二维周期基数插值小波尺度函数

设f（x）是一个Fourier系数为正的周期函数，我们构造了关f（x）的二维周期基数插值小波的尺度函数，并得到了一些对构造小波函数有重要意义的性质．     

一类周期紧小波框架的构造

从L2(Rd)上构造紧小波框架的一般方法(即延拓原理)出发,利用函数的周期化过程,给出了L2([0,1]d)上一类紧小波框架的构造方法.     

一类带限的插值小波

Ｓｈａｎｎｏｎ尺度函数具有带限性质，正交性质、取样性质，但它不在Ｌ（Ｒ）中，本文引入小波，它的尺度函数不仅具有上述性质而且在Ｌ（Ｒ）中，甚至更多。     

Morlet小波在确定局部周期中的应用

本文通过引入改进的Morlet小波变换核函数,得到了等幅值的Morlet小波变换(MMWT)和功率谱(MMPS).理论及实验均表明,MMPS不但能够准确的确定信号的局部周期,而且使相同振幅(强度)的谐波产生了相同大小的MMPS,弥补了MPS的不足.对于MMWT还给出了相应的Morlet小波变换尺度与频率转化公式.     

一类二元半正交小波包的构造

本文给出伸缩矩阵行列式为2的一类二元半正交小波包的构造算法.该小波包是以频域给出的,随着用于小波包分裂的滤波器选取的不同会得到L2(R2)中形态各异的Riesz基,这样使得L2(R2)中小波基的选择更灵活.     

一类尺度函数与小波的构造

利用卷积的定义及性质,构造出了一类尺度函数与小波,并通过算例加以说明.     

一类向量值正交小波的设计与性质

引入整数因子伸缩的向量值正交小波与向量值小波包的概念.运用仿酉向量滤波器理论和矩阵理论,给出具有整数因子伸缩的向量值正交小波存在的充要条件.提供了紧支撑向量值正交的构建算法,给出了相应的构建算例.利用时频分析方法与算子理论,刻画了一类向量值正交小波包的性质,得到了整数伸缩的向量值小波包的正交公式.     

周期多尺度分析的特征及它的一个应用

在这篇文章里，我们研究了周期多尺度分析的性质，给出了尺度函数序列的一个特征．这个特征能够使我们从一个尺度函数序列得到另一个尺度函数序列．最后，我们给出了主要结果的一个应用．     

Meyer型正交小波基的构造与性质

本文基于多分辨分析理论与A．W．W方法将Meyer正交小波的构造规范化,给出其设计方法,并证明此类Meyer型小波母函数ψ（x)及相应的尺度函数ψ(x)具有优良的性质,如速降性O（│x│^-N-1(│x│→∞）、N阶消失矩、线性相位、对称性、频谱有限性、并且双尺度序列（滤波器）hn=ψ（n/2）等,并给出N＝2时构造小波函的具体实例。     

多维周期双正交向量小波的构造

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     

Local Properties of Cardinal Interpolatory Function

In [1], a kind of periodic cardinal interpolatory function (PCIF) is constructed, and they also use it to construct periodic wavelets. But the localization of PCIF is not known yet. In this paper, we study the local property of PCIF using two different methods. The results show that PCIF has very good localization. Some new properties of Bernoulli spline are also introduced. The first author is supported partially by NFSC Grant The second author supported by LAPC Grant. Current address: Nadec, Institute of Automation, Academia Sinica, Beijing, 100080, China     

Characterization of periodic multiresolution analysis and an application

In this paper, we study the properties of periodic multiresolution analysis, and present a complete characterization of the scaling function sequence, which enables us to construct a new scaling function sequence from a given one. An application of the main results is given at the end.     

Periodic Prolate Spheroidal Wavelets

Prolate spheroidal wavelets (PS wavelets) were recently introduced by the authors. They were based on the first prolate spheroidal wave function (PSWF) and had many desirable properties lacking in other wavelets. In particular, the subspaces belonging to the associated multiresolution analysis (MRA) were shown to be closed under differentiation and translation. In this paper, we introduce periodic prolate spheroidal wavelets. These periodic wavelets are shown to possess properties inherited from PS wavelets such as differentiation and translation. They have the potential for applications in modeling periodic phenomena as an alternative to the usual periodic wavelets as well as the Fourier basis.     

局部谱性质与摄动

It is shown that local spectral properties such as the single-valued extension property, Dunford's property(C), Bishop's property(β), the decomposition property(δ), or decomposability are stable under commuting perturbations whose spectra are finite.     

L~2[0,1]上的正交小波基

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     

Construction of Periodic Prolate Spheroidal Wavelets Using Interpolation

Periodic prolate spheroidal wavelets (periodic PS wavelets), based on the periodizaton of the first prolate spheroidal wave function (PSWF), were recently introduced by the authors. Because of localization and other properties, these periodic PS wavelets could serve as an alternative to Fourier series for applications in modeling periodic signals. In this paper, we continue our work with periodic PS wavelets and direct our attention to their construction via interpolation. We show that they have a representation in terms of interpolation with the modified Dirichlet kernel. We then derive a group of formulas of interpolation type based on this representation. These formulas enable one to obtain a simple procedure for the calculation of the periodic PS wavelets and finding expansion coefficients. In particular, they are used to compute filter coefficients for the periodic PS wavelets. This is done for a number of concrete cases.     

一致概周期矩阵函数的一些性质

利用纯量概周期函数性质讨论了一致概周期矩阵函数的一些性质.