On Dual Wavelet Tight Frames
On Dual Wavelet Tight Frames
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DOI：
10.1006/acha.1997.0217
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发表时间：
1997-10
影响因子：
2.5
通讯作者：
B. Han
中科院分区：
文献类型：
--
作者：
B. Han
摘要给出了任意一般伸缩矩阵的多元对偶小波紧框架的一个刻画。作为应用，Lawton关于L2(R)上的小波紧框架的结果被推广到当时维的情形。给出了构造L2(Rn)中某些对偶小波紧框架的两种方法。最后给出了L2(R)和H2(R)中光滑小波紧框架的例子。特别地，给出了一个例子，证明了存在一个函数ψ，它的傅里叶变换是正的，紧支撑的，无穷可微的，它产生了一个非MRA小波紧框架InH2(R)。
Abstract A characterization of multivariate dual wavelet tight frames for any general dilation matrix is presented in this paper. As an application, Lawton's result on wavelet tight frames inL2( R ) is generalized to then-dimensional case. Two ways of constructing certain dual wavelet tight frames inL2( R n) are suggested. Finally, examples of smooth wavelet tight frames inL2( R ) andH2( R ) are provided. In particular, an example is given to demonstrate that there is a function ψ whose Fourier transform is positive, compactly supported, and infinitely differentiable which generates a non-MRA wavelet tight frame inH2( R ).