{"id":"https://openalex.org/W2152188033","doi":"https://doi.org/10.1109/tit.1969.1054270","title":"Minimum bandwidth of M signals with specified code or correlation matrix","display_name":"Minimum bandwidth of M signals with specified code or correlation matrix","publication_year":1969,"publication_date":"1969-01-01","ids":{"openalex":"https://openalex.org/W2152188033","doi":"https://doi.org/10.1109/tit.1969.1054270","mag":"2152188033"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1969.1054270","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054270","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/A5025643476","display_name":"Albert H. Nuttall","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. Nuttall","raw_affiliation_strings":["Litton Industries, Inc., Waltham, MA, USA"],"affiliations":[{"raw_affiliation_string":"Litton Industries, Inc., Waltham, MA, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042735748","display_name":"William Floyd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"W. Floyd","raw_affiliation_strings":["Litton Industries, Inc., Waltham, MA, USA"],"affiliations":[{"raw_affiliation_string":"Litton Industries, Inc., Waltham, MA, USA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025643476"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0029,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7588487,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"1","first_page":"38","last_page":"48"},"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9955000281333923,"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":0.9896000027656555,"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/bandwidth","display_name":"Bandwidth (computing)","score":0.5832496881484985},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5302400588989258},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.47484615445137024},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45779094099998474},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4508419632911682},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39365154504776},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3526875972747803},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33721399307250977},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.27587783336639404},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.07523980736732483}],"concepts":[{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.5832496881484985},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5302400588989258},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.47484615445137024},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45779094099998474},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4508419632911682},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39365154504776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3526875972747803},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33721399307250977},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27587783336639404},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.07523980736732483},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1969.1054270","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054270","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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1982366877","https://openalex.org/W2036666800","https://openalex.org/W2067111814","https://openalex.org/W2078530740","https://openalex.org/W2101801747","https://openalex.org/W2117476053","https://openalex.org/W2148234153","https://openalex.org/W2165731899","https://openalex.org/W2322256962","https://openalex.org/W3142915818","https://openalex.org/W4213062135","https://openalex.org/W4240906956"],"related_works":["https://openalex.org/W2152992791","https://openalex.org/W2112835755","https://openalex.org/W2349674371","https://openalex.org/W2361403716","https://openalex.org/W2904061867","https://openalex.org/W4289115725","https://openalex.org/W2967798957","https://openalex.org/W3144644423","https://openalex.org/W2024384195","https://openalex.org/W2514587231"],"abstract_inverted_index":{"The":[0,25,76,119],"minimum":[1],"bandwidth":[2,28,117],"of":[3,15,27,32,35,53,78,89,93,107,129,139,147],"<tex":[4,95,102,142],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[5,96,103,143],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">M</tex>":[6],"real":[7],"equi-energy":[8],"signals":[9,59],"is":[10,29,74],"derived":[11],"for":[12],"the":[13,33,36,45,58,70,79,85,90,100,112,116,126,130,140,148,152],"cases":[14],"either":[16],"a":[17,21,40,50,64,66,108],"specified":[18,22],"code":[19],"or":[20],"correlation":[23,91,131],"matrix.":[24],"definition":[26],"in":[30,63,115,157],"terms":[31],"ratio":[34,81],"energy":[37,80],"passed":[38],"by":[39,136],"linear":[41,137],"time-invariant":[42],"filter":[43,113],"to":[44,111],"input":[46],"energy,":[47],"and":[48,98,133,162,168],"incorporates":[49],"great":[51],"variety":[52],"definitions.":[54],"In":[55],"one":[56],"instance,":[57],"are":[60,134,154,160,166],"time":[61,72],"limited;":[62],"second,":[65],"weighted":[67],"integral":[68],"over":[69],"infinite":[71],"interval":[73],"restrained.":[75],"extremum":[77],"depends":[82],"only":[83],"on":[84,99,125,151],"nonzero":[86],"characteristic":[87,105,127,145],"numbers":[88,106],"matrix":[92,132],"rank":[94],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">r</tex>":[97,104,144],"first":[101,141],"kernel":[109],"related":[110],"used":[114],"definition.":[118],"optimum":[120],"signal":[121],"waveforms":[122],"also":[123],"depend":[124],"vectors":[128],"given":[135],"sums":[138],"functions":[146],"kernel.":[149],"Bounds":[150],"extrema":[153],"given,":[155],"approximations":[156],"narrow-band":[158],"situations":[159],"developed,":[161],"several":[163],"useful":[164],"examples":[165],"presented":[167],"solved.":[169]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}