caa a22 4500 463247000 CHVBK 20180405153328.0 cr unu---uuuuu 170326e20071001xx s 000 0 eng 10.1007/s00041-006-6080-3 doi (NATIONALLICENCE)springer-10.1007/s00041-006-6080-3 Johnson Brody Dylan Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, USA aut Stable Filtering Schemes with Rational Dilations [Elektronische Daten] [Brody Dylan Johnson] The relationship between multiresolution analysis and filtering schemes is a well known facet of wavelet theory. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. This work seeks to establish a means for the construction of stable filtering schemes with rational dilations through the theory of shift-invariant spaces. In particular, principal shift-invariant spaces will be shown to offer frame wavelet decompositions for rational dilations even when the associated scaling function is not refinable. Moreover, it will be shown that such decompositions give rise to stable filtering schemes with finitely supported filters, reminiscent of those studied by Kovacevic and Vetterli. Birkhauser Boston, 2007 Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 607-621 1069-5869 13:5<607 2007 13 41 https://doi.org/10.1007/s00041-006-6080-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6080-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Johnson Brody Dylan Department of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, USA aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/5(2007-10-01), 607-621 1069-5869 13:5<607 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer