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1.
从尺度因子 M =4的正交小波基出发 ,利用折叠方法得到了 L 2 [0 ,1 ]空间的正交小波基 .这种小波不同于折叠前的小波基 ,它是完全限制在有限区间 [0 ,1 ]上 ,且保持小波基的正交性 ,并在使用过程中拥有更大的灵活性 .也可用类似方法对一般尺度小波进行折叠  相似文献   

2.
给出一类具有广义插值的正交多尺度函数的构造方法, 并给出对应多小波的显示构造公式. 证明了该文构造的多小波拥有与多尺度函数相同的广义基插值性.从而建立了多小波子空间上的采样定理. 最后基于该文提供的算法构造出若干具有广义基插值的正交多尺度函数和多小波.  相似文献   

3.
本文研究了一元α尺度紧支撑、双正交多小波的构造.在区间[-1,1],给出了利用α尺度双正交尺度向量构造α尺度双正交多小波的推导过程得到了一种有效的小波构造算法,并给出了数值算例.  相似文献   

4.
1 引言 在小波的构造和应用中,对于2尺度单一小波已有相当成熟的理论,特别是在小波构造方面,若知道正交单一尺度函数,相应的单一小波是很容易构造出的。对于a尺度紧支撑多小波,如何从已知的a尺度紧支撑多重尺度函数构造出相应的多小波,到目前为止尚没有一般的构造方法。W.Lanton等用仿酉矩阵扩充的方法构造出相应的多小  相似文献   

5.
a尺度正交多尺度函数和正交多小波   总被引:4,自引:0,他引:4       下载免费PDF全文
基于a 尺度正交单尺度函数,分别给出重数为2和3的a 尺度正交多尺度函数的构造算法。并给出对应正交多小波的显式构造。最后给出伸缩因子为3的正交多小波的构造算例。  相似文献   

6.
a尺度正交的多小波   总被引:2,自引:0,他引:2  
给出一种构造 a尺度正交多小波的方法 .它是由任意 a尺度正交的单小波及一组滤波器构造出来的 .由于 a尺度单正交尺度函数选取的任意性和滤波器的选取有相当大的自由度 ,使得有可能构造出大量 a尺度正交的多小波 .  相似文献   

7.
α尺度紧支撑正交多小波的构造   总被引:10,自引:0,他引:10  
1.引 言 自从Geronimo,Hardin和Massopust[1]使用分形插值函数构造出 GHM-多小波以来,对多小波的研究己引起很多人的关注(see[2]~[5]).出于多通道滤波理论的需要及欲获得比2尺度小波有更大灵活性的小波,a尺度多小波理论被引入.我们知道,2尺度单一小波己相当成熟,特别是在小波的构造方面,己由I.Daubechies[6]得到非常完美的公式:  相似文献   

8.
给出一种由a尺度紧支撑正交多尺度函数构造短支撑正交多小波的方法,其过程仅仅应用矩阵的正交扩充和求解方程组。如果r重尺度函数的支撑区间较大,可以将其转化为ar重短支撑情形,从而使得本文的方法适用于任意紧支撑正交多小波的构造,文后给出多小波的构造算例。  相似文献   

9.
本文研究了一元a尺度紧支撑、双正交多小波的构造.在区间[-1,1],给出了利用a尺度双正交尺度向量构造a尺度双正交多小波的推导过程得到了一种有效的小波构造算法,并给出了数值算例.  相似文献   

10.
L~2([0,1])的半正交小波基及其对偶小波基   总被引:1,自引:0,他引:1  
本文从样条函数出发利用折叠法得到了L2([0,1])空间的两组相互对偶的半正交小波基,这两组小波基有显式表达式,并导出了他们的小波分解与重建算法.进一步,应用这些小波基给出了刻划高阶Holder空间的一个充分条件.  相似文献   

11.
Construction of multivariate compactly supported orthonormal wavelets   总被引:2,自引:0,他引:2  
We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1,. . .,ψn with n>3 such that {2kψj(2kx−ℓ,2kym), k,ℓ,mZ, j=1,. . .,n} is an orthonormal basis for L2(ℝ2). Here, n is dependent on the size of the support of φ. With parallel processes in modern computer, it is possible to use these orthonormal wavelets for applications. Furthermore, the constructive method can be extended to construct compactly supported multi-wavelets for any given compactly supported orthonormal multi-scaling vector. Finally, we mention that the constructions can be generalized to the multivariate setting. Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday Mathematics subject classifications (2000) 42C15, 42C30.  相似文献   

12.
紧支撑正交对称和反对称小波的构造   总被引:10,自引:0,他引:10  
杨守志  杨晓忠 《计算数学》2000,22(3):333-338
1.引言 近年来,人们分别从数学和信号的观点对正交小波进行了广泛的研究.尤其是2尺度小波,它克服了短时 Fourier变换的一些缺陷.目前最常用的 2尺度小波是 Daubechies 小波,但 2尺度小波也存在一些问题:如 Daubechies[2]已证明了除 Haar小波外不存在既正交又对称的紧支撑 2尺度小波.因此人们提出了 a尺度小波理论[3]-[6],文献[4]-[6]对 4尺度小波迸行研究.本文的目的是研究4尺度因子时紧支撑正交对称和反对称小波的构造方法.并指出对同一紧支撑正交对称尺度函数而言,…  相似文献   

13.
This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions. It was shown in [7] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the trivial case; and also shown in [10,18] that there is no compactly supported interpolatory orthonormal dyadic refinable function. Hence, for the dyadic dilation case, compactly supported wavelets generated by interpolatory refinable functions have to be biorthogonal wavelets. The key step to construct the biorthogonal wavelets is to construct a compactly supported dual function for a given interpolatory refinable function. We provide two explicit iterative constructions of such dual functions with desired regularity. When the dilation factors are larger than 3, we provide several examples of compactly supported interpolatory orthonormal symmetric refinable functions from a general method. This leads to several examples of orthogonal symmetric (anti‐symmetric) wavelets generated by interpolatory refinable functions. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

14.
Progressive functions at time t involve only the progressive functions at time before t and some nice compactly supported function at time t. We give sufficient conditions and explicit formulas to construct progressive functions with exponential decay and characterize the conditions on which the positive integer translates of a progressive function are orthonormal or a Riesz sequence. We provide explicit ways for construction of orthonormal progressive functions and for construction of the biorthogonal functions of nonorthogonal progressive functions. Such progressive functions can be used to construct wavelets with arbitrary smoothness on the half line if they are generated by a smooth refinable compactly supported function.  相似文献   

15.
In this paper, we provide a family of compactly supported orthonormal complex wavelets with dilation 4 such that their generating wavelet functions have symmetry and the shortest possible supports with respect to their increasing orders of vanishing moments.  相似文献   

16.
This paper is devoted to the study and construction of compactly supported tight frames of multivariate multi-wavelets. In particular, a necessary condition for their existence is derived to provide some useful guide for constructing such MRA tight frames, by reducing the factorization task of the associated polyphase matrix-valued Laurent polynomial to that of certain scalar-valued non-negative ones. We illustrate our construction method with examples of both multivariate scalar- and vector-valued subdivision schemes. Since our constructions for C1 and C2 piecewise cubic schemes are quite involved, we also include the corresponding Matlab code in the Appendix.  相似文献   

17.
The centers and radii of orthonormal scaling functions and wavelets are found in time and frequency domains using a two-scale relation. All compactly supported orthogonal wavelets with support on the interval [0, 3] fail to have radii in the frequency domain. On the other hand, a Daubechies wavelet with support on the interval [0, 3] has optimal resolution in the frequency domain. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 8 pp. 432–455, October–December, 1995.  相似文献   

18.
Symmetric orthonormal scaling functions and wavelets with dilation factor 4   总被引:8,自引:0,他引:8  
It is well known that in the univariate case, up to an integer shift and possible sign change, there is no dyadic compactly supported symmetric orthonormal scaling function except for the Haar function. In this paper we are concerned with the construction of symmetric orthonormal scaling functions with dilation factor d=4. Several examples of such orthonormal scaling functions are provided in this paper. In particular, two examples of C 1 orthonormal scaling functions, which are symmetric about 0 and 1/6, respectively, are presented. We will then discuss how to construct symmetric wavelets from these scaling functions. We explicitly construct the corresponding orthonormal symmetric wavelets for all the examples given in this paper. This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献   

19.
As in earlier works, we consider {0,1}n as a sample space with a probability measure on it, thus making pseudo-Boolean functions into random variables. Under the assumption that the coordinate random variables are independent, we show it is very easy to give an orthonormal basis for the space of pseudo-Boolean random variables of degree at most k. We use this orthonormal basis to find the transform of a given pseudo-Boolean random variable and to answer various least squares minimization questions.  相似文献   

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