{"id":"https://openalex.org/W2010990103","doi":"https://doi.org/10.1142/s0218126693000411","title":"THEORY OF GENERALIZED INTERPOLATORY APPROXIMATION OF MULTI-DIMENSIONAL SIGNALS","display_name":"THEORY OF GENERALIZED INTERPOLATORY APPROXIMATION OF MULTI-DIMENSIONAL SIGNALS","publication_year":1993,"publication_date":"1993-09-01","ids":{"openalex":"https://openalex.org/W2010990103","doi":"https://doi.org/10.1142/s0218126693000411","mag":"2010990103"},"language":"en","primary_location":{"id":"doi:10.1142/s0218126693000411","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126693000411","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and Computers","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/A5111065230","display_name":"Takuro Kida","orcid":null},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"TAKURO KIDA","raw_affiliation_strings":["Department of Information Processing, Graduate School of Nagatsuta, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama-shi, 227, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Information Processing, Graduate School of Nagatsuta, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama-shi, 227, Japan","institution_ids":["https://openalex.org/I114531698"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111065230"],"corresponding_institution_ids":["https://openalex.org/I114531698"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.26920073,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"03","issue":"03","first_page":"673","last_page":"699"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10534","display_name":"Structural Health Monitoring Techniques","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/orthogonality","display_name":"Orthogonality","score":0.7871162295341492},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.7863917350769043},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7425409555435181},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.5187999606132507},{"id":"https://openalex.org/keywords/trigonometric-interpolation","display_name":"Trigonometric interpolation","score":0.47542694211006165},{"id":"https://openalex.org/keywords/approximation-error","display_name":"Approximation error","score":0.4743436872959137},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45540696382522583},{"id":"https://openalex.org/keywords/envelope","display_name":"Envelope (radar)","score":0.4541049897670746},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4468459188938141},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.4228460192680359},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.3111136555671692},{"id":"https://openalex.org/keywords/nearest-neighbor-interpolation","display_name":"Nearest-neighbor interpolation","score":0.23668745160102844},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14490976929664612},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09825405478477478},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0872393250465393}],"concepts":[{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.7871162295341492},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.7863917350769043},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7425409555435181},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5187999606132507},{"id":"https://openalex.org/C28537468","wikidata":"https://www.wikidata.org/wiki/Q464356","display_name":"Trigonometric interpolation","level":5,"score":0.47542694211006165},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.4743436872959137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45540696382522583},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.4541049897670746},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4468459188938141},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.4228460192680359},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.3111136555671692},{"id":"https://openalex.org/C207214200","wikidata":"https://www.wikidata.org/wiki/Q4202129","display_name":"Nearest-neighbor interpolation","level":4,"score":0.23668745160102844},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14490976929664612},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09825405478477478},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0872393250465393},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218126693000411","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218126693000411","pdf_url":null,"source":{"id":"https://openalex.org/S167602672","display_name":"Journal of Circuits Systems and Computers","issn_l":"0218-1266","issn":["0218-1266","1793-6454"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Circuits, Systems and Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2373827582","https://openalex.org/W1565653811","https://openalex.org/W1589517457","https://openalex.org/W2071815454","https://openalex.org/W2036543038","https://openalex.org/W2469842298","https://openalex.org/W2803516188","https://openalex.org/W2059995070","https://openalex.org/W1989702898","https://openalex.org/W2194319978"],"abstract_inverted_index":{"In":[0,67,146],"this":[1,123],"paper,":[2],"we":[3,71],"present":[4],"a":[5,14,40,132,150],"systematic":[6],"theory":[7],"of":[8,13,16,30,50,58,78,104,108,138,140,179,197],"the":[9,27,48,56,59,65,68,75,88,93,101,105,109,117,126,135,143,147,160,165,182,189,198,202],"optimum":[10,95,118],"subband":[11],"interpolation":[12,79,96,119,166,173],"family":[15],"n-dimensional":[17,110],"signals":[18,32],"which":[19,52],"are":[20,85,98,168],"not":[21],"necessarily":[22],"band-limited.":[23],"We":[24],"assume":[25,72],"that":[26,74,116,159],"Fourier":[28],"spectrums":[29],"these":[31,172],"have":[33],"weighted":[34],"L":[35],"2":[36],"norms":[37],"smaller":[38],"than":[39],"given":[41],"positive":[42],"number.":[43],"The":[44],"proposed":[45,183],"method":[46],"minimizes":[47],"measure":[49],"error":[51,141,180],"is":[53,153,157,162,191,205],"equal":[54],"to":[55,64],"envelope":[57],"approximation":[60,90,199],"errors":[61],"with":[62,81],"respect":[63],"signals.":[66],"following":[69],"discussion,":[70],"initially":[73],"infinite":[76],"number":[77,107],"functions":[80,97,120,167,174],"different":[82],"functional":[83],"forms":[84],"used":[86],"in":[87,122,188,201],"corresponding":[89],"formula.":[91],"However,":[92,155],"resultant":[94],"expressed":[99],"as":[100,131],"parallel":[102],"shifts":[103],"finite":[106],"functions.":[111],"It":[112],"should":[113],"be":[114],"noted":[115],"presented":[121],"paper":[124],"satisfy":[125],"generalized":[127],"discrete":[128],"orthogonality":[129],"and,":[130],"result,":[133],"minimize":[134,176],"wide":[136],"variety":[137],"measures":[139,178],"at":[142],"same":[144],"time.":[145],"literature,":[148],"6":[149],"similar":[151],"discussion":[152],"presented.":[154],"it":[156],"assumed":[158],"signal":[161],"band-limited":[163],"and":[164],"compulsorily":[169],"time-limited.":[170],"Hence,":[171],"cannot":[175],"other":[177],"except":[181],"one.":[184],"Interesting":[185],"reciprocal":[186],"relation":[187],"approximation,":[190],"also":[192],"discussed.":[193],"An":[194],"equivalent":[195],"expression":[196],"formula":[200],"frequency":[203],"domain":[204],"derived.":[206]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}