{"id":"https://openalex.org/W2982564049","doi":"https://doi.org/10.1109/msp.2019.2923025","title":"The Superposition Principle of Linear Time-Invariant Systems [Lecture Notes]","display_name":"The Superposition Principle of Linear Time-Invariant Systems [Lecture Notes]","publication_year":2019,"publication_date":"2019-10-30","ids":{"openalex":"https://openalex.org/W2982564049","doi":"https://doi.org/10.1109/msp.2019.2923025","mag":"2982564049"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2019.2923025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2019.2923025","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","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/A5100447279","display_name":"Ming Zhang","orcid":"https://orcid.org/0000-0002-5796-4754"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming Zhang","raw_affiliation_strings":["Electronic Science and Technology, Xi\u2019an Jiaotong University, China","Information and Communications Engineering, Xi'an Jiaotong University, Xi'an, China","Information and Communications Engineering, Xi'an Jiaotong University, China"],"raw_orcid":"https://orcid.org/0000-0002-5796-4754","affiliations":[{"raw_affiliation_string":"Electronic Science and Technology, Xi\u2019an Jiaotong University, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Information and Communications Engineering, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Information and Communications Engineering, Xi'an Jiaotong University, China","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014183376","display_name":"Anxue Zhang","orcid":"https://orcid.org/0000-0002-4690-2718"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Anxue Zhang","raw_affiliation_strings":["Electronic Science and Technology, Xi\u2019an Jiaotong University, China","Information and Communications Engineering, Xi'an Jiaotong University, Xi'an, China","Information and Communications Engineering, Xi'an Jiaotong University, China"],"raw_orcid":"https://orcid.org/0000-0002-4690-2718","affiliations":[{"raw_affiliation_string":"Electronic Science and Technology, Xi\u2019an Jiaotong University, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Information and Communications Engineering, Xi'an Jiaotong University, Xi'an, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Information and Communications Engineering, Xi'an Jiaotong University, China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100447279"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":null,"apc_paid":null,"fwci":1.3477,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.81721549,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"6","first_page":"153","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11236","display_name":"Control Systems and Identification","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9966999888420105,"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":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.9495768547058105},{"id":"https://openalex.org/keywords/lti-system-theory","display_name":"LTI system theory","score":0.6694517731666565},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6185158491134644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5709680318832397},{"id":"https://openalex.org/keywords/invariance-principle","display_name":"Invariance principle","score":0.5318045020103455},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4465298354625702},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3303777575492859},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.08789828419685364}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.9495768547058105},{"id":"https://openalex.org/C87698059","wikidata":"https://www.wikidata.org/wiki/Q1808960","display_name":"LTI system theory","level":3,"score":0.6694517731666565},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6185158491134644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5709680318832397},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.5318045020103455},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4465298354625702},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3303777575492859},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.08789828419685364},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2019.2923025","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2019.2923025","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3476118584","display_name":null,"funder_award_id":"Grant 61801368","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6463436827","display_name":null,"funder_award_id":"Grant 2018M640990","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W658512522","https://openalex.org/W1487444668","https://openalex.org/W1582706191","https://openalex.org/W1766888123","https://openalex.org/W2097415784","https://openalex.org/W2107221565","https://openalex.org/W2263224228","https://openalex.org/W2564517383","https://openalex.org/W2595897327","https://openalex.org/W2955672675","https://openalex.org/W3109938142","https://openalex.org/W4243513962","https://openalex.org/W4301621763"],"related_works":["https://openalex.org/W2053005959","https://openalex.org/W2299538996","https://openalex.org/W2027136373","https://openalex.org/W2144143333","https://openalex.org/W3169827016","https://openalex.org/W4386631510","https://openalex.org/W2276636510","https://openalex.org/W2105658174","https://openalex.org/W3163145068","https://openalex.org/W1990421243"],"abstract_inverted_index":{"One":[0],"of":[1,6,21,29,37,42],"the":[2,12,18,33,38,43,64,74,88],"most":[3],"important":[4],"properties":[5],"linear":[7],"time-invariant":[8],"(LTI)":[9],"systems":[10],"is":[11,31,72,86],"superposition":[13,65,76,90],"principle,":[14,77],"which":[15],"states":[16],"that":[17],"overall":[19],"response":[20],"an":[22],"LTI":[23],"system":[24],"to":[25,40],"a":[26,54],"weighted":[27,35],"sum":[28,36],"signals":[30],"simply":[32],"same":[34],"responses":[39],"each":[41],"individual":[44],"signals.":[45],"In":[46,60],"this":[47,58],"\"Lecture":[48],"Notes\"":[49],"column,":[50],"we":[51],"will":[52],"provide":[53],"deeper":[55],"insight":[56],"into":[57],"principle.":[59],"what":[61],"follows,":[62],"if":[63,79],"principle":[66,91],"has":[67,81],"finitely":[68],"many":[69,83],"terms,":[70,84],"it":[71,80,85],"called":[73,87],"weak":[75],"whereas,":[78],"infinitely":[82],"strong":[89],"(SSP).":[92]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}