共查询到19条相似文献,搜索用时 107 毫秒
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<正>1引言基于多分辨分析方法,已经构造了大量各种各样的单小波,如紧支撑的正交的Daubechies小波,紧支撑半正交的样条小波等.Daubechies证明了除Haar小波外不存在紧支撑正交对称的2带单小波.为了弥补2带单小波的不足,许多数学工作者将它进行推广得到了:双正交小波、多小波、多带小波等几大分支.而在实际应用中有时需要处理一些具有相对窄的带宽的高频信号,所以很有必要研究多带小波.同时多带小波能同时拥 相似文献
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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
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[0,1]区间上的r重正交多小波基 总被引:6,自引:1,他引:6
本文利用L2(R)上的紧支撑正交的多尺度函数和多小波构造出有限区间[0,1]上的正交多尺度函数及相应的正交多小波.本文构造的逼近空间Vj[0,1]与相应的小波子空间Wj[0,1]具有维数相同的特点,从而给它的应用带来巨大方便.最后给出重数为2时的[0,1]区间上的正交多小波基构造算例. 相似文献
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《数学的实践与认识》2015,(21)
框架理论在信号处理和图像处理等工程领域具有重要的作用.具有不规则平移的复合伸缩小波框架被构造.特别地,对称的小波框架被得到.这推广了存在的结果到不规则平移的情形. 相似文献
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研究了L2(Rd)的有限生成仿射子空间中小波标架的构造.证明了任意有限生成仿射子空间都容许一个具有有限多个生成元的Parseval小波标架,并且得到了仿射子空间是约化子空间的一个充分条件.对其傅里叶变换是一个特征函数的单个函数生成的仿射子空间,得到了与小波标架构造相关的投影算子在傅里叶域上的明确表达式,同时也给出了一些例子. 相似文献
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Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces
This is a continuation of the investigation into the theory of wavelet frames for general affine subspaces. The main focus of this paper is on the structural properties of affine subspaces. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces, while every reducing subspace (with respect to the dilation and translation operators) is the orthogonal direct sum of two purely non-reducing ones. This result is obtained through considering the basic question as to when the orthogonal complement of an affine subspace in another one is still affine. Motivated by the fundamental question as to whether every affine subspace is singly-generated, and by a recent result that every singly generated purely non-reducing subspace admits a singly generated wavelet frame, we prove that every affine subspace can be decomposed into the direct sum of a singly generated affine subspace and some space of “small size”. As a consequence we establish a connection between the above mentioned two questions. 相似文献
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Lawrence W. Baggett Nadia S. Larsen Kathy D. Merrill Judith A. Packer Iain Raeburn 《Journal of Fourier Analysis and Applications》2009,15(5):616-633
Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space ℋ that fail to be multiresolution
analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed
scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space ℋ is L
2(ℝ
n
), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition, which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity
function m. 相似文献
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For the construction of multiwavelets, there are no unified, explicit formulas as that in the scalar case available so far. In this paper, by studying the relationship between length 3 and length 4 filter sequences of orthogonal multiwavelets based on the result of Chui for the construction of length 3 orthogonal multiwavelets, a set of explicit formulas is given for the construction of length 4 high-pass filter sequence. Examples demonstrate that our proposed approach not only provides explicit formulas for the construction of length 4 high-pass filter sequence with multiplicity r, but also yields a set of new low-pass and high-pass filter sequences with length 3 and multiplicity 2r. 相似文献
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紧支撑正交插值的多小波和多尺度函数 总被引:10,自引:0,他引:10
本文给出一类伸缩因子为α的紧支撑正交插值多尺度函数和多小波的构造方法.设{Vj}是尺度函数Φ(x)=[φ1(x),φ2(x),…,φa(x)]T生成的多分辨分析,Vj(?)L2(R)是{a-j/2φ(?)(ajx-k),k∈Z,(?)=1,2,…,a)线性扩张构成的子空间,其插值性是指φ1(x),φ2(x),…,φa(x)满足φj(k+(?)/a)=δk,0δj,e,j,(?)∈{1,2,…,a).当Φ(x)是正交插值的,则多分辨分析的分解或重构系数能用采样点表示而不需要用计算内积的方法产生.基于此,我们建立多小波采样定理,即如果一个连续信号f(x)∈VN,则f(x)=∑i=0a-1∑k∈Zf(k/aN+i/aN+1)φi+1(aNx-k),并给出对应多小波的显式构造公式.更进一步,证明了本文构造的多小波也有插值性.最后,还给出一个构造算例. 相似文献
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In this paper, we introduce and study vector-valued multiresolution analysis with multiplicity r (VMRA) and m-band orthogonal vector-valued multiwavelets which have potential to form a convenient tool for analyzing vector-valued signals. Necessary conditions for orthonormality of vector-valued multiwavelets are presented in terms of filter banks. The existence of m-band vector-valued orthonormal multiwavelets is proved by means of bi-infinite matrix. The relationship between vector-valued multiwavelets and traditional multiwavelets are considered, and it is found that multiwavelets can be derived from row vector of vector-valued multiwavelets. The construction of vector-valued multiwavelets from several scalar-valued wavelets is proposed. Furthermore, we show how to construct vector-valued multiwavelets by using paraunitary multifilter bank, in particular, we give formulations of highpass filters when its corresponding lowpass filters satisfy certain conditions and m=2. An example is provided to illustrate this algorithm. At last, we present fast vector-valued multiwavelets transform in form of bi-infinite vector. 相似文献
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This paper focuses on the density of the minimal subspaces generated by a class of discrete linear Hamiltonian systems. It is shown that the minimal subspace is densely defined if and only if the maximal subspace is an operator; that is, it is single valued. In addition, it is shown that, if the interval on which the systems are defined is bounded from below or above, then the minimal subspace is non-densely defined in any non-trivial case. 相似文献
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It is shown that a weakly closed subspace S of a nest algebraA is closed under conjugation by invertible elements in A, thatis, a1Sa=S if and only if S is a Lie ideal. A similarresult holds for not-necessarily-closed subspaces of algebrasof infinite multiplicity. An explicit characterisation of weaklyclosed Lie ideals in a nest algebra is given. 相似文献
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Sobolev圆盘代数的不变子空间 总被引:1,自引:1,他引:0
研究了Sobolev圆盘代数R(D)上乘自变量算子M_z的不变子空间,给出了M_z在任何不变子空间上限制的基本性质,证明了M_z分别限制在两个不变子空间上酉等价当且仅当这两个不变子空间相等,并描述了M_z的一类公共零点在边界的不变子空间的结构. 相似文献