{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T14:42:37Z","timestamp":1761057757595},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Wavelets Multiresolut Inf. Process."],"published-print":{"date-parts":[[2003,6]]},"abstract":"<jats:p> It is well known that the Shannon Sampling Theorem allows us to fully recover a continuous-time bandlimited signal from its digital samples, as long as the sampling rate to be chosen is not smaller than the Nyquist frequency. This theory applies to all bandlimited signals, which may or may not occupy the entire frequency band. Hence, it is intuitively convincing that for continuous-time signals, such as those in speech, that do not fully utilize the entire frequency intervals, less digital samples are required for their full recovery. Current techniques in sub-band coding are used for achieving this goal. The objective of this paper is to present a wavelet theory for establishing the mathematical foundation of this sub-band coding approach. A wavelet packet decomposition of the signal provides the optimal sub-band coding bit-rate by using the Shannon wavelet library introduced in this paper. <\/jats:p>","DOI":"10.1142\/s0219691303000098","type":"journal-article","created":{"date-parts":[[2003,7,8]],"date-time":"2003-07-08T10:12:53Z","timestamp":1057659173000},"page":"233-242","source":"Crossref","is-referenced-by-count":2,"title":["Shannon Wavelet Approach to Sub-Band Coding"],"prefix":"10.1142","volume":"01","author":[{"given":"Charles K.","family":"Chui","sequence":"first","affiliation":[{"name":"Department of Mathematics &amp; Computer Science, University of Missouri-St.Louis, St. Louis, MO 63121, USA"}]},{"given":"Jianzhong","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77341, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,1,5]]},"reference":[{"key":"rf1","volume-title":"An Introduction to Wavelets","author":"Chui C. K.","year":"1992"},{"key":"rf2","first-page":"1633","author":"Crochiere R. E.","journal-title":"Bell System Tech. J."},{"key":"rf3","first-page":"621","author":"Crochiere R. E.","journal-title":"IEEE Trans. Commun."},{"key":"rf5","first-page":"1432","author":"Kohlenberg A.","journal-title":"J. Appl. Phys."},{"key":"rf6","volume-title":"Digital Coding of Waveforms: Principles and Applications to Speech and Video","author":"Jayant N. S.","year":"1984"},{"key":"rf7","first-page":"1565","author":"Jerri A. B.","journal-title":"Proc. IEEE"},{"key":"rf8","first-page":"69","volume":"315","author":"Mallat S.","journal-title":"Trans. Amer. Math. Soc."},{"key":"rf9","volume-title":"Ondelettes et Op\u00e9rateurs I: Ondelettes","author":"Meyer Y.","year":"1990"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1201\/9781420049985"}],"container-title":["International Journal of Wavelets, Multiresolution and Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219691303000098","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:30:21Z","timestamp":1565181021000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219691303000098"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,6]]},"references-count":9,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,1,5]]},"published-print":{"date-parts":[[2003,6]]}},"alternative-id":["10.1142\/S0219691303000098"],"URL":"https:\/\/doi.org\/10.1142\/s0219691303000098","relation":{},"ISSN":["0219-6913","1793-690X"],"issn-type":[{"value":"0219-6913","type":"print"},{"value":"1793-690X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,6]]}}}