ON THE ASYMPTOTIC CONVERGENCE OF B-SPLINE WAVELETS TO GABOR FUNCTIONS

被引：191

作者：

UNSER, M

ALDROUBI, A

EDEN, M

机构：

[1] Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bethesda, MD 20892, Building 13

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 1992年 / 38卷 / 02期

关键词：

WAVELET TRANSFORM; GABOR TRANSFORM; UNCERTAINTY PRINCIPLE; POLYNOMIAL SPLINE; BETA-SPLINES; TIME-FREQUENCY LOCALIZATION;

D O I：

10.1109/18.119742

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A family of nonorthogonal polynomial spline wavelet transforms is considered. These transforms are fully reversible and can be implemented efficiently. The corresponding wavelet functions have a compact support. It is proven that these B-spline wavelets converge to Gabor functions (modulated Gaussian) pointwise and in all L(p)-norms with 1 less-than-or-equal-to p < + infinity as the order of the spline (n) tends to infinity. In fact, the approximation error for the cubic B-spline wavelet (n = 3) is already less than 3%; this function is also near optimal in terms of its time/frequency localization in the sense that its variance product is within 2% of the limit specified by the uncertainty principle.

引用

页码：864 / 871

页数：8