{"id":"https://openalex.org/W2045877198","doi":"https://doi.org/10.1109/tit.1983.1056630","title":"On the implementation of the Shannon sampling series for band-limited signals (Corresp.)","display_name":"On the implementation of the Shannon sampling series for band-limited signals (Corresp.)","publication_year":1983,"publication_date":"1983-03-01","ids":{"openalex":"https://openalex.org/W2045877198","doi":"https://doi.org/10.1109/tit.1983.1056630","mag":"2045877198"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1983.1056630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056630","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/A5089022492","display_name":"P. L. Butzer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210145899","display_name":"Westf\u00e4lische Hochschule","ror":"https://ror.org/04p7ekn23","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210145899"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"P. Butzer","raw_affiliation_strings":["Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany","[Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany]"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I4210145899"]},{"raw_affiliation_string":"[Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany]","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066057306","display_name":"W. Engels","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]},{"id":"https://openalex.org/I4210145899","display_name":"Westf\u00e4lische Hochschule","ror":"https://ror.org/04p7ekn23","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210145899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"W. Engels","raw_affiliation_strings":["Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany","[Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany]"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany","institution_ids":["https://openalex.org/I4210145899"]},{"raw_affiliation_string":"[Lehrstuhl A fur Mathematik Rheinisch-Westfaische, Technische Hochschule Aachen, Aachen, Germany]","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089022492"],"corresponding_institution_ids":["https://openalex.org/I4210145899","https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.20983103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"29","issue":"2","first_page":"314","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.991599977016449,"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":0.991599977016449,"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":0.9907000064849854,"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":0.9739999771118164,"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/taylor-series","display_name":"Taylor series","score":0.7963455319404602},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.7585653066635132},{"id":"https://openalex.org/keywords/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.609219491481781},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5971137881278992},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5955129861831665},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.577660083770752},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5749959349632263},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5485501885414124},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5253550410270691},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.5251060128211975},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5143522024154663},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5089433193206787},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4445911645889282},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43044358491897583},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.42245227098464966},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24376055598258972},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2098606526851654},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17256933450698853}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.7963455319404602},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.7585653066635132},{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.609219491481781},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5971137881278992},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5955129861831665},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.577660083770752},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5749959349632263},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5485501885414124},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5253550410270691},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.5251060128211975},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5143522024154663},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5089433193206787},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4445911645889282},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43044358491897583},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.42245227098464966},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24376055598258972},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2098606526851654},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17256933450698853},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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/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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1983.1056630","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1983.1056630","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":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W145184629","https://openalex.org/W1964802140","https://openalex.org/W1972177092","https://openalex.org/W1997404420","https://openalex.org/W2123716859","https://openalex.org/W2135479785","https://openalex.org/W4234608269","https://openalex.org/W4249058433","https://openalex.org/W4252713891"],"related_works":["https://openalex.org/W1990789772","https://openalex.org/W280651834","https://openalex.org/W1988068451","https://openalex.org/W2018113562","https://openalex.org/W2169184289","https://openalex.org/W2082506709","https://openalex.org/W2020790120","https://openalex.org/W2048005557","https://openalex.org/W2126315543","https://openalex.org/W41207949"],"abstract_inverted_index":{"The":[0,46,81,98],"sinc":[1,32],"function":[2],"occuring":[3],"in":[4,68,93],"the":[5,25,40,52,58,65,75,87,96],"classical":[6],"Shannon":[7],"sampling":[8,60,77],"theorem":[9],"is":[10,20,49,79,84,91],"replaced":[11],"by":[12,102],"algebraic":[13,26],"polynomials.":[14],"It":[15],"turns":[16],"out":[17],"that":[18,63,72],"it":[19],"not":[21],"necessary":[22],"to":[23,31,50,86],"take":[24],"polynomial":[27],"of":[28,39,54,57,64,74],"best":[29],"approximation":[30],"<tex":[33],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[34],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">t;</tex>":[35],"a":[36,70],"finite":[37],"sum":[38],"Taylor":[41,66],"series":[42],"expansion":[43,61,67,78],"already":[44],"suffices.":[45],"basic":[47],"problem":[48],"couple":[51],"number":[53],"terms":[55],"taken":[56],"truncated":[59],"with":[62,95],"such":[69],"fashion":[71],"convergence":[73],"modified":[76],"guaranteed.":[80],"resulting":[82],"error":[83,89],"additive":[85],"truncation":[88],"and":[90],"negligible":[92],"comparison":[94],"latter.":[97],"results":[99],"are":[100],"illustrated":[101],"two":[103],"representative":[104],"examples.":[105]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}