{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:12:17Z","timestamp":1753884737623,"version":"3.41.2"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p> In signal processing, rational [Formula: see text]-wavelets are preferable than the wavelets corresponding to dyadic MRA because it allows more variations in scale factors of signal components. In this paper, for a rational number [Formula: see text] and [Formula: see text], we consider a collection [Formula: see text], the space of all continuous functions in [Formula: see text] that are linear on [Formula: see text] and [Formula: see text] for all [Formula: see text]. For [Formula: see text], under certain conditions, we prove that, if [Formula: see text] generates a [Formula: see text]-MRA, then [Formula: see text]. Also, we show that if [Formula: see text], there exists a function [Formula: see text], satisfying the above conditions, that generates [Formula: see text]-MRA. In addition, we construct orthonormal [Formula: see text]-wavelets corresponding to [Formula: see text]-MRA. <\/jats:p>","DOI":"10.1142\/s0219691323500066","type":"journal-article","created":{"date-parts":[[2023,1,19]],"date-time":"2023-01-19T06:02:10Z","timestamp":1674108130000},"source":"Crossref","is-referenced-by-count":0,"title":["Rational Franklin MRA and its Wavelets"],"prefix":"10.1142","volume":"21","author":[{"given":"S. Pitchai","family":"Murugan","sequence":"first","affiliation":[{"name":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India"}]},{"given":"G. P.","family":"Youvaraj","sequence":"additional","affiliation":[{"name":"Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chepauk, Chennai 600005, India"}]}],"member":"219","published-online":{"date-parts":[[2023,3,23]]},"reference":[{"key":"S0219691323500066BIB002","first-page":"439","volume-title":"Wavelets and Their Applications","author":"Auscher P.","year":"1992"},{"key":"S0219691323500066BIB003","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1016\/j.sigpro.2004.06.001","volume":"84","author":"Baussarda A.","year":"2004","journal-title":"Signal Process."},{"issue":"8","key":"S0219691323500066BIB004","doi-asserted-by":"crossref","first-page":"2957","DOI":"10.1109\/TSP.2009.2020756","volume":"57","author":"Bayram I.","year":"2009","journal-title":"IEEE Trans. Signal Process."},{"key":"S0219691323500066BIB005","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970104","volume-title":"Ten Lectures on Wavelets","author":"Daubechies I.","year":"1992"},{"key":"S0219691323500066BIB006","doi-asserted-by":"crossref","DOI":"10.1201\/9780367802349","volume-title":"A First Course on Wavelets","author":"Hern\u00e0ndez E.","year":"1996"},{"key":"S0219691323500066BIB007","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1109\/CISP.2014.7003953","volume-title":"2014 7th Int. Congress on Image and Signal Processing","author":"Li Z.","year":"2014"},{"issue":"4","key":"S0219691323500066BIB008","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1142\/S0219691308002525","volume":"6","author":"Li H.-G.","year":"2008","journal-title":"Int. J. Wavelets Multiresolution Inf. Process."},{"issue":"7","key":"S0219691323500066BIB009","doi-asserted-by":"crossref","first-page":"2150126","DOI":"10.1142\/S1793557121501266","volume":"14","author":"Pitchai Murugan S.","year":"2021","journal-title":"Asian-Eur. J. Math."},{"issue":"6","key":"S0219691323500066BIB010","doi-asserted-by":"crossref","first-page":"2150032","DOI":"10.1142\/S0219691321500326","volume":"19","author":"Pitchai Murugan S.","year":"2021","journal-title":"Int. J. Wavelets Multiresolution Inf. Process."},{"key":"S0219691323500066BIB011","doi-asserted-by":"crossref","first-page":"4819","DOI":"10.1007\/s00009-016-0777-6","volume":"13","author":"Rostami Y.","year":"2016","journal-title":"Mediterr. J. Math."},{"key":"S0219691323500066BIB012","first-page":"605","volume-title":"2005 Asia-Pacific Conference on Communications","author":"Yu L.","year":"2005"},{"key":"S0219691323500066BIB013","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1109\/LSP.2006.874393","volume":"13","author":"Yu L.","year":"2006","journal-title":"IEEE Signal Process. Lett."}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691323500066","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,3]],"date-time":"2023-07-03T08:44:32Z","timestamp":1688373872000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219691323500066"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,23]]},"references-count":12,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["10.1142\/S0219691323500066"],"URL":"https:\/\/doi.org\/10.1142\/s0219691323500066","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"type":"print","value":"0219-6913"},{"type":"electronic","value":"1793-690X"}],"subject":[],"published":{"date-parts":[[2023,3,23]]},"article-number":"2350006"}}