共查询到20条相似文献,搜索用时 3 毫秒
1.
2.
Bin Han 《Applied and Computational Harmonic Analysis》1997,4(4):380-413
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(
) is generalized to then-dimensional case. Two ways of constructing certain dual wavelet tight frames inL2(
n) are suggested. Finally, examples of smooth wavelet tight frames inL2(
) andH2(
) 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(
). 相似文献
3.
Given g∈L2(R n ), we consider irregular wavelet for the form\(\left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j \) > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L2(R n ) are given. For a class of functions g∈L22(R n ) we prove that certain growth conditions on {λ j } will frames, and that some other types of sequences exclude the frame property. We also give a sufficient condition for a Gabor system\(\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} \)to be a frame. 相似文献
4.
Given g { l\fracn2 g( lj x - kb ) }jezjezn ,where lj \left\{ {\lambda ^{\frac{n}{2}} g\left( {\lambda _j x - kb} \right)} \right\}_{j\varepsilon zj\varepsilon z^n } ,where\;\lambda _j > 0 and b > 0. Sufficient conditions for the wavelet system to constitute a frame for L
2(R
n
) are given. For a class of functions g{ ezrib( j,x ) g( x - lk ) }jezn ,kez\left\{ {e^{zrib\left( {j,x} \right)} g\left( {x - \lambda _k } \right)} \right\}_{j\varepsilon z^n ,k\varepsilon z} to be a frame. 相似文献
5.
Gitta Kutyniok 《Constructive Approximation》2007,25(3):239-253
For a large class of irregular wavelet frames we derive a fundamental relationship between the affine density of the set of
indices, the frame bounds, and the admissibility constant of the wavelet. Several implications of this theorem are studied.
For instance, this result reveals one reason why wavelet systems do not display a Nyquist phenomenon analogous to Gabor systems,
a question asked in Daubechies' Ten Lectures book. It also implies that the affine density of the set of indices associated
with a tight wavelet frame has to be uniform. Finally, we show that affine density conditions can even be used to characterize
the existence of wavelet frames, thus serving, in particular, as sufficient conditions. 相似文献
6.
We consider the construction of tight Gabor frames (h, a=1,
b=1) from Gabor systems (g, a=1, b=1) with g a window
having few zeros in the Zak transform domain via the operation
h=Z
-1(Zg/|Zg|), where Z is the standard Zak transform. We
consider this operation with g the Gaussian, the hyperbolic
secant, and for g belonging to a class of positive, even,
unimodal, rapidly decaying windows of which the two-sided
exponential is a typical example. All these windows g have the
property that Zg has a single zero, viz. at
(1/2,\1/2), in the unit square [0,1)2. The Gaussian
and hyperbolic secant yield a frame for any a,b > 0 with ab < 1,
and we show that so does the two-sided exponential. For these
three windows it holds that S
a
-1/2
g
h as a
1,
where S
a
is the frame operator corresponding to the Gabor frame
(g,a,a). It turns out that the hs corresponding to gs of
the above type look and behave quite similarly when scaling
parameters are set appropriately. We give a particular detailed
analysis of the h corresponding to the two-sided exponential. We
give several representations of this h, and we show that
, and is continuous and
differentiable everywhere except at the half-integers, etc., and
we pay particular attention to the cases that the time constant of
the two-sided exponential g tends to
. We also consider
the cases that the time constants of the Gaussian and of the
hyperbolic secant tend to 0 or to
. It so turns out that
h thus obtained changes from the box function
into its Fourier transform
when the time constant changes from 0 to
相似文献
7.
Super-Wavelets and Decomposable Wavelet Frames 总被引:4,自引:0,他引:4
A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. Decomposable
wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient
conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there
exists a Parseval wavelet frame which is m-decomposable for any 1 < m ≤ n, but not k-decomposable for any k > n. Moreover,
there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists
a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m ≤ n, but can not be extended to
any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is
investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given. 相似文献
8.
Ole Christensen Baiqiao Deng Christopher Heil 《Applied and Computational Harmonic Analysis》1999,7(3):292
A Gabor system is a set of time-frequency shifts S(g, Λ) ={e2 π ibxg(x − a)}(a, b) Λ of a function g L2(Rd). We prove that if a finite union of Gabor systems k = 1rS(gk, Λk) forms a frame for L2(Rd) then the lower and upper Beurling densities of Λ = k = 1r Λk satisfy D−(Λ) ≥ 1 and D + (Λ) < ∞. This extends recent work of Ramanathan and Steger. Additionally, we prove the conjecture that no collection k = 1r{gk(x − a)}a Γk of pure translates can form a frame for L2(Rd). 相似文献
9.
Lili Zang 《Numerical Functional Analysis & Optimization》2013,34(9):1090-1101
One of the fundamental problems in the study of wavelet frames is to find conditions on the wavelet function and the dilation and translation parameters so that the corresponding wavelet system forms a frame. In this article, we obtain some inequalities for a discrete wavelet system to be a frame. Our result improves known ones by Chui, Shi, and Chen. 相似文献
10.
In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic. 相似文献
11.
12.
13.
S. Albeverio S. Evdokimov M. Skopina 《Journal of Fourier Analysis and Applications》2010,16(5):693-714
We study p-adic multiresolution analyses (MRAs). A complete characterization of test functions generating an MRA (scaling functions)
is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling
functions generate the Haar MRA. We also suggest a method for constructing sets of wavelet functions and prove that any set
of wavelet functions generates a p-adic wavelet frame. 相似文献
14.
矩阵频域乘子是由本质有界可测函数组成的矩阵,它能将多重小波紧框架映射成多重小波紧框架.引入二元多重小波紧框架的矩阵频域乘子的概念,给出了一个矩阵值函数成为二元多重小波紧框架的矩阵乘子的充要条件,并给出了构造例子. 相似文献
15.
本文首先给出了希尔伯特空间H上两个半小波框架序列成为小波框架的一个充分条件,该结论与框架的扰动理论有关.然后建立了通过膨胀与平移母函数生成L~2(R)上的小波框架的膨胀参数,平移参数以及母函数的一些充分条件.这些结果推广了小波框架理论中经典文献中的相关结论.我们还对贝塞尔序列进行了讨论,并得到了一些有趣的结论. 相似文献
16.
该文研究对应于3带尺度函数的小波紧框架,这个小波紧框架是由V_1中的l个函数ψ^1, ψ^2, ψ^n 构成.给出这l个函数构成小波紧框架的充分条件.由此给出由3 带尺度函数构造出一个小波紧框架的显式公式.特别的,如果给定尺度函数的符号是有理函数,则可以构造出符号为有理函数的小波紧框架.最后还给出类似于小波的小波紧框架的分解与重构算法. 相似文献
17.
Uwe Kähler 《PAMM》2006,6(1):633-634
In this paper we will construct frames for the continuous spherical wavelet transform. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
David G. Glynn 《Designs, Codes and Cryptography》2004,31(1):43-50
We solve some problems concerning the orthogonality of geometric codes associated with sets of i- and j-dimensional subspaces of PG(n, q). Various applications are found, and we discuss all the interesting cases in small dimensional spaces. 相似文献
19.
Zhijing Zhao 《Numerical Functional Analysis & Optimization》2013,34(11-12):1394-1407
Finding verifiable conditions for wavelet systems to be wavelet frames is among the core problems in wavelet analysis. In this paper, we give some simple and sufficient conditions that ensure a multidimensional irregular wavelet system to be a frame or a weighted frame. Quantitative results are provided, and explicit frame bounds are given. 相似文献
20.
研究了L2(R)中小波框架{ψj,k}j,k={sjψ(sj·-kb)}j,k∈Z的膨胀列{sj}j的性质.如果{ψj,k}j,k是L2(R)的一个小波框架,那么膨胀列是无界的,在某些条件下{sj}j∈Z一定能够被重排为指标集Z上的一个非减数列,而且存在常数λ,μ∈(0,1)和p∈Z ,使得对j∈Z有λ相似文献