{"id":"https://openalex.org/W2906301928","doi":"https://doi.org/10.1109/tit.2019.2934688","title":"Discrete Sampling: A Graph Theoretic Approach to Orthogonal Interpolation","display_name":"Discrete Sampling: A Graph Theoretic Approach to Orthogonal Interpolation","publication_year":2019,"publication_date":"2019-08-12","ids":{"openalex":"https://openalex.org/W2906301928","doi":"https://doi.org/10.1109/tit.2019.2934688","mag":"2906301928"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2934688","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2934688","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1411.7086","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071798008","display_name":"Aditya Siripuram","orcid":"https://orcid.org/0000-0002-8210-7113"},"institutions":[{"id":"https://openalex.org/I65181880","display_name":"Indian Institute of Technology Hyderabad","ror":"https://ror.org/01j4v3x97","country_code":"IN","type":"education","lineage":["https://openalex.org/I65181880"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Aditya Siripuram","raw_affiliation_strings":["Department of Electrical Engineering, IIT Hyderabad, Hyderabad, India","Dept. of Electrical Engineering, IIT Hyderabad, Hyderabad, India"],"raw_orcid":"https://orcid.org/0000-0002-8210-7113","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, IIT Hyderabad, Hyderabad, India","institution_ids":["https://openalex.org/I65181880"]},{"raw_affiliation_string":"Dept. of Electrical Engineering, IIT Hyderabad, Hyderabad, India","institution_ids":["https://openalex.org/I65181880"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026966260","display_name":"William Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William D. Wu","raw_affiliation_strings":["Quantitative Engineering Design (QED), Sheridan, USA","Quantitative Engineering Design (QED), Sheridan, WY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Quantitative Engineering Design (QED), Sheridan, USA","institution_ids":[]},{"raw_affiliation_string":"Quantitative Engineering Design (QED), Sheridan, WY, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081621247","display_name":"Brad Osgood","orcid":"https://orcid.org/0000-0001-9186-0732"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brad Osgood","raw_affiliation_strings":["Department of Electrical Engineering, Stanford University, Stanford, USA","Department of Electrical Engineering, Stanford University, Stanford, CA, USA#TAB#"],"raw_orcid":"https://orcid.org/0000-0001-9186-0732","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Electrical Engineering, Stanford University, Stanford, CA, USA#TAB#","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00481144,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"12","first_page":"8119","last_page":"8130"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T14438","display_name":"Advanced Scientific Research Methods","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/1106","display_name":"Food Science"},"field":{"id":"https://openalex.org/fields/11","display_name":"Agricultural and Biological Sciences"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9350000023841858,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9027000069618225,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bandlimiting","display_name":"Bandlimiting","score":0.5866033434867859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.577125072479248},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5391741991043091},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4803413152694702},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.4585639238357544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4552520513534546},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4347915053367615},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4269344210624695},{"id":"https://openalex.org/keywords/orthogonal-basis","display_name":"Orthogonal basis","score":0.4119469225406647},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.309792160987854}],"concepts":[{"id":"https://openalex.org/C129997835","wikidata":"https://www.wikidata.org/wiki/Q806263","display_name":"Bandlimiting","level":3,"score":0.5866033434867859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.577125072479248},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5391741991043091},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4803413152694702},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.4585639238357544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4552520513534546},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4347915053367615},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4269344210624695},{"id":"https://openalex.org/C187064257","wikidata":"https://www.wikidata.org/wiki/Q3306808","display_name":"Orthogonal basis","level":2,"score":0.4119469225406647},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.309792160987854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2019.2934688","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2934688","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"},{"id":"pmh:oai:arXiv.org:1411.7086","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.7086","pdf_url":"https://arxiv.org/pdf/1411.7086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2906301928","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1411.7086v3","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:raiith.iith.ac.in:7313","is_oa":false,"landing_page_url":"http://raiith.iith.ac.in/7313/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400292","display_name":"Research Archive of Indian Institute of Technology Hyderabad (Indian Institute of Technology Hyderabad)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I65181880","host_organization_name":"Indian Institute of Technology Hyderabad","host_organization_lineage":["https://openalex.org/I65181880"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1411.7086","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1411.7086","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1411.7086","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.7086","pdf_url":"https://arxiv.org/pdf/1411.7086","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2906301928.pdf","grobid_xml":"https://content.openalex.org/works/W2906301928.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1579049696","https://openalex.org/W1604193998","https://openalex.org/W1677183711","https://openalex.org/W1973199140","https://openalex.org/W1976047764","https://openalex.org/W1993774137","https://openalex.org/W1996692478","https://openalex.org/W2014871086","https://openalex.org/W2022031920","https://openalex.org/W2027360963","https://openalex.org/W2038182478","https://openalex.org/W2038583166","https://openalex.org/W2055064119","https://openalex.org/W2063753890","https://openalex.org/W2064436512","https://openalex.org/W2078289947","https://openalex.org/W2081826993","https://openalex.org/W2099526591","https://openalex.org/W2121743251","https://openalex.org/W2129638195","https://openalex.org/W2145073008","https://openalex.org/W2160900467","https://openalex.org/W2164452299","https://openalex.org/W2516153412","https://openalex.org/W2963716738"],"related_works":["https://openalex.org/W2967205996","https://openalex.org/W2466766312","https://openalex.org/W2973795992","https://openalex.org/W3008709738","https://openalex.org/W2992270377","https://openalex.org/W2751562296","https://openalex.org/W2890458614","https://openalex.org/W2963813647","https://openalex.org/W2032261599","https://openalex.org/W2900733261","https://openalex.org/W2751809630","https://openalex.org/W2791138598","https://openalex.org/W2149494781","https://openalex.org/W2297306388","https://openalex.org/W3200334977","https://openalex.org/W2884080932","https://openalex.org/W2990047715","https://openalex.org/W872941030","https://openalex.org/W2754235070","https://openalex.org/W1871399435"],"abstract_inverted_index":{"We":[0,61],"study":[1],"the":[2,16,55,63,71,82,97,101],"problem":[3,29,56,73],"of":[4,8,18,36,57,66,100],"finding":[5,58],"unitary":[6],"submatrices":[7],"the$N":[9],"\\times":[10],"N$discrete":[11],"Fourier":[12],"transform":[13],"matrix,":[14],"in":[15,84],"context":[17],"interpolating":[19],"a":[20,33,49,76],"discrete":[21],"bandlimited":[22],"signal":[23],"using":[24],"an":[25],"orthogonal":[26],"basis.":[27],"This":[28],"is":[30],"related":[31],"to":[32,54,86],"diverse":[34],"set":[35],"questions":[37],"on":[38],"idempotents":[39],"on$\\mathbb":[40],"{Z}_{N}$and":[41],"tiling$\\mathbb":[42],"{Z}_{N}$.":[43],"In":[44],"this":[45],"work,":[46],"we":[47,80,89],"establish":[48],"graph-theoretic":[50],"approach":[51],"and":[52,79,96],"connections":[53,92],"maximum":[59],"cliques.":[60],"identify":[62,81],"key":[64],"properties":[65,95],"these":[67],"graphs":[68],"that":[69],"make":[70],"interpolation":[72],"tractable":[74],"when$N$is":[75],"prime":[77],"power,":[78],"challenges":[83],"generalizing":[85],"arbitrary$N$.":[87],"Finally,":[88],"investigate":[90],"some":[91],"between":[93],"graph":[94],"spectral-tile":[98],"direction":[99],"Fuglede":[102],"conjecture.":[103]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
