{"id":"https://openalex.org/W2107282653","doi":"https://doi.org/10.1109/tsp.2009.2037063","title":"Quasi-Interpolation by Means of Filter-Banks","display_name":"Quasi-Interpolation by Means of Filter-Banks","publication_year":2009,"publication_date":"2009-11-30","ids":{"openalex":"https://openalex.org/W2107282653","doi":"https://doi.org/10.1109/tsp.2009.2037063","mag":"2107282653"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2009.2037063","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2037063","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://oa.upm.es/9450/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088293110","display_name":"G. P\u00e9rez-Villal\u00f3n","orcid":"https://orcid.org/0000-0003-2061-917X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"G. Perez-Villalon","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada a la Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain","Dept. de Mat. Aplic. a la Telecomun., Univ. Politec. de Madrid, Madrid, Spain"],"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada a la Telecomunicaci\u00f3n, Universidad Polit\u00e9cnica de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]},{"raw_affiliation_string":"Dept. de Mat. Aplic. a la Telecomun., Univ. Politec. de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088293110"],"corresponding_institution_ids":["https://openalex.org/I88060688"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13985411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"3","first_page":"1628","last_page":"1637"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9995999932289124,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9995999932289124,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9991000294685364,"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/upsampling","display_name":"Upsampling","score":0.6825507879257202},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.5331999659538269},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.45522746443748474},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4486796259880066},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.44534507393836975},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.42931604385375977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4243052899837494},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41484469175338745},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4137086868286133},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3449074327945709},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3235798478126526},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24394309520721436},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18229714035987854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16360196471214294}],"concepts":[{"id":"https://openalex.org/C110384440","wikidata":"https://www.wikidata.org/wiki/Q1143270","display_name":"Upsampling","level":3,"score":0.6825507879257202},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.5331999659538269},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.45522746443748474},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4486796259880066},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.44534507393836975},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.42931604385375977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4243052899837494},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41484469175338745},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4137086868286133},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3449074327945709},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3235798478126526},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24394309520721436},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18229714035987854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16360196471214294},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsp.2009.2037063","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2009.2037063","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:hispana.mcu.es:17509837","is_oa":false,"landing_page_url":"https://oa.upm.es/9450/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, ISSN 1053-587X, 2010-02, Vol. 58, No. 3","raw_type":"info:eu-repo/semantics/acceptedVersion"},{"id":"pmh:oai:dnet:archivodigit::0d8af153a25212a33b044b130fa5ea3b","is_oa":true,"landing_page_url":"http://oa.upm.es/9450/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, ISSN 1053-587X, 2010-02, Vol. 58, No. 3","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dnet:archivodigit::0d8af153a25212a33b044b130fa5ea3b","is_oa":true,"landing_page_url":"http://oa.upm.es/9450/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Signal Processing, ISSN 1053-587X, 2010-02, Vol. 58, No. 3","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1481646516","https://openalex.org/W1483569328","https://openalex.org/W1489213177","https://openalex.org/W1500590279","https://openalex.org/W1552869711","https://openalex.org/W1615872493","https://openalex.org/W1879125087","https://openalex.org/W1986869180","https://openalex.org/W2009801033","https://openalex.org/W2012992134","https://openalex.org/W2050447092","https://openalex.org/W2056700839","https://openalex.org/W2065628492","https://openalex.org/W2073431334","https://openalex.org/W2084633773","https://openalex.org/W2096086749","https://openalex.org/W2101789093","https://openalex.org/W2116751005","https://openalex.org/W2122776646","https://openalex.org/W2153608957","https://openalex.org/W2163889321","https://openalex.org/W2166500461","https://openalex.org/W2171342370","https://openalex.org/W2984425774","https://openalex.org/W4205354563","https://openalex.org/W4255137765"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2062399876","https://openalex.org/W2607795551","https://openalex.org/W3155117723","https://openalex.org/W1991429770","https://openalex.org/W1983892167","https://openalex.org/W2281134365","https://openalex.org/W4310746709","https://openalex.org/W4385574037","https://openalex.org/W2383860647"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,59,76,87,98,103,133,147,150,160,172,208],"problem":[3],"of":[4,27,31,34,61,97,136,149,159],"approximating":[5],"a":[6,16,24,28,35,56,94,105,118,137,143,165,181],"regular":[7],"function":[8],"f(t)":[9,22],"from":[10],"its":[11],"samples,":[12,134],"f(nT),":[13],"taken":[14],"in":[15,55,146,195,207],"uniform":[17],"grid.":[18],"Quasi-interpolation":[19],"schemes":[20,71,92,185],"approximate":[21],"with":[23,117],"dilated":[25],"version":[26],"linear":[29],"combination":[30],"shifted":[32],"versions":[33],"kernel":[36],"\u00bf(t),":[37],"specifically":[38],"f":[39],"<sub":[40,49,106],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,44,50,81,107],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">approx</sub>":[42],"<sup":[43,80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">T</sup>":[45],"(t)":[46],"=":[47,170],"\u00bfa":[48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">f</sub>":[51,108],"[n]\u00bf(t/T":[52],"-":[53],"n),":[54],"way":[57],"that":[58],"polynomials":[60],"degree":[62],"at":[63],"most":[64],"L-1":[65],"are":[66],"recovered":[67],"exactly.":[68],"These":[69],"approximation":[70,116,151,192],"give":[72,190],"order":[73],"L,":[74],"i.e.,":[75],"error":[77],"is":[78,86],"O(T":[79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</sup>":[82],")":[83],"where":[84],"T":[85],"sampling":[88],"period.":[89],"Recently,":[90],"quasi-interpolation":[91],"using":[93],"discrete":[95],"prefiltering":[96],"samples":[99],"f(nT)":[100],"to":[101,131,177,180,187],"obtain":[102],"coefficients":[104],"[n],":[109],"have":[110,198],"been":[111],"proposed.":[112],"They":[113],"provide":[114],"tight":[115],"low":[119],"computational":[120,200],"cost.":[121],"In":[122],"this":[123],"work,":[124],"we":[125],"generalize":[126],"considering":[127],"rational":[128,161],"filter":[129,162],"banks":[130],"prefilter":[132],"instead":[135],"simple":[138,182],"filter.":[139,183],"This":[140],"generalization":[141],"provides":[142],"greater":[144],"flexibility":[145],"design":[148],"scheme.":[152],"The":[153],"upsampling":[154],"and":[155,202],"downsampling":[156],"ratio":[157],"r":[158,169],"bank":[163],"plays":[164],"significant":[166],"role.":[167],"When":[168],"1,":[171],"scheme":[173],"has":[174],"similar":[175],"characteristics":[176],"those":[178],"related":[179],"Approximation":[184],"corresponding":[186],"smaller":[188],"ratios":[189],"less":[191,199,204],"quality,":[193],"but,":[194],"return,":[196],"they":[197],"cost":[201],"involve":[203],"storage":[205],"load":[206],"system.":[209]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
