openalex.org/S154637859","display_name":"Signal Processing","issn_l":"0165-1684","issn":["0165-1684","1872-7557"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/s0165-1684(99)00058-4","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008238783","display_name":"Paul Hughett","orcid":null},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul Hughett","raw_affiliation_strings":["Brain Behavior Laboratory, University of Pennsylvania, 3400 Spruce Street, Philadelphia, PA 19104, USA"],"affiliations":[{"raw_affiliation_string":"Brain Behavior Laboratory, University of Pennsylvania, 3400 Spruce Street, Philadelphia, PA 19104, USA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008238783"],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":{"value":3200,"currency":"USD","value_usd":3200},"apc_paid":{"value":3200,"currency":"USD","value_usd":3200},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12599952,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"78","issue":"2","first_page":"177","last_page":"189"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.995199978351593,"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":0.995199978351593,"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":0.9947999715805054,"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":0.9819999933242798,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8201799988746643},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34943974018096924}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8201799988746643},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34943974018096924}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0165-1684(99)00058-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0165-1684(99)00058-4","pdf_url":null,"source":{"id":"https://openalex.org/S154637859","display_name":"Signal Processing","issn_l":"0165-1684","issn":["0165-1684","1872-7557"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal Processing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/s0165-1684(99)00058-4","is_oa":true,"landing_page_url":"https://doi.org/10.1016/s0165-1684(99)00058-4","pdf_url":null,"source":{"id":"https://openalex.org/S154637859","display_name":"Signal Processing","issn_l":"0165-1684","issn":["0165-1684","1872-7557"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Signal Processing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1963601724","https://openalex.org/W1966960911","https://openalex.org/W2007082278","https://openalex.org/W2017698131","https://openalex.org/W2039319516"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"The":[0],"vector":[1],"space":[2,28,38,57],"of":[3,10,32,48,65,71,82],"two-sided":[4],"sequences":[5],"expressible":[6],"as":[7],"finite":[8],"sums":[9],"unit":[11,18],"sample":[12],"sequences,":[13,16],"complex":[14],"exponential":[15],"the":[17,30,76],"step":[19],"sequence,":[20],"and":[21,46,79],"their":[22],"elementwise":[23,44],"products":[24],"forms":[25],"a":[26,63],"natural":[27],"for":[29],"theory":[31],"discrete-time":[33],"linear":[34,49],"shift-invariant":[35],"operators.":[36],"This":[37],"is":[39,74],"(algebraically)":[40],"closed":[41],"under":[42],"translation,":[43,223],"multiplication,":[45],"solution":[47,231],"constant-coefficient":[50],"difference":[51],"equations.":[52],"Every":[53],"sequence":[54],"in":[55,144],"this":[56,72],"can":[58,86],"be":[59,87],"uniquely":[60],"decomposed":[61],"into":[62],"sum":[64],"elementary":[66],"sequences.":[67],"An":[68],"unexpected":[69],"consequence":[70],"decomposition":[73],"that":[75],"impulse":[77],"response":[78,81],"frequency":[80],"an":[83],"LSI":[84,273],"operator":[85],"specified":[88],"independently.":[89],"Der":[90],"Vektorraum":[91],"zweiseitiger":[92],"Folgen,":[93],"die":[94,116],"als":[95],"endliche":[96],"Summe":[97,146],"des":[98,171,206],"Einheitsimpulses,":[99],"komplexer":[100],"Exponentialfolgen,":[101],"der":[102],"Sprungfolge":[103],"und":[104,130,159],"deren":[105],"elementweisen":[106],"Produkten":[107],"ausgedr\u00fcckt":[108],"werden":[109,168],"k\u00f6nnen,":[110],"formt":[111],"den":[112],"nat\u00fcrlichen":[113],"Raum":[114,123],"f\u00fcr":[115],"Theorie":[117],"zeitdiskreter,":[118],"linearer,":[119],"verschiebungsinvarianter":[120],"Operatoren.":[121],"Dieser":[122],"ist":[124],"(algebraisch)":[125],"unter":[126],"Verschiebungen,":[127],"elementweise":[128],"Multiplikationen":[129],"L\u00f6sung":[131],"linearer":[132],"Differenzengleichungen":[133],"mit":[134],"konstanten":[135],"Koeffizienten":[136],"abgeschlossen.":[137],"Jede":[138],"Folge":[139,153],"dieses":[140],"Raumes":[141],"kann":[142],"eindeutig":[143],"eine":[145],"elementarer":[147],"Folgen":[148],"zerlegt":[149],"werden.":[150],"Eine":[151],"unerwartete":[152],"dieser":[154],"Zerlegung":[155],"ist,":[156],"da\u00df":[157],"Impulsantwort":[158],"\u00dcbertragungsfunktion":[160],"eines":[161],"linearen,":[162],"verschiebungsinvarianten":[163],"Operators":[164],"unabh\u00e4ngig":[165],"voneinander":[166],"bestimmt":[167],"k\u00f6nnen.":[169],"L'espace":[170],"vecteurs":[172],"de":[173,181,185,189,247,253,259],"s\u00e9quences":[174,182,186,190,254],"bilat\u00e9rales":[175],"exprimables":[176],"comme":[177],"une":[178,251],"somme":[179,252],"finie":[180],"d\u2019\u00e9chantillons":[183],"unit\u00e9s,":[184,192],"d'exponentielles":[187],"complexes,":[188],"d\u2019\u00e9chelons":[191],"et":[193,229,267],"leurs":[194],"produits":[195],"\u00e9l\u00e9ment":[196,226,228],"par":[197,227],"\u00e9l\u00e9ment,":[198],"forment":[199],"un":[200],"espace":[201,217,243],"naturel":[202],"pour":[203],"la":[204,222,224,230,264,268],"th\u00e9orie":[205],"op\u00e9rateurs":[207],"lin\u00e9aires":[208,235],"invariants":[209],"en":[210,250],"d\u00e9calage":[211],"(LSI)":[212],"\u00e0":[213,236],"temps":[214],"discret.":[215],"Cet":[216],"est":[218,262],"(alg\u00e9briquement)":[219],"ferm\u00e9":[220],"sous":[221],"multiplication":[225],"d\u2019\u00e9quations":[232],"aux":[233],"diff\u00e9rences":[234],"coefficients":[237],"constants.":[238],"Chaque":[239],"s\u00e9quence":[240],"dans":[241],"cet":[242],"peut":[244,274],"\u00eatre":[245,275],"d\u00e9compos\u00e9e":[246],"fa\u00e7on":[248],"unique":[249],"\u00e9l\u00e9mentaires.":[255],"Une":[256],"cons\u00e9quence":[257],"inattendue":[258],"cette":[260],"d\u00e9composition":[261],"que":[263],"r\u00e9ponse":[265,269],"impulsionnelle":[266],"fr\u00e9quencielle":[270],"d'un":[271],"op\u00e9rateur":[272],"sp\u00e9cifi\u00e9e":[276],"ind\u00e9pendamment.":[277]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
