{"id":"https://openalex.org/W2111609347","doi":"https://doi.org/10.1109/tit.1969.1054335","title":"Bounds for truncation error in sampling expansions of band-limited signals","display_name":"Bounds for truncation error in sampling expansions of band-limited signals","publication_year":1969,"publication_date":"1969-07-01","ids":{"openalex":"https://openalex.org/W2111609347","doi":"https://doi.org/10.1109/tit.1969.1054335","mag":"2111609347"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1969.1054335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054335","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/A5111987519","display_name":"Jerram L. Brown","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Brown","raw_affiliation_strings":["Ordnance Research Laboratory, Pennsylvania State University, University Park, PA, USA","[Ordnance Research Laboratory, Pennsylvania State University, University Park, PA, USA]"],"affiliations":[{"raw_affiliation_string":"Ordnance Research Laboratory, Pennsylvania State University, University Park, PA, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"[Ordnance Research Laboratory, Pennsylvania State University, University Park, PA, USA]","institution_ids":["https://openalex.org/I130769515"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111987519"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":53,"citation_normalized_percentile":{"value":0.27110074,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"440","last_page":"444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9957000017166138,"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":0.9957000017166138,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9890999794006348,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9803000092506409,"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/truncation","display_name":"Truncation (statistics)","score":0.5618267059326172},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42392072081565857},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3570384383201599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.343313992023468},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31659871339797974},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2606615424156189}],"concepts":[{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5618267059326172},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42392072081565857},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3570384383201599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.343313992023468},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31659871339797974},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2606615424156189}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1969.1054335","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054335","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1805871248","https://openalex.org/W1997404420","https://openalex.org/W2019204967","https://openalex.org/W2070048887","https://openalex.org/W2081469452"],"related_works":["https://openalex.org/W2748952813","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/W2911598644"],"abstract_inverted_index":{"For":[0],"<tex":[1,9,42,51,59,82,91,109,115,121,131,137,159,172,180,186,207,220,229,235,289],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,10,43,52,60,83,92,110,116,122,132,138,160,173,181,187,208,221,230,236,290],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f(t)</tex>":[3,44],"a":[4,48,280],"real-valued":[5],"signal":[6,177,194,226,271],"band-limited":[7,193],"to":[8,293],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-":[11],"\\pi":[12,17,124,141],"r":[13,18,21],"\\leq":[14,16],"\\omega":[15],"(0":[19],"&lt;":[20,22],"1)</tex>":[23],"and":[24,86,129,179,190,228,239,255],"represented":[25],"by":[26,54,158,206,253],"its":[27,68],"Fourier":[28,107],"integral,":[29],"upper":[30],"bounds":[31],"are":[32,100,259],"established":[33],"for":[34,102,286],"the":[35,38,73,79,96,106,151,176,191,201,224,240,245,270,276,283],"magnitude":[36,154],"of":[37,58,90,185,234,282,288],"truncation":[39,152],"error":[40,153,202],"when":[41],"is":[45,112,118,134,148,155,183,203,223,232],"approximated":[46],"at":[47,95],"generic":[49],"time":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t</tex>":[53],"an":[55],"appropriate":[56],"selection":[57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N_{1}":[61],"+":[62,64,168,216],"N_{2}":[63],"1</tex>":[65],"terms":[66],"from":[67],"Shannon":[69],"sampling":[70],"series":[71],"expansion,":[72],"latter":[74],"expansion":[75],"being":[76,195],"associated":[77],"with":[78,269],"full":[80],"band":[81],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[-\\pi,":[84,123],"\\pi]</tex>":[85],"thus":[87],"involving":[88],"samples":[89],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f</tex>":[93],"taken":[94],"integer":[97],"points.":[98],"Results":[99],"presented":[101],"two":[103],"cases:":[104],"1)":[105,146],"transform":[108],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">F(\\omega)</tex>":[111],"such":[113],"that":[114,150],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">|F(\\omega)|^{2}</tex>":[117],"integrable":[119,135],"on":[120,136],"r]</tex>":[125,142],"(finite":[126],"energy":[127,178],"case),":[128],"2)":[130,200],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">|F(\\omega)|</tex>":[133],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">[-\\pi":[139],"r,":[140],".":[143],"In":[144,273],"case":[145,199,274],"it":[147],"shown":[149],"bounded":[156,204],"above":[157,205],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">g(r,":[161],"t)":[162,210],"\\cdot":[163,165,211,213],"\\sqrt{E}":[164],"\\left(":[166,214],"\\frac{1}{N_{1}}":[167,215],"\\frac{1}{N_{2}}":[169,217],"\\right)</tex>":[170,218],"where":[171,219],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">E</tex>":[174],"denotes":[175],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">g</tex>":[182],"independent":[184,233],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N_{1},":[188,237],"N_{2}</tex>":[189,238],"particular":[192],"approximated.":[196],"Correspondingly,":[197],"in":[198,267],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h(r,":[209],"M":[212],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">M</tex>":[222],"maximum":[225],"amplitude":[227],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">h</tex>":[231],"signal.":[241],"These":[242],"estimates":[243],"possess":[244],"same":[246],"asymptotic":[247],"behavior":[248],"as":[249],"those":[250],"exhibited":[251],"earlier":[252],"Yao":[254],"Thomas":[256],"[2],":[257],"but":[258],"derived":[260],"here":[261],"using":[262],"only":[263],"real":[264],"variable":[265],"methods":[266],"conjunction":[268],"representation.":[272],"1),":[275],"estimate":[277],"obtained":[278],"represents":[279],"sharpening":[281],"Yao-Thomas":[284],"bound":[285],"values":[287],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</tex>":[291],"dose":[292],"unity.":[294]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
