Accession Number : ADA301762

Title :   Wavelet Analysis and Its Applications.

Descriptive Note : Final rept. 1 Apr 93-30 Nov 94,

Corporate Author : TEXAS A AND M UNIV COLLEGE STATION DEPT OF MATHEMATICS

Personal Author(s) : Chui, Charles K.

PDF Url : ADA301762

Report Date : 24 JAN 1995

Pagination or Media Count : 5

Abstract : Time-frequency localization is one of the most essential features of the wavelet transform. It was shown that while high order Daubechies and Battle-Lemarie wavelets give poor time-frequency localizations, the Chui-Wang spline-wavelets provide asymptotically optimal time- frequency windows. On the other hand, we also showed that by using the scale 3 instead of 2, symmetry can be achieved by orthonormal wavelets with compact support. Multivariate wavelets, particularly those with matrix dilation, were studied, and the theory of oversampling frames was extended to this setting. Interpolating wavelets have distributional duals that lead to the notion of functional wavelet transform. Other extensions required a study of the stability issue and algorithmic construction in multivariate splines. Applications to systems theory lead to the study of Hankel approximation and localization of neural networks.

Descriptors :   *TRANSFORMATIONS(MATHEMATICS), MATHEMATICAL MODELS, ALGORITHMS, LINEAR SYSTEMS, NEURAL NETS, OPTIMIZATION, TIME DEPENDENCE, MULTIVARIATE ANALYSIS, MATRICES(MATHEMATICS), APPROXIMATION(MATHEMATICS), INTERPOLATION, SPECIAL FUNCTIONS(MATHEMATICS), SPLINES(GEOMETRY).

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE