{"id":"https://openalex.org/W2131617412","doi":"https://doi.org/10.1109/tcom.1973.1091743","title":"A Spectral Theory for Hybrid Modulation","display_name":"A Spectral Theory for Hybrid Modulation","publication_year":1973,"publication_date":"1973-07-01","ids":{"openalex":"https://openalex.org/W2131617412","doi":"https://doi.org/10.1109/tcom.1973.1091743","mag":"2131617412"},"language":"en","primary_location":{"id":"doi:10.1109/tcom.1973.1091743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1973.1091743","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Communications","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/A5086472156","display_name":"G.B. Lockhart","orcid":"https://orcid.org/0000-0001-6584-1423"},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"G. Lockhart","raw_affiliation_strings":["Department of Electrical Engineering, University of Leeds, Leeds, UK","Dept. of Electr. Eng., Univ. of Leeds, England"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Leeds, Leeds, UK","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"Dept. of Electr. Eng., Univ. of Leeds, England","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086472156"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":null,"apc_paid":null,"fwci":1.2736,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.81155728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"21","issue":"7","first_page":"790","last_page":"800"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11248","display_name":"Advanced Power Amplifier Design","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11248","display_name":"Advanced Power Amplifier Design","score":0.9997000098228455,"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/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.9977999925613403,"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/T11607","display_name":"Microwave and Dielectric Measurement Techniques","score":0.9957000017166138,"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/modulation","display_name":"Modulation (music)","score":0.6651414632797241},{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.6135493516921997},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5899039506912231},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.5213828682899475},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.514907717704773},{"id":"https://openalex.org/keywords/amplitude-modulation","display_name":"Amplitude modulation","score":0.44958850741386414},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44833120703697205},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.44171229004859924},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.4340437948703766},{"id":"https://openalex.org/keywords/sideband","display_name":"Sideband","score":0.4145433008670807},{"id":"https://openalex.org/keywords/frequency-modulation","display_name":"Frequency modulation","score":0.3630688786506653},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.351107656955719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.339584618806839},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3292636573314667},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2895970940589905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25616326928138733},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14032268524169922},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12003359198570251},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.1109270453453064},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.06737732887268066}],"concepts":[{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.6651414632797241},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.6135493516921997},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5899039506912231},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.5213828682899475},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.514907717704773},{"id":"https://openalex.org/C201905106","wikidata":"https://www.wikidata.org/wiki/Q183755","display_name":"Amplitude modulation","level":4,"score":0.44958850741386414},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44833120703697205},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.44171229004859924},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4340437948703766},{"id":"https://openalex.org/C2776499502","wikidata":"https://www.wikidata.org/wiki/Q2267009","display_name":"Sideband","level":3,"score":0.4145433008670807},{"id":"https://openalex.org/C11930861","wikidata":"https://www.wikidata.org/wiki/Q181417","display_name":"Frequency modulation","level":3,"score":0.3630688786506653},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.351107656955719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.339584618806839},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3292636573314667},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2895970940589905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25616326928138733},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14032268524169922},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12003359198570251},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.1109270453453064},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.06737732887268066},{"id":"https://openalex.org/C44838205","wikidata":"https://www.wikidata.org/wiki/Q127995","display_name":"Microwave","level":2,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcom.1973.1091743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcom.1973.1091743","pdf_url":null,"source":{"id":"https://openalex.org/S4210170832","display_name":"IRE Transactions on Communications Systems","issn_l":"0096-2244","issn":["0096-2244","2162-2132"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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 Communications","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":18,"referenced_works":["https://openalex.org/W1968249360","https://openalex.org/W1999195298","https://openalex.org/W2013119153","https://openalex.org/W2038062095","https://openalex.org/W2044650918","https://openalex.org/W2054817256","https://openalex.org/W2065366926","https://openalex.org/W2093894424","https://openalex.org/W2111352071","https://openalex.org/W2129405344","https://openalex.org/W2131295257","https://openalex.org/W2133148419","https://openalex.org/W2138333112","https://openalex.org/W2148054531","https://openalex.org/W2156621864","https://openalex.org/W2160780119","https://openalex.org/W2163729192","https://openalex.org/W2527558138"],"related_works":["https://openalex.org/W2003931752","https://openalex.org/W2065370401","https://openalex.org/W2029032980","https://openalex.org/W2169415245","https://openalex.org/W2076462400","https://openalex.org/W2130944956","https://openalex.org/W2038062095","https://openalex.org/W2719918066","https://openalex.org/W2551220619","https://openalex.org/W2500038031"],"abstract_inverted_index":{"Certain":[0],"properties":[1,70],"of":[2,9,14,18,33,42,48,71,92,117,142],"periodic":[3],"signals":[4],"are":[5,79],"defined":[6],"in":[7,81,90,101,140],"terms":[8,91,141],"the":[10,40,46,72,82],"zeros":[11],"and":[12,37,60,95,132],"singularities":[13],"associated":[15,57],"analytic":[16,34],"functions":[17],"a":[19,31,102],"complex":[20],"time":[21],"variable":[22],"<tex":[23,50],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[24,51],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z</tex>":[25,52],".":[26],"This":[27],"algebraic":[28],"approach":[29,104],"is":[30,65,87,99,112,137],"generalization":[32],"signal":[35],"theory,":[36],"leads":[38],"to":[39,105,123],"conception":[41],"hybrid":[43],"modulation":[44,109,136],"as":[45,76],"superposition":[47],"two":[49,115],"-plane":[53],"zero-singularity":[54],"(ZS)":[55],"patterns":[56],"with":[58],"amplitude-":[59],"angle-modulating":[61],"signals,":[62],"respectively.":[63],"It":[64,111],"shown":[66,113],"that":[67,114],"important":[68],"spectral":[69],"modulated":[73],"signal,":[74],"such":[75],"band":[77],"limitation,":[78],"explicit":[80],"resultant":[83],"pattern.":[84],"Signal":[85],"design":[86],"then":[88],"interpreted":[89],"ZS":[93,145],"manipulation":[94],"placement.":[96],"The":[97,128],"theory":[98],"applied":[100],"unified":[103],"compatible":[106],"singlesideband":[107],"(CSSB)":[108],"systems.":[110],"types":[116],"proposed":[118],"CSSB":[119],"systems":[120],"give":[121],"rise":[122],"essentially":[124],"nonband-limited":[125],"output":[126],"signals.":[127],"relation":[129],"between":[130],"conventional":[131],"single-sideband":[133],"(SSB)":[134],"angle":[135],"also":[138],"discussed":[139],"their":[143],"characteristic":[144],"patterns.":[146]},"counts_by_year":[{"year":2022,"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"}