{"id":"https://openalex.org/W2016515914","doi":"https://doi.org/10.1109/tsp.2012.2197618","title":"Discrete-Time LTI Systems Beyond Convolution","display_name":"Discrete-Time LTI Systems Beyond Convolution","publication_year":2012,"publication_date":"2012-06-16","ids":{"openalex":"https://openalex.org/W2016515914","doi":"https://doi.org/10.1109/tsp.2012.2197618","mag":"2016515914"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2197618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2197618","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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/A5064674180","display_name":"Peter Vogel","orcid":null},"institutions":[{"id":"https://openalex.org/I75356249","display_name":"Hochschule D\u00fcsseldorf University of Applied Sciences","ror":"https://ror.org/00ftx0026","country_code":"DE","type":"education","lineage":["https://openalex.org/I75356249"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Vogel","raw_affiliation_strings":["Department of Medientechnik, University of Applied Sciences, Dusseldorf, Germany","Dept. of Medientechnik, Univ. of Appl. Sci., Dusseldorf, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Medientechnik, University of Applied Sciences, Dusseldorf, Germany","institution_ids":["https://openalex.org/I75356249"]},{"raw_affiliation_string":"Dept. of Medientechnik, Univ. of Appl. Sci., Dusseldorf, Germany","institution_ids":["https://openalex.org/I75356249"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064674180"],"corresponding_institution_ids":["https://openalex.org/I75356249"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.17048213,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"60","issue":"8","first_page":"4055","last_page":"4064"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9914000034332275,"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/impulse-response","display_name":"Impulse response","score":0.6727719306945801},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.6347715258598328},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6087871193885803},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5995176434516907},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5956305861473083},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5212912559509277},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.436906635761261},{"id":"https://openalex.org/keywords/impulse","display_name":"Impulse (physics)","score":0.43335235118865967},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4243980050086975},{"id":"https://openalex.org/keywords/discrete-time-signal","display_name":"Discrete-time signal","score":0.41783276200294495},{"id":"https://openalex.org/keywords/finite-impulse-response","display_name":"Finite impulse response","score":0.4176750183105469},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3453482389450073},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3219336271286011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28007957339286804},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25217700004577637},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.19687971472740173},{"id":"https://openalex.org/keywords/analog-signal","display_name":"Analog signal","score":0.16373959183692932},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1106809675693512},{"id":"https://openalex.org/keywords/signal-transfer-function","display_name":"Signal transfer function","score":0.10287046432495117}],"concepts":[{"id":"https://openalex.org/C72279823","wikidata":"https://www.wikidata.org/wiki/Q1139726","display_name":"Impulse response","level":2,"score":0.6727719306945801},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.6347715258598328},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6087871193885803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5995176434516907},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5956305861473083},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5212912559509277},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.436906635761261},{"id":"https://openalex.org/C70836080","wikidata":"https://www.wikidata.org/wiki/Q837940","display_name":"Impulse (physics)","level":2,"score":0.43335235118865967},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4243980050086975},{"id":"https://openalex.org/C146749787","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete-time signal","level":5,"score":0.41783276200294495},{"id":"https://openalex.org/C198386975","wikidata":"https://www.wikidata.org/wiki/Q117785","display_name":"Finite impulse response","level":2,"score":0.4176750183105469},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3453482389450073},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3219336271286011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28007957339286804},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25217700004577637},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.19687971472740173},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.16373959183692932},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1106809675693512},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.10287046432495117},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2197618","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2197618","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","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":14,"referenced_works":["https://openalex.org/W607467417","https://openalex.org/W620580272","https://openalex.org/W1026276223","https://openalex.org/W1534416612","https://openalex.org/W1605188195","https://openalex.org/W1621550773","https://openalex.org/W1977325693","https://openalex.org/W2017698131","https://openalex.org/W2155564398","https://openalex.org/W2313078168","https://openalex.org/W2317724667","https://openalex.org/W2504536357","https://openalex.org/W4249058433","https://openalex.org/W6626804215"],"related_works":["https://openalex.org/W156274020","https://openalex.org/W4388903858","https://openalex.org/W2797141387","https://openalex.org/W4312799022","https://openalex.org/W4300927690","https://openalex.org/W2978433730","https://openalex.org/W2001917356","https://openalex.org/W116180589","https://openalex.org/W2809806046","https://openalex.org/W2105679457"],"abstract_inverted_index":{"Examples":[0],"for":[1,53],"LTI":[2,55,59,111,117,172],"systems":[3,56,60,118],"are":[4,61,80,101,175],"found":[5],"in":[6,106],"the":[7,45,140,159,163],"literature":[8],"that":[9,35,124],"cannot":[10],"be":[11,19,130],"represented":[12],"as":[13,28],"a":[14,50,64,69,76,89,146],"convolution.":[15],"Their":[16],"outputs":[17,22,156],"can":[18,129],"approximated":[20],"by":[21,119,145],"of":[23,44],"FIR":[24],"filters":[25],"and":[26,37,84,98,126],"considered":[27],"generalized":[29,178],"convolution":[30,179],"systems.":[31,112,180],"These":[32],"examples":[33],"illustrate":[34],"impulse":[36,125],"frequency":[38,127],"response":[39,128],"provide":[40],"no":[41],"complete":[42],"description":[43],"system.":[46],"In":[47],"this":[48],"paper,":[49],"general":[51],"theory":[52],"discrete-time":[54,168],"is":[57,68,143,151],"represented.":[58],"defined":[62,131],"on":[63],"signal":[65,104,141,164],"space,":[66,71],"which":[67,174],"vector":[70,91],"closed":[72],"with":[73],"respect":[74],"to":[75,88,103,108,137,158,166],"shift":[77],"operation.":[78],"Signals":[79],"not":[81,86,176],"necessarily":[82],"bounded":[83],"need":[85],"belong":[87],"normed":[90],"space.":[92],"Vector":[93],"space":[94,142,165],"concepts":[95],"like":[96],"dependent":[97],"independent":[99,120],"vectors":[100],"transferred":[102],"spaces":[105],"order":[107],"define":[109],"arbitrary":[110],"A":[113],"first":[114],"method,":[115,139],"defining":[116],"input":[121],"signals,":[122],"shows":[123],"independently":[132],"from":[133],"each":[134],"other.":[135],"According":[136],"another":[138],"extended":[144],"new":[147,160],"input.":[148,161],"An":[149],"equation":[150],"given":[152],"describing":[153],"all":[154,167],"possible":[155],"belonging":[157],"Extending":[162],"signals":[169],"reveals":[170],"universal":[171],"systems,":[173],"even":[177]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}