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 transfor...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.展开更多
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...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 chaxacterized by some inequalities and equalities.展开更多
The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vec...The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.展开更多
The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavel...The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.展开更多
In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar...In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.展开更多
文摘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.
基金Supported by the Natural Science Foundation of Ningxia Province(NZ0691)
文摘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 chaxacterized by some inequalities and equalities.
基金the Science Research Foundation of Education Department of ShaanxiProvince (08JK340)the Items of Xi’an University of Architecture and Technology(RC0701JC0718)
文摘The notion of vector-valued multiresolution analysis is introduced and the concept of orthogonal vector-valued wavelets with 3-scale is proposed. A necessary and sufficient condition on the existence of orthogonal vector-valued wavelets is given by means of paraunitary vector filter bank theory. An algorithm for constructing a class of compactly supported orthogonal vector-valued wavelets is presented. Their characteristics is discussed by virtue of operator theory, time-frequency method. Moreover, it is shown how to design various orthonormal bases of space L^2（R, C^n） from these wavelet packets.
基金Supported by Natural Science Foundation of Henan Province（0511013500）
文摘The notion of a sort of biorthogonal multiple vector-valued bivariate wavelet packets,which are associated with a quantity dilation matrix,is introduced.The biorthogonality property of the multiple vector-valued wavelet packets in higher dimensions is studied by means of Fourier transform and integral transform biorthogonality formulas concerning these wavelet packets are obtained.
基金Foundation item： Supported by the Natural Science Foundation of China（10571113）
文摘In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.
