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ON BANDLIMITED scaling function

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Journal of Computational Mathematics 2002年第4期20卷 373-380页

作者： Wei Chen Qiao Yang Wei-jun Jiang Si-long Peng Insitute of Mathematics Academy of Mathematics and System SciencesChinese Academy of SciencesBeijing 100080China Department of Mathematics Institute of Water Conservancy and Hydroelectric PowerZhengzhou 450045China Nadec Institute of AutomationChinese Academy of SciencesBeijing 100080China

This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At th... 详细信息

关键词： scaling function oversampling property weakly translation invariance aliasing error

Four-band compactly supported orthogonal symmetric interpolating scaling function

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Progress in Natural Science:Materials International 2001年第4期11卷 63-70页

作者：水鹏朗保铮 China Key Laboratory for Radar Signal Processing Xi an 710071 Xidian University

An efficient method is proposed to design 4-band scaling functions with the following five advantages : compact support, orthogonality, symmetry, regularity, and interpolation; and a family of such scaling functions w... 详细信息

关键词： sampling theorem scaling function interpolation symmetry.

The Study on scaling function of L^2(R^s)

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Chinese Quarterly Journal of Mathematics 2007年第4期22卷 567-573页

作者： HUANG Yong-dong LI Hua WU Guo-chang Department of Mathematics North University for Nationalities Yinchuan 750021 China Department of Mathematics and Computer Xinyang Vocational and Technical College Xinyang 464000 China School of Sciences Xi＇an Jiaotong University Xi＇an 710049 China

In this paper, using the orthonormal multiresolution analysis（MRA） of L^2（R^s）, we get two important properties of the scaling function with dilation matrix A = MI of L^2 （R^s）. These properties axe chaxacterize... 详细信息

关键词： multiresolution analysis compact support scaling function Fouries transform.

Notes on the scaling function

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Chinese Quarterly Journal of Mathematics 2004年第2期19卷 188-191页

作者： WUHua-an ZHANGGui-zhen CollegeofScience WuhanUniversityofTechnologyWuhan430063China DepartmentofBasicCourses HenanJudicialPoliceVocationalCollegeLuohe473000China

Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.

关键词： multiresolution analysis scaling function Fourier transform

On a Class of Finitely Supported scaling functions with Properties of Interpolation and Symmetry

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Acta Mathematica Sinica,English Series 2001年第2期17卷 333-338页

作者： Ze Yin ZHANG Center for Mathematical Sciences. Zhejiang University. Hangzhou 310027. P. R. China Center for Mathematical Sciences Zhejiang University Hangzhou 310027 P. R. China

In this paper, a class of finitely supported orthogonal filters with interpolation and sym metry is constructed.

关键词： Filter scaling function

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M带含参数对称正交插值尺度函数的构造

高等学校计算数学学报 2010年第2期32卷 173-178页

作者：杨守志刘华伟汕头大学数学系

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... 详细信息

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

关键词： scaling function symmetry orthogonality interpolation

PARAMETERIZATION OF SYMMETRIC scaling functionS

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Applied Mathematics(A Journal of Chinese Universities) 2004年第1期19卷 77-80页

作者： ZhangZeyin ZhejiangUniv. Hangzhou310027Chinazeyinz@***

In this paper,the factorization for filters with length Km of scaling functions into simple blocks is considered.

关键词： scaling function filter bank wavelet,polyphase representation.

Characterization of Compact Support of Fourier Transform for Orthonormal Wavelets of L^2(R^d)

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Acta Mathematica Sinica,English Series 2005年第4期21卷 855-864页

作者： Zhi Hua ZHANG (Zhihua ZHANG) Department of Mathematics,University of California,Davis,California.95616,USA Department of Mathematics University of California Davis California 95616 USA

Let{ψμ} be an orthonormal wavelet of L^2（R^d） and the support of a whole of its Fourier transform be Uμsupp{ψμ}=Пi=1^d[Ai, Di]-Пi=1^d（Bi, Ci）, Ai≤Bi≤Ci≤Di. Under the weakest condition that each │ψμ│,... 详细信息

关键词： Orthonormal wavelets Multiresolution analysis scaling function Compact support

function projective synchronization in partially linear drive-response chaotic systems

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Chinese Physics B 2010年第12期19卷 120-125页

作者：张荣徐振源 School of Science Jiangnan University

This paper gives the definition of function projective synchronization with less conservative demand for a scaling function, and investigates the function projective synchronization in partially linear drive-response chaotic systems. Based on the Lyapunov stability theory, it has been shown that the function projective synchronization with desired scaling function can be realized by simple control law. Moreover it does not need scaling function to be differentiable, bounded and non-vanished. The numerical simulations are provided to verify the theoretical result.

关键词： function projective synchronization projective synchronization scaling function partially linear system