首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到18条相似文献,搜索用时 62 毫秒
1.
研究多尺度多重向量值双正交小波的构建算法与性质.运用向量细分格式、矩阵理论和多重向量值多分辨分析,证明了与一对给定的多尺度多重向量值双正交尺度函数对应的多尺度多重向量值双正交小波函数的存在性.提出了紧支撑多尺度多重向量值双正交小波的构造算法.讨论了多尺度多重向量值小波包的性质,得到了多重向量值小波包的双正交公式与向量值小波包基.  相似文献   

2.
a尺度多重正交小波包   总被引:27,自引:1,他引:26  
本文给出了a尺度多重正交小波包的构造方法,它是通过对a尺度多重正交小波向量等长截取为a-1个子向量之后得到的,对同一多重正交小波而言,采用本方法可以构造多种不同的正交小波包,从而使多重正交小波包不仅具有传统的小波包的特点,而且在应用中具有较强的灵活性。  相似文献   

3.
α尺度紧支撑双正交多小波   总被引:7,自引:0,他引:7  
本文给出一种由双正交多尺度函数构造双正交多小波的方法,其构造方法如构造双正交单一小波那样容易。最后给出双正交多小波的构造算例。  相似文献   

4.
1引言 小波分析是二十世纪八十年代中期发展起来的一个数学分枝,其应用涉及自然科学与工程技术的许多领域[1-3].向量值小波从属多小波理论范畴.文献[4]引入向量值小波的概念,讨论了多重向量值双正交小波的存在性及其构造.Bacchelli等[5]证明了多重向量值双正交小波的存在性.文献[6]运用多重向量值双正交小波变换研究海洋涡流现象.  相似文献   

5.
本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质.利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基.  相似文献   

6.
向量值正交小波包   总被引:6,自引:0,他引:6  
引进对应于2尺度向量值尺度函数的多分辨分析和向量值小波的概念.给出向量值小波包的定义及其构造算法,研究了向量值正交小波包的正交性,并讨论了空间L2(R,CN)的正交分解.  相似文献   

7.
一对拟双正交框架小波   总被引:1,自引:0,他引:1  
张之华 《数学学报》2008,51(1):81-90
对于一对对偶框架多尺度分析,借助于滤波器,我们构造一对对偶框架小波和一对拟双正交框架小波,并且指出一对对偶框架小波和一对拟双正交框架小波的滤波器所满足的充分必要条件.  相似文献   

8.
二元多重双正交小波包的性质   总被引:3,自引:0,他引:3  
陈清江等:二元多重双正交小波包的性质 第1期 1引言 小波包川由于拥有优良的特性而受到人们的关注.它己被应用在信号处理{“】,图像 压缩【“】,编码理论【41等工程方面.我们知道,由护(功中的函数生成的正交小波基具有 较差的频率局部化性能,为了克服这一缺陷,Coifman,Me  相似文献   

9.
多维周期双正交向量小波的构造   总被引:1,自引:0,他引:1  
本文研究了多维周期双正交向量小波的构造.通过使用矩阵分解,给出具有矩阵伸缩的周期双正交向量小波构造的一种算法.  相似文献   

10.
双正交多重小波的一种构造方法   总被引:2,自引:0,他引:2  
朱春喜  徐长发 《应用数学》1999,12(4):121-125
多重小波是近年来新兴的小波研究方向,它具有许多一维小波所不具备的优越性质.完全正交的多重小波在构造上有很大的难度,所以在许多应用中人们都可以用双正交多重小波作为分析的工具  相似文献   

11.
In this article, compactly supported totally interpolating biorthogonal multiwavelet systems are studied. Necessary and sufficient conditions for such systems to have given approximation orders are stated in simple equations. It is shown that the shorter nontrivial filter component that has the minimum possible length for a given approximation order is uniquely determined up to a discrete parameter. Among systems with such property, we provide all totally interpolating biorthogonal stable multiwavelet systems of approximation orders 2 and 3 with minimal total length whose scaling vectors have minimal lengths as well.  相似文献   

12.
In this paper, we introduce biorthogonal multiple vector-valued wavelets which are wavelets for vector fields. We proved that, like in the scalar and multiwavelet case, the existence of a pair of biorthogonal multiple vector-valued scaling functions guarantees the existence of a pair of biorthogonal multiple vector-valued wavelet functions. Finally, we investigate the construction of a class of compactly supported biorthogonal multiple vector-valued wavelets.  相似文献   

13.
研究由三元双正交插值尺度函数构造对应的双正交小波滤波器的矩阵扩充问题.当给定的一对三元双正交尺度函数中有一个为插值函数时,利用提升思想与矩阵多相分解方法,给出一类三元双正交小波滤波器的显示构造公式和一个计算实例.讨论了三元双正交小波包的的性质.  相似文献   

14.
In this paper we characterize all totally interpolating biorthogonal finite impulse response (FIR) multifilter banks of multiplicity two, and provide a design framework for corresponding compactly supported multiwavelet systems with high approximation order. In these systems, each component of the analysis and synthesis portions possesses the interpolating property. The design framework is based on scalar filter banks, and examples with approximation order two and three are provided. We show that our multiwavelet systems preserve almost all of the desirable properties of the generalized interpolating scalar wavelet systems, including the dyadic-rational nature of the filter coefficients, equality of the flatness degree of the low-pass filters and the approximation order of the corresponding functions, and equality between the uniform samples of a signal and its projection coefficients for a given scale. This last property allows us to avoid the cumbersome prefiltering associated with standard multiwavelet systems. We also show that there are no symmetric totally interpolating biorthogonal multifilter banks of multiplicity two. Finally, we point out that our design framework incorporates a simple relationship between the multiscaling functions and multiwavelets that substantially simplifies the implementation of the system.  相似文献   

15.
In this article, we introduce vector-valued multiresolution analysis and the biorthogonal vector-valued wavelets with four-scale. The existence of a class of biorthogonal vector-valued wavelets with compact support associated with a pair of biorthogonal vector-valued scaling functions with compact support is discussed. A method for designing a class of biorthogonal compactly supported vector-valued wavelets with four-scale is proposed by virtue of multiresolution analysis and matrix theory. The biorthogonality properties concerning vector-valued wavelet packets are characterized with the aid of time–frequency analysis method and operator theory. Three biorthogonality formulas regarding them are presented.  相似文献   

16.
In this paper, we introduce a class of vector-valued wavelet packets of space L2(R2,Cκ), which are generalizations of multivariate wavelet packets. A procedure for constructing a class of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality properties are characterized by virtue of matrix theory, time–frequency analysis method, and operator theory. Three biorthogonality formulas regarding these wavelet packets are derived. Moreover, it is shown how to gain new Riesz bases of space L2(R2,Cκ) from these wavelet packets. Relation to some physical theories such as the Higgs field is also discussed.  相似文献   

17.
The orthonormal basis generated by a wavelet ofL 2(ℝ) has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis ofL 2(ℝ d ) is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases ofL 2(ℝ d ) from the multiwavelet packets.  相似文献   

18.
A note on biorthogonal ensembles   总被引:1,自引:0,他引:1  
We study multiple orthogonal polynomials in the context of biorthogonal ensembles of random matrices. In these ensembles, the eigenvalue probability density function factorizes into a product of two determinants while the eigenvalue correlation functions can be written as a determinant of a kernel function. We show that the kernel is itself an average of a single ratio of characteristic polynomials. In the same vein, we prove that the type I multiple polynomials can be expressed as an average of the inverse of a characteristic polynomial. We finally introduce a new biorthogonal matrix ensemble, namely the chiral unitary perturbed by a source term, whose multiple polynomials are related to the modified Bessel function of the first kind.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号