{"id":"https://openalex.org/W1970484603","doi":"https://doi.org/10.1109/tit.1969.1054358","title":"Second-order properties of products of clipped Gaussian processes","display_name":"Second-order properties of products of clipped Gaussian processes","publication_year":1969,"publication_date":"1969-09-01","ids":{"openalex":"https://openalex.org/W1970484603","doi":"https://doi.org/10.1109/tit.1969.1054358","mag":"1970484603"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1969.1054358","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054358","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/A5045630895","display_name":"David A. Pitassi","orcid":null},"institutions":[{"id":"https://openalex.org/I1306686416","display_name":"RTX (United States)","ror":"https://ror.org/0354t7b78","country_code":"US","type":"company","lineage":["https://openalex.org/I1306686416"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Pitassi","raw_affiliation_strings":["Raytheon Company, Newport, RI, USA"],"affiliations":[{"raw_affiliation_string":"Raytheon Company, Newport, RI, USA","institution_ids":["https://openalex.org/I1306686416"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045630895"],"corresponding_institution_ids":["https://openalex.org/I1306686416"],"apc_list":null,"apc_paid":null,"fwci":1.162,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77590361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"5","first_page":"535","last_page":"540"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9832000136375427,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9832000136375427,"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/T12300","display_name":"Advanced Electrical Measurement Techniques","score":0.9807999730110168,"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"}},{"id":"https://openalex.org/T12564","display_name":"Sensor Technology and Measurement Systems","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/variance","display_name":"Variance (accounting)","score":0.5229336023330688},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4971814453601837},{"id":"https://openalex.org/keywords/autocorrelation","display_name":"Autocorrelation","score":0.4723842144012451},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.46081867814064026},{"id":"https://openalex.org/keywords/coincidence","display_name":"Coincidence","score":0.44944480061531067},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4329458475112915},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4324198365211487},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.4308801293373108},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4200558662414551},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4186059236526489},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41549837589263916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4022921323776245},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3467283844947815},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3458380699157715},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3200923800468445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16763770580291748},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09124952554702759}],"concepts":[{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5229336023330688},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4971814453601837},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.4723842144012451},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.46081867814064026},{"id":"https://openalex.org/C2779832538","wikidata":"https://www.wikidata.org/wiki/Q2308809","display_name":"Coincidence","level":3,"score":0.44944480061531067},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4329458475112915},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4324198365211487},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.4308801293373108},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4200558662414551},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4186059236526489},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41549837589263916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4022921323776245},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3467283844947815},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3458380699157715},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3200923800468445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16763770580291748},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09124952554702759},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"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.1969.1054358","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054358","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":16,"referenced_works":["https://openalex.org/W249378134","https://openalex.org/W256058813","https://openalex.org/W1965760932","https://openalex.org/W1986340188","https://openalex.org/W1994615352","https://openalex.org/W2021141721","https://openalex.org/W2028167607","https://openalex.org/W2049685281","https://openalex.org/W2053637529","https://openalex.org/W2116059849","https://openalex.org/W2120894588","https://openalex.org/W2138117794","https://openalex.org/W2477688680","https://openalex.org/W4234061723","https://openalex.org/W4250346491","https://openalex.org/W4301253858"],"related_works":["https://openalex.org/W90906771","https://openalex.org/W2018828772","https://openalex.org/W2529185025","https://openalex.org/W3029319512","https://openalex.org/W3033220593","https://openalex.org/W2138100553","https://openalex.org/W4389454697","https://openalex.org/W2809723425","https://openalex.org/W2007743448","https://openalex.org/W2070733898"],"abstract_inverted_index":{"Closed-form":[0],"expressions":[1],"are":[2,41,87,109,150],"derived":[3],"for":[4,164,173,191],"the":[5,11,15,37,49,80,84,92,101,104,113,116,140,144,156,177],"partial":[6,68],"derivatives":[7,69],"with":[8,54],"respect":[9],"to":[10,73,111,188],"time":[12],"delays":[13],"of":[14,52,62,103,115,122,129,143],"fourth":[16,64],"product":[17,65],"moment":[18],"<tex":[19,38,168,183],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[20,39,169,184],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">W(t_{1},":[21],"t_{2},":[22],"t_{3})":[23],"=":[24],"E[":[25],"Y_{1}(t)":[26],"Y_{2}(t":[27],"+":[28,31,34],"t_{1})":[29],"Y_{3}(t":[30],"t_{2})":[32],"Y_{4}(t":[33],"t_{3})]</tex>":[35],"when":[36,83,91],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">Y_{i}(t)</tex>":[40],"infinitely":[42,55],"clipped,":[43],"zero-mean,":[44],"jointly":[45],"Gaussian":[46],"processes.":[47],"Since":[48],"output":[50,76,93,117,157,178],"autocorrelation":[51],"systems":[53,131],"clipped":[56],"inputs":[57,86,149],"is":[58,94,153],"often":[59],"a":[60,120],"sum":[61],"such":[63,78],"moments,":[66],"these":[67],"can":[70],"be":[71],"used":[72],"determine":[74],"second-order":[75],"properties,":[77],"as":[79,119,160],"power":[81],"spectrum,":[82],"system's":[85],"correlated.":[88],"In":[89],"particular":[90],"low-pass":[95],"filtered,":[96],"one":[97],"numerical":[98],"integration":[99],"determines":[100],"variance":[102,158,179],"smoothed":[105],"process.":[106],"The":[107],"results":[108],"applied":[110],"study":[112],"behavior":[114],"variance,":[118],"function":[121],"signal-to-noise":[123],"ratio":[124],"(SNR)":[125],"and":[126,147,172],"input":[127],"bandwidth,":[128],"two":[130],"which":[132],"signal":[133,146],"process":[134],"using":[135],"polarity":[136],"coincidence":[137],"techniques.":[138],"When":[139],"normalized":[141],"spectra":[142],"independent":[145],"noise":[148,193],"identical,":[151],"it":[152],"shown":[154],"that":[155],"decreases":[159],"SNR":[161,165],"increases,":[162],"but,":[163],"less":[166],"than":[167],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</tex>":[170],"dB":[171,186],"all":[174],"bandwidths":[175],"considered,":[176],"deviates":[180],"at":[181],"most":[182],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">-1</tex>":[185],"relative":[187],"its":[189],"value":[190],"uncorrelated,":[192],"only,":[194],"inputs.":[195]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
