{"id":"https://openalex.org/W1992472354","doi":"https://doi.org/10.1109/iscit.2012.6380999","title":"Degrees of freedom of band limited signals measured over space","display_name":"Degrees of freedom of band limited signals measured over space","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W1992472354","doi":"https://doi.org/10.1109/iscit.2012.6380999","mag":"1992472354"},"language":"en","primary_location":{"id":"doi:10.1109/iscit.2012.6380999","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscit.2012.6380999","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 International Symposium on Communications and Information Technologies (ISCIT)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5085788293","display_name":"Farhana Bashar","orcid":"https://orcid.org/0000-0003-4847-913X"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Farhana Bashar","raw_affiliation_strings":["Research School of Engineering, College of Engineering and Computer Science (CECS), Australian National University, Canberra, ACT, Australia","Research School of Engineering, College of Engineering and Computer Science (CECS), The Australian National University (ANU), Canberra 0200 ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research School of Engineering, College of Engineering and Computer Science (CECS), Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Research School of Engineering, College of Engineering and Computer Science (CECS), The Australian National University (ANU), Canberra 0200 ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003018152","display_name":"Thushara D. Abhayapala","orcid":"https://orcid.org/0000-0001-6937-7218"},"institutions":[{"id":"https://openalex.org/I118347636","display_name":"Australian National University","ror":"https://ror.org/019wvm592","country_code":"AU","type":"education","lineage":["https://openalex.org/I118347636"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Thushara D. Abhayapala","raw_affiliation_strings":["Research School of Engineering, College of Engineering and Computer Science (CECS), Australian National University, Canberra, ACT, Australia","Research School of Engineering, College of Engineering and Computer Science (CECS), The Australian National University (ANU), Canberra 0200 ACT, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research School of Engineering, College of Engineering and Computer Science (CECS), Australian National University, Canberra, ACT, Australia","institution_ids":["https://openalex.org/I118347636"]},{"raw_affiliation_string":"Research School of Engineering, College of Engineering and Computer Science (CECS), The Australian National University (ANU), Canberra 0200 ACT, Australia","institution_ids":["https://openalex.org/I118347636"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I118347636"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":null,"first_page":"735","last_page":"740"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9962000250816345,"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/T10931","display_name":"Direction-of-Arrival Estimation Techniques","score":0.9962000250816345,"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/T10860","display_name":"Speech and Audio Processing","score":0.9955999851226807,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/nyquist\u2013shannon-sampling-theorem","display_name":"Nyquist\u2013Shannon sampling theorem","score":0.876692533493042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6302158832550049},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.6279683709144592},{"id":"https://openalex.org/keywords/bandwidth","display_name":"Bandwidth (computing)","score":0.602319061756134},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5477645993232727},{"id":"https://openalex.org/keywords/sampling","display_name":"Sampling (signal processing)","score":0.5347980856895447},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.4954937696456909},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49068892002105713},{"id":"https://openalex.org/keywords/nyquist-frequency","display_name":"Nyquist frequency","score":0.44796422123908997},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24154475331306458},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.21546602249145508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1577206552028656},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.13747522234916687}],"concepts":[{"id":"https://openalex.org/C288623","wikidata":"https://www.wikidata.org/wiki/Q679800","display_name":"Nyquist\u2013Shannon sampling theorem","level":2,"score":0.876692533493042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6302158832550049},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.6279683709144592},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.602319061756134},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5477645993232727},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5347980856895447},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.4954937696456909},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49068892002105713},{"id":"https://openalex.org/C98273374","wikidata":"https://www.wikidata.org/wiki/Q1501757","display_name":"Nyquist frequency","level":3,"score":0.44796422123908997},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24154475331306458},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.21546602249145508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1577206552028656},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.13747522234916687},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/iscit.2012.6380999","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iscit.2012.6380999","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 International Symposium on Communications and Information Technologies (ISCIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/65377","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/65377","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.iscit2012.org/","raw_type":"Conference paper"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8100000023841858,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W25977736","https://openalex.org/W1523113578","https://openalex.org/W1617851430","https://openalex.org/W2043644866","https://openalex.org/W2067111814","https://openalex.org/W2084052726","https://openalex.org/W2086710291","https://openalex.org/W2097959015","https://openalex.org/W2102083017","https://openalex.org/W2110403504","https://openalex.org/W2124164696","https://openalex.org/W2135479785","https://openalex.org/W2140296346","https://openalex.org/W2142413028","https://openalex.org/W2143447102","https://openalex.org/W2144730780","https://openalex.org/W2160063707","https://openalex.org/W2168733443","https://openalex.org/W3024018030","https://openalex.org/W4252713891","https://openalex.org/W4292027041","https://openalex.org/W6601047954","https://openalex.org/W6631224076","https://openalex.org/W6636635686","https://openalex.org/W6674728311"],"related_works":["https://openalex.org/W1500996803","https://openalex.org/W2081608853","https://openalex.org/W2788446302","https://openalex.org/W2071732377","https://openalex.org/W1526881856","https://openalex.org/W2356666806","https://openalex.org/W2315093958","https://openalex.org/W1997066351","https://openalex.org/W2362083308","https://openalex.org/W2801332561"],"abstract_inverted_index":{"In":[0,102],"this":[1],"paper,":[2],"we":[3,104],"provide":[4],"the":[5,53,56,83,88,94,99,111,142,145,150,155,159],"degrees":[6,95,112,151],"of":[7,9,52,63,90,96,98,113,115,132,144,152,154],"freedom":[8,97,114,153],"a":[10,16,21,49,73,106,116,127,165],"band":[11,120],"limited":[12,121],"signal":[13,100,117,157,167],"observed":[14,118],"over":[15,119,158],"finite":[17],"spatial":[18,91,148],"window":[19],"at":[20,126],"given":[22,166],"time":[23,129],"instant.":[24],"The":[25,43,60,75],"limit":[26],"is":[27,36,45,78],"based":[28],"on":[29,93],"Claude":[30],"E.":[31],"Shannon's":[32],"sampling":[33,41],"theorem":[34],"which":[35],"also":[37],"known":[38],"as":[39],"Whittaker-Nyquist-Kotelnikov-Shannon":[40],"theorem.":[42],"result":[44,77],"derived":[46,76],"by":[47,140],"using":[48],"series":[50],"expansion":[51],"solution":[54],"to":[55,70,82,109],"Helmholtz":[57],"wave":[58,64],"equation.":[59],"expanded":[61],"terms":[62,131],"equation":[65],"are":[66],"then":[67],"bounded":[68],"exponentially":[69],"zero":[71],"beyond":[72],"threshold.":[74],"more":[79],"general":[80],"compared":[81],"existing":[84],"ones":[85],"and":[86,122,134],"explores":[87],"effects":[89],"information":[92],"observed.":[101],"addition,":[103],"derive":[105],"new":[107],"expression":[108],"calculate":[110],"spatially":[123],"constrained":[124],"channel":[125],"constant":[128],"in":[130],"wavelengths":[133],"fractional":[135],"bandwidth.":[136,168],"We":[137],"show":[138],"that":[139],"increasing":[141],"size":[143],"three":[146],"dimensional":[147],"region,":[149],"observable":[156],"region":[160],"can":[161],"be":[162],"increased":[163],"for":[164]},"counts_by_year":[{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}