共查询到19条相似文献,搜索用时 125 毫秒
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研究了当窗函数变化时非均匀Gabor框架的稳定性.对紧支撑Gabor框架,将均匀情况下关于稳定性的结论推广到了非均匀的情况;对一般的Gabor框架,利用W(L^∞,e^1)范数给出了其稳定的一个充分条件. 相似文献
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本文引入了酉系统中的(C,C’)-受控融合框架生成子和(C,C’)-受控K-融合框架生成子的概念,它们都是框架的推广.研究了酉系统中的(C,C’)-受控融合框架生成子和融合框架生成子之间的关系,并给出了(C,C’)-受控K-融合框架生成子的一些刻画.此外,探讨了Hilbert空间H的一个闭子空间成为(C,C’)-受控融合框架生成子以及(C,C’)-受控K-融合框架生成子的条件. 相似文献
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引进了三维紧框架小波的概念,它是由框架多分辨分析中子空间X_1中的若干个三维函数Γ~1(y),Γ~2(y),…,Γ~n(y)构成的.研究了对应于三维尺度函数的三维紧框架小波的存在性.运用时频分析方法、滤波器理论、算子理论,给出这n个三维函数生成小波紧框架的充分条件,得到了由一个尺度函数Ψ(y)构造三维紧框架小波的显式公式. 相似文献
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给出了$m$个函数生成$N$维2带小波紧框架的充分条件和$N$维2带小波紧框架的显式构造算法, 讨论了小波紧框架的分解算法与重构算法. 提出的构造方法很有普遍性, 容易推广到$N(N\geq2)$维$M(M\geq 2)$带小波紧框架的情形,也可以得到类似的小波紧框架的分解算法与重构算法. 相似文献
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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
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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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二元3带小波紧框架的构造 总被引:1,自引:0,他引:1
研究二元3带小波紧框架的结构.首先给出二元3带小波紧框架的充分条件.并给出这种小波紧框架的显式公式.若给定的尺度函数的符号函数是有理函数,则可以构造出符号函数为有理函数的小波紧框架.文中给出了数值例子,还给出了二元3带小波紧框架的分解和重构算法. 相似文献
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《数学的实践与认识》2017,(17)
研究了由酉拓展原理构造的一类多尺度仿射框架包的性质.运用时频分析与泛函分析方法,建立了紧仿射框架包与面具函数的关系式,提出了仿射框架包构成L~2(R)规范紧仿射框架的充分条件,进而,给出多尺度紧仿射框架包子空间对空间L~2(R)的直交分解. 相似文献
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In this paper we give sufficient conditions for irregular Gabor systems to be frames. We show that for a large class of window functions, every relatively uniformly discrete sequence in with sufficiently high density will generate a Gabor frame. Explicit frame bounds are given. We also study the stability of irregular Gabor frames and show that every Gabor frame with arbitrary time-frequency parameters is stable if the window function is nice enough. Explicit stability bounds are given.
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We look at the time–frequency localization of generators of lattice Gabor systems. For a generator of a Riesz basis, this
localization is described by the classical Balian–Low theorem. We establish Balian–Low type theorems for complete and minimal
Gabor systems with a frame-type approximation property. These results describe how the best possible localization of a generator
is limited by the degree of control over the coefficients in approximations given by the system, and provide a continuous
transition between the classical Balian–Low conditions and the corresponding conditions for generators of complete and minimal
systems. Moreover, this holds for the non-symmetric generalizations of these theorems as well. 相似文献
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Finding general and verifiable conditions which imply that Gabor systems are (resp. cannot be) Gabor frames is among the core problems in Gabor analysis. In their paper on atomic decompositions for coorbit spaces [H.G. Feichtinger and K. Gröchenig, Banach spaces related to integrable group representations, and their atomic decomposition, I, J. Funct. Anal. 86 (1989), 307–340], the authors proved that every Gabor system generated with a relatively uniformly discrete and sufficiently dense time-frequency sequence will allow series expansions for a large class of Banach spaces if the window function is nice enough. In particular, such a Gabor system is a frame for the Hilbert space of square integrable functions. However, their proof is based on abstract analysis and does not give direct information on how to determine the density in the sense of directly applicable estimates. It is the goal of this paper to present a constructive version of the proof and to provide quantitative results. Specifically, we give a criterion for the general case and explicit density for some cases. We also study the existence of Gabor frames and show that there is some smooth window function such that the corresponding Gabor system is incomplete for arbitrary time-frequency lattices. 相似文献
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刘有明 《数学物理学报(B辑英文版)》2006,26(3):415-420
A necessary condition is given for general nonuniform Gabor frames, which generalizes Benedetto and Walnut's theorem. A sufficient and necessary condition for a class of nonuniform Gabor frames is proved. 相似文献
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Summary We study the stability of Gabor frames with arbitrary sampling points in the time-frequency plane, in several aspects. We
prove that a Gabor frame generated by a window function in the Segal algebra S0(Rd) remains a frame even if (possibly) all the sampling points undergo an arbitrary perturbation, as long as this is uniformly
small. We give explicit stability bounds when the window function is nice enough, showing that the allowed perturbation depends
only on the lower frame bound of the original family and some qualitative parameters of the window under consideration. For
the perturbation of window functions we show that a Gabor frame generated by any window function with arbitrary sampling points
remains a frame when the window function has a small perturbation in S0(Rd) sense. We also study the stability of dual frames, which is useful in practice but has not found much attention in the literature.
We give some general results on this topic and explain consequences to Gabor frames. 相似文献
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Franz Luef 《Expositiones Mathematicae》2018,36(2):221-227
We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor–Riesz bases and a constant curvature connection on projective modules over noncommutative tori. 相似文献
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V. P. Palamodov 《Journal d'Analyse Mathématique》2003,91(1):247-268
The stability problem is studied for reconstruction of the refraction coefficient from boundary measurements of solutions
of the Helmholtz equation at a fixed time-frequency. An answer is given in terms of Gabor means of the coefficient. A domain
in the phase space is shown where the Gabor means can be stably reconstructed. As a corollary, a rigorous form is given to
the basic theorem of diffraction tomography. 相似文献
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H. Führ 《Advances in Computational Mathematics》2008,29(4):357-373
We derive frame bound estimates for vector-valued Gabor systems with window functions belonging to Schwartz space. The main
result provides estimates for windows composed of Hermite functions. The proof is based on a recently established sampling
theorem for the simply connected Heisenberg group, which is translated to a family of frame bound estimates via a direct integral
decomposition.
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