{"id":"https://openalex.org/W2156468761","doi":"https://doi.org/10.1109/tit.1956.1056819","title":"Rectification of two signals in random noise","display_name":"Rectification of two signals in random noise","publication_year":1956,"publication_date":"1956-12-01","ids":{"openalex":"https://openalex.org/W2156468761","doi":"https://doi.org/10.1109/tit.1956.1056819","mag":"2156468761"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1956.1056819","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1956.1056819","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/A5015288543","display_name":"L. Campbell","orcid":"https://orcid.org/0000-0002-8302-7430"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. Campbell","raw_affiliation_strings":["Defence Research Board, Radio Physics Laboratory, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"Defence Research Board, Radio Physics Laboratory, Ottawa, Canada","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015288543"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.28162564,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"4","first_page":"119","last_page":"124"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/signal-transfer-function","display_name":"Signal transfer function","score":0.7107410430908203},{"id":"https://openalex.org/keywords/noise-floor","display_name":"Noise floor","score":0.6389065384864807},{"id":"https://openalex.org/keywords/noise-spectral-density","display_name":"Noise spectral density","score":0.6126132011413574},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.6100149750709534},{"id":"https://openalex.org/keywords/noise-temperature","display_name":"Noise temperature","score":0.5285702347755432},{"id":"https://openalex.org/keywords/noise-figure","display_name":"Noise figure","score":0.5185006856918335},{"id":"https://openalex.org/keywords/stochastic-resonance","display_name":"Stochastic resonance","score":0.5152493119239807},{"id":"https://openalex.org/keywords/noise-generator","display_name":"Noise generator","score":0.5050745606422424},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.4858376681804657},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.46227604150772095},{"id":"https://openalex.org/keywords/noise-power","display_name":"Noise power","score":0.4568113386631012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4492916464805603},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.4490188956260681},{"id":"https://openalex.org/keywords/signal-to-noise-ratio","display_name":"Signal-to-noise ratio (imaging)","score":0.44722217321395874},{"id":"https://openalex.org/keywords/noise-measurement","display_name":"Noise measurement","score":0.42681729793548584},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.4263148307800293},{"id":"https://openalex.org/keywords/gradient-noise","display_name":"Gradient noise","score":0.4168826639652252},{"id":"https://openalex.org/keywords/effective-input-noise-temperature","display_name":"Effective input noise temperature","score":0.41589608788490295},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4136022925376892},{"id":"https://openalex.org/keywords/analog-signal","display_name":"Analog signal","score":0.3338766396045685},{"id":"https://openalex.org/keywords/phase-noise","display_name":"Phase noise","score":0.25883498787879944},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.2437456250190735},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23219230771064758},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22806012630462646},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.20753544569015503},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19534844160079956},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.19302210211753845},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.15124961733818054},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.13873013854026794},{"id":"https://openalex.org/keywords/amplifier","display_name":"Amplifier","score":0.08544036746025085}],"concepts":[{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.7107410430908203},{"id":"https://openalex.org/C187612029","wikidata":"https://www.wikidata.org/wiki/Q17083130","display_name":"Noise floor","level":4,"score":0.6389065384864807},{"id":"https://openalex.org/C133976006","wikidata":"https://www.wikidata.org/wiki/Q3023291","display_name":"Noise spectral density","level":5,"score":0.6126132011413574},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.6100149750709534},{"id":"https://openalex.org/C52660251","wikidata":"https://www.wikidata.org/wiki/Q17083145","display_name":"Noise temperature","level":3,"score":0.5285702347755432},{"id":"https://openalex.org/C112806910","wikidata":"https://www.wikidata.org/wiki/Q746825","display_name":"Noise figure","level":4,"score":0.5185006856918335},{"id":"https://openalex.org/C207658827","wikidata":"https://www.wikidata.org/wiki/Q1999781","display_name":"Stochastic resonance","level":4,"score":0.5152493119239807},{"id":"https://openalex.org/C74342258","wikidata":"https://www.wikidata.org/wiki/Q2133526","display_name":"Noise generator","level":5,"score":0.5050745606422424},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.4858376681804657},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.46227604150772095},{"id":"https://openalex.org/C203234222","wikidata":"https://www.wikidata.org/wiki/Q2133519","display_name":"Noise power","level":3,"score":0.4568113386631012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4492916464805603},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.4490188956260681},{"id":"https://openalex.org/C13944312","wikidata":"https://www.wikidata.org/wiki/Q7512748","display_name":"Signal-to-noise ratio (imaging)","level":2,"score":0.44722217321395874},{"id":"https://openalex.org/C29265498","wikidata":"https://www.wikidata.org/wiki/Q7047719","display_name":"Noise measurement","level":3,"score":0.42681729793548584},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.4263148307800293},{"id":"https://openalex.org/C200378446","wikidata":"https://www.wikidata.org/wiki/Q4147391","display_name":"Gradient noise","level":5,"score":0.4168826639652252},{"id":"https://openalex.org/C12252657","wikidata":"https://www.wikidata.org/wiki/Q5347266","display_name":"Effective input noise temperature","level":5,"score":0.41589608788490295},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4136022925376892},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.3338766396045685},{"id":"https://openalex.org/C89631360","wikidata":"https://www.wikidata.org/wiki/Q1428766","display_name":"Phase noise","level":2,"score":0.25883498787879944},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2437456250190735},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23219230771064758},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22806012630462646},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.20753544569015503},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19534844160079956},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.19302210211753845},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.15124961733818054},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.13873013854026794},{"id":"https://openalex.org/C194257627","wikidata":"https://www.wikidata.org/wiki/Q211554","display_name":"Amplifier","level":3,"score":0.08544036746025085},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.0},{"id":"https://openalex.org/C46362747","wikidata":"https://www.wikidata.org/wiki/Q173431","display_name":"CMOS","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1956.1056819","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1956.1056819","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":9,"referenced_works":["https://openalex.org/W204407452","https://openalex.org/W1581541217","https://openalex.org/W1971568424","https://openalex.org/W2012836969","https://openalex.org/W2057253658","https://openalex.org/W2080479690","https://openalex.org/W2114509411","https://openalex.org/W3136463145","https://openalex.org/W4246607339"],"related_works":["https://openalex.org/W4243333603","https://openalex.org/W1988257008","https://openalex.org/W3021392142","https://openalex.org/W4236509694","https://openalex.org/W977887189","https://openalex.org/W2099930065","https://openalex.org/W2171323768","https://openalex.org/W1990652426","https://openalex.org/W2103288005","https://openalex.org/W2545661456"],"abstract_inverted_index":{"The":[0,28,39],"spectrum":[1,44],"of":[2,5,18,25,41,50,70,89,101,128,154,163],"the":[3,16,32,42,55,62,68,71,76,80,87,90,96,102,110,116,120,129,138,141,150,164,169,174],"output":[4,43,72,81,151],"a":[6,155,161],"half-wave":[7],"rectifier":[8],"is":[9,15,31,65,84,105,113,135,144,158,172],"derived":[10],"for":[11,137],"an":[12],"input":[13,56,91,103,165],"which":[14],"sum":[17],"random":[19],"noise":[20,82,121],"and":[21,119],"two":[22,97],"sinusoidal":[23],"signals":[24,57,104],"different":[26],"frequencies.":[27,98],"method":[29,35],"used":[30],"characteristic":[33],"function":[34,162],"described":[36],"by":[37],"Rice.":[38],"components":[40],"are":[45,122],"given":[46],"as":[47,160],"infinite":[48],"series":[49],"hypergeometric":[51],"functions.":[52],"If":[53,99],"both":[54],".are":[58],"small":[59],"compared":[60,108],"with":[61,109],"noise,":[63,111],"it":[64,112],"shown":[66,114],"that":[67,115],"ratio":[69,153],"signal":[73,118,143],"power":[74,83,93],"at":[75,95],"difference":[77],"frequency":[78,125],"to":[79,86],"proportional":[85],"product":[88],"signal-to-noise":[92,130,152,166],"ratios":[94],"one":[100],"very":[106],"large":[107,142,147],"other":[117],"translated":[123],"in":[124],"without":[126],"alteration":[127],"ratio.":[131],"A":[132],"correction":[133],"factor":[134],"obtained":[136],"case":[139],"where":[140],"not":[145],"quite":[146],"enough.":[148],"Finally,":[149],"single-sideband":[156],"detector":[157],"calculated":[159],"ratio,":[167],"when":[168],"sideband":[170],"amplitude":[171],"one-half":[173],"carrier":[175],"amplitude.":[176]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
