{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T05:00:00Z","timestamp":1648530000529},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2010,11]]},"abstract":"<jats:p> Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function \u03d5, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function \u03d5 is compactly supported conjugate symmetric, then we prove that there exists a compactly supported conjugate symmetric\/anti-symmetric complex tight wavelet frame \u03a8 = {\u03c8<jats:sup>1<\/jats:sup>, \u03c8<jats:sup>2<\/jats:sup>, \u03c8<jats:sup>3<\/jats:sup>} associated with \u03d5. Secondly, under the conditions that both the low-pass filters and high-pass filters are unknown, we give a parametric formula for constructing a class of smooth conjugate symmetric\/anti-symmetric complex tight wavelet frames. Free parameters in the algorithm are explicitly identified, and can be used to optimize the result with respect to other criteria. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames. <\/jats:p>","DOI":"10.1142\/s0219691310003857","type":"journal-article","created":{"date-parts":[[2010,11,2]],"date-time":"2010-11-02T04:16:50Z","timestamp":1288671410000},"page":"861-874","source":"Crossref","is-referenced-by-count":9,"title":["CONSTRUCTION OF COMPACTLY SUPPORTED CONJUGATE SYMMETRIC COMPLEX TIGHT WAVELET FRAMES"],"prefix":"10.1142","volume":"08","author":[{"given":"SHOUZHI","family":"YANG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China"}]},{"given":"YANMEI","family":"XUE","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shantou University, Shantou, Guangdong 515063, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2000.0337"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-002-0522-1"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/acha.2000.0301"},{"key":"rf4","first-page":"445","volume":"46","author":"Peng L. Z.","journal-title":"Sci. China"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002653"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691308002240"},{"key":"rf7","first-page":"294","volume":"18","author":"Cui L. H.","journal-title":"Signal Process."},{"key":"rf8","first-page":"160","volume":"25","author":"Cui L. H.","journal-title":"Numerical Mathematics A Journal of Chinese Universities"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/78.258098"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1109\/78.469843"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/78.752601"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0219691309003094"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1109\/78.157221"},{"key":"rf15","volume-title":"An Introduction to Wavelet","author":"Chui C. K.","year":"1992"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3079"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1006\/acha.1997.0237"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691310003857","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:17:24Z","timestamp":1565133444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691310003857"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11]]},"references-count":16,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2010,11]]}},"alternative-id":["10.1142\/S0219691310003857"],"URL":"https:\/\/doi.org\/10.1142\/s0219691310003857","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,11]]}}}