{"id":"https://openalex.org/W2170182872","doi":"https://doi.org/10.1109/tsp.2012.2210887","title":"Sampling and Reconstruction of Signals in Function Spaces Associated With the Linear Canonical Transform","display_name":"Sampling and Reconstruction of Signals in Function Spaces Associated With the Linear Canonical Transform","publication_year":2012,"publication_date":"2012-07-31","ids":{"openalex":"https://openalex.org/W2170182872","doi":"https://doi.org/10.1109/tsp.2012.2210887","mag":"2170182872"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2012.2210887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2210887","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/A5032530028","display_name":"Jun Shi","orcid":"https://orcid.org/0000-0001-6194-4433"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jun Shi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112545348","display_name":"Xiaoping Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoping Liu","raw_affiliation_strings":["Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083179738","display_name":"Xuejun Sha","orcid":"https://orcid.org/0000-0002-6204-0839"},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuejun Sha","raw_affiliation_strings":["Communication Research Center, Harbin Institute of Technology, Harbin, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communication Research Center, Harbin Institute of Technology, Harbin, China","institution_ids":["https://openalex.org/I204983213"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103452615","display_name":"Naitong Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naitong Zhang","raw_affiliation_strings":["Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China","institution_ids":["https://openalex.org/I204983213"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9092,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.9559741,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"60","issue":"11","first_page":"6041","last_page":"6047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9998999834060669,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.996399998664856,"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":0.9916999936103821,"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/bandlimiting","display_name":"Bandlimiting","score":0.8338707685470581},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6447973251342773},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.6383919715881348},{"id":"https://openalex.org/keywords/function-space","display_name":"Function space","score":0.6332709789276123},{"id":"https://openalex.org/keywords/nonuniform-sampling","display_name":"Nonuniform sampling","score":0.5812599062919617},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5645085573196411},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.49637705087661743},{"id":"https://openalex.org/keywords/sampling-theory","display_name":"Sampling theory","score":0.46931836009025574},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.4618256688117981},{"id":"https://openalex.org/keywords/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.44619259238243103},{"id":"https://openalex.org/keywords/signal-reconstruction","display_name":"Signal reconstruction","score":0.42420631647109985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41585367918014526},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32925164699554443},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32107529044151306},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2892519235610962},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2597212791442871},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.16143804788589478},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.13853302597999573},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12437531352043152}],"concepts":[{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.8338707685470581},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6447973251342773},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.6383919715881348},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.6332709789276123},{"id":"https://openalex.org/C20326153","wikidata":"https://www.wikidata.org/wiki/Q7049638","display_name":"Nonuniform sampling","level":3,"score":0.5812599062919617},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5645085573196411},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49637705087661743},{"id":"https://openalex.org/C2985880046","wikidata":"https://www.wikidata.org/wiki/Q7410168","display_name":"Sampling theory","level":3,"score":0.46931836009025574},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.4618256688117981},{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.44619259238243103},{"id":"https://openalex.org/C70958404","wikidata":"https://www.wikidata.org/wiki/Q7512728","display_name":"Signal reconstruction","level":4,"score":0.42420631647109985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41585367918014526},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32925164699554443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32107529044151306},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2892519235610962},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2597212791442871},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.16143804788589478},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.13853302597999573},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12437531352043152},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2012.2210887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2012.2210887","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":38,"referenced_works":["https://openalex.org/W361217659","https://openalex.org/W586299271","https://openalex.org/W606473257","https://openalex.org/W1976640663","https://openalex.org/W1977433593","https://openalex.org/W1983702508","https://openalex.org/W1999198554","https://openalex.org/W2002495280","https://openalex.org/W2004421506","https://openalex.org/W2018609850","https://openalex.org/W2021387829","https://openalex.org/W2030262316","https://openalex.org/W2033499985","https://openalex.org/W2044350368","https://openalex.org/W2044516693","https://openalex.org/W2057809775","https://openalex.org/W2075599780","https://openalex.org/W2084633773","https://openalex.org/W2096504426","https://openalex.org/W2097961244","https://openalex.org/W2100653569","https://openalex.org/W2111121062","https://openalex.org/W2113114772","https://openalex.org/W2118726884","https://openalex.org/W2119133199","https://openalex.org/W2119337797","https://openalex.org/W2124300121","https://openalex.org/W2129299867","https://openalex.org/W2129555100","https://openalex.org/W2146262488","https://openalex.org/W2161697193","https://openalex.org/W2166500461","https://openalex.org/W2170014524","https://openalex.org/W2170411504","https://openalex.org/W2171342370","https://openalex.org/W2253210145","https://openalex.org/W2484198296","https://openalex.org/W4292170079"],"related_works":["https://openalex.org/W2160209843","https://openalex.org/W3012217557","https://openalex.org/W2144601817","https://openalex.org/W2949625467","https://openalex.org/W4297783100","https://openalex.org/W2002495280","https://openalex.org/W2161203685","https://openalex.org/W3010427284","https://openalex.org/W1973881903","https://openalex.org/W2170182872"],"abstract_inverted_index":{"The":[0],"linear":[1],"canonical":[2],"transform":[3,22,182],"(LCT)":[4],"has":[5],"been":[6],"shown":[7],"to":[8,107],"be":[9],"useful":[10],"and":[11,63,81,93,103,144,170],"powerful":[12],"in":[13,43,51,140,157],"signal":[14,152],"processing,":[15],"optics,":[16],"etc.":[17],"Many":[18],"results":[19],"of":[20,33,39,69,91,114,195,203],"this":[21,57],"are":[23,54,190,207],"already":[24],"known,":[25],"including":[26],"sampling":[27,31,62,135,147,165,173],"theory.":[28],"Most":[29],"existing":[30,172],"theories":[32,174],"the":[34,37,44,74,97,108,123,128,138,141,158,180,184,188,196,204],"LCT":[35,139,189],"consider":[36],"class":[38,68],"bandlimited":[40,176],"signals.":[41],"However,":[42],"real":[45,85],"world,":[46],"many":[47],"analog":[48],"signals":[49,177],"arising":[50],"engineering":[52],"applications":[53,202],"non-bandlimited.":[55],"In":[56],"correspondence,":[58],"we":[59,88,100,130],"propose":[60],"a":[61,67,79,115,119,132,146,151],"reconstruction":[64],"strategy":[65],"for":[66,84,96,122,137,167,175],"function":[70,117,124,142,159],"spaces":[71,160,169],"associated":[72,178],"with":[73,179],"LCT,":[75,109],"which":[76,111,149],"can":[77],"provide":[78],"suitable":[80],"realistic":[82],"model":[83],"applications.":[86],"First,":[87],"introduce":[89],"definitions":[90],"semi-":[92],"fully-discrete":[94],"convolutions":[95],"LCT.":[98],"Then,":[99],"derive":[101],"necessary":[102],"sufficient":[104],"conditions":[105],"pertaining":[106],"under":[110],"integer":[112],"shifts":[113],"chirp-modulated":[116],"generate":[118],"Riesz":[120],"basis":[121],"spaces.":[125],"By":[126],"applying":[127],"results,":[129],"present":[131],"more":[133],"comprehensive":[134],"theory":[136,206],"spaces,":[143],"further,":[145],"theorem":[148],"recovers":[150],"from":[153],"its":[154],"own":[155],"samples":[156],"is":[161],"established.":[162],"Moreover,":[163],"some":[164,171,200],"theorems":[166],"shift-invariant":[168],"Fourier":[181],"(FT),":[183],"fractional":[185],"FT,":[186],"or":[187],"noted":[191],"as":[192],"special":[193],"cases":[194],"derived":[197,205],"results.":[198],"Finally,":[199],"potential":[201],"presented.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}