{"id":"https://openalex.org/W4317399517","doi":"https://doi.org/10.1142/s0219691323500066","title":"Rational Franklin MRA and its Wavelets","display_name":"Rational Franklin MRA and its Wavelets","publication_year":2023,"publication_date":"2023-01-19","ids":{"openalex":"https://openalex.org/W4317399517","doi":"https://doi.org/10.1142/s0219691323500066"},"language":"en","primary_location":{"id":"doi:10.1142/s0219691323500066","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0219691323500066","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"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":"International Journal of Wavelets, Multiresolution and Information Processing","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/A5039936938","display_name":"S. Pitchai Murugan","orcid":null},"institutions":[{"id":"https://openalex.org/I215927","display_name":"University of Madras","ror":"https://ror.org/04jmt9361","country_code":"IN","type":"education","lineage":["https://openalex.org/I215927"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"S. Pitchai Murugan","raw_affiliation_strings":["Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India"],"affiliations":[{"raw_affiliation_string":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India","institution_ids":["https://openalex.org/I215927"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091789184","display_name":"G. P. Youvaraj","orcid":null},"institutions":[{"id":"https://openalex.org/I215927","display_name":"University of Madras","ror":"https://ror.org/04jmt9361","country_code":"IN","type":"education","lineage":["https://openalex.org/I215927"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"G. P. Youvaraj","raw_affiliation_strings":["Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India"],"affiliations":[{"raw_affiliation_string":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India","institution_ids":["https://openalex.org/I215927"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091789184"],"corresponding_institution_ids":["https://openalex.org/I215927"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01592304,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"04","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9987999796867371,"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/T11034","display_name":"Digital Filter Design and Implementation","score":0.9771999716758728,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6505545973777771},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5677451491355896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4797160029411316},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3471391201019287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20911237597465515},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12848570942878723},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1282556653022766}],"concepts":[{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6505545973777771},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5677451491355896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4797160029411316},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3471391201019287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20911237597465515},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12848570942878723},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1282556653022766},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219691323500066","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0219691323500066","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"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":"International Journal of Wavelets, Multiresolution and Information Processing","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":12,"referenced_works":["https://openalex.org/W1595505223","https://openalex.org/W1984287426","https://openalex.org/W2067204686","https://openalex.org/W2086770443","https://openalex.org/W2129231728","https://openalex.org/W2155441809","https://openalex.org/W2513196354","https://openalex.org/W3085708735","https://openalex.org/W3196989013","https://openalex.org/W4241109547","https://openalex.org/W4252040385","https://openalex.org/W4255272544"],"related_works":["https://openalex.org/W2370850565","https://openalex.org/W1979597421","https://openalex.org/W2381894435","https://openalex.org/W2007980826","https://openalex.org/W2296214397","https://openalex.org/W2951195293","https://openalex.org/W2029951831","https://openalex.org/W2168986779","https://openalex.org/W1975945902","https://openalex.org/W2392110000"],"abstract_inverted_index":{"In":[0,27,121],"signal":[1,25],"processing,":[2],"rational":[3,32],"[Formula:":[4,34,38,45,55,62,66,71,75,85,90,94,102,109,118,126,131],"see":[5,35,39,46,56,63,67,72,76,86,91,95,103,110,119,127,132],"text]-wavelets":[6,128],"are":[7,59],"preferable":[8],"than":[9],"the":[10,48,113],"wavelets":[11],"corresponding":[12,129],"to":[13,130],"dyadic":[14],"MRA":[15],"because":[16],"it":[17],"allows":[18],"more":[19],"variations":[20],"in":[21,54],"scale":[22],"factors":[23],"of":[24,50],"components.":[26],"this":[28],"paper,":[29],"for":[30,69],"a":[31,43,89,107],"number":[33],"text]":[36,57,64,68,87],"and":[37,65],"text],":[40,47,77,104,111],"we":[41,81,98,123],"consider":[42],"collection":[44],"space":[49],"all":[51,70],"continuous":[52],"functions":[53],"that":[58,100,116],"linear":[60],"on":[61],"text].":[73,96],"For":[74],"under":[78],"certain":[79],"conditions,":[80,115],"prove":[82],"that,":[83],"if":[84,101],"generates":[88,117],"text]-MRA,":[92],"then":[93],"Also,":[97],"show":[99],"there":[105],"exists":[106],"function":[108],"satisfying":[112],"above":[114],"text]-MRA.":[120,133],"addition,":[122],"construct":[124],"orthonormal":[125]},"counts_by_year":[],"updated_date":"2025-12-24T23:09:58.560324","created_date":"2025-10-10T00:00:00"}