The Characteristics of a Type of Biorthogonal Wavelet Packets with Eight-scale Factor in Higher Dimensions

2010 ◽  
Author(s):  
Shuyun Song ◽  
Ailian Huo
Keyword(s):  
Higher Dimensions ◽  
Scale Factor ◽  
Wavelet Packets ◽  
Biorthogonal Wavelet

The Biorthogonality Property of the Multidimensional Wavelet Packets with Multi-Scale Factor

2010 ◽  
Vol 439-440 ◽  
pp. 1093-1098
Author(s):  
Jian Feng Zhou ◽  
Ping An Wang
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
Higher Dimensions ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Analysis Method ◽  
Time Frequency ◽  
Multi Scale ◽  
Vector Valued

In this article, we introduce a sort of vector-valued wavelet packets with multi-scale dilation of space , which are generalizations of multivariaale wavelet packets. A method for designing a sort of biorthogonal vector-valued wavelet packets in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three biorthogonality formulas regarding these wavelet packets are established. Furtherore, it is shown how to obtain new Riesz bases of space from these wavelet packets.

The Nice Characters of Biorthogonal Four-Element Wavelet Packets with Two-Scale

2011 ◽  
Vol 460-461 ◽  
pp. 351-356
Author(s):  
Yu Li ◽  
Jin Shun Feng
Keyword(s):  
Iteration Method ◽  
Wavelet Packets ◽  
Constructive Method ◽  
Biorthogonal Wavelet ◽  
New Approach ◽  
Novel Approach ◽  
Affine Frames

In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets, which is the generalization of orthogonal univariate wavelet packets, is introduced. A new approach for constructing them is presented by iteration method. A novel approach for constructing two-directional biorthogonal wavelet packets is developed. The biorthogonality property of four-dimensional wavelet packets is discussed. Three biorthogonality formulas concerning these wavelet packets are estabished. A constructive method for affine frames of is proposed.

On the Instability of Arbitrary Biorthogonal Wavelet Packets

1993 ◽  
Vol 24 (5) ◽  
pp. 1340-1354 ◽  
Author(s):  
A. Cohen ◽  
I. Daubechies
Keyword(s):  
Wavelet Packets ◽  
Biorthogonal Wavelet

The properties of orthogonal matrix-valued wavelet packets in higher dimensions

2006 ◽  
Vol 22 (3) ◽  
pp. 41-53 ◽  
Author(s):  
Qing-jiang Chen ◽  
Jin-shun Feng ◽  
Zheng-xing Cheng
Keyword(s):  
Higher Dimensions ◽  
Orthogonal Matrix ◽  
Wavelet Packets

SCALE FACTOR DUALITY WITH MATTER

2011 ◽  
Vol 26 (15) ◽  
pp. 1137-1145 ◽  
Author(s):  
SUNGGEUN LEE
Keyword(s):  
Equation Of State ◽  
Extra Dimensions ◽  
Higher Dimensions ◽  
Scale Factor ◽  
Scalar Tensor Theory ◽  
Duality Transformation ◽  
Four Dimensions ◽  
Tensor Theory ◽  
Six Dimensions

We investigate the scale factor duality of the scalar–tensor theory in four and ten dimensions with matter. It is shown that when the pressure of the matter vanishes (γ = 0 for the equation of state p = γρ), the action is invariant under the duality. In addition, the action is invariant again under the change of the sign of the pressure (p→-p or γ→-γ). In higher dimensions, we distinguish the matter, e.g., in four dimensions px = γxρ and for extra six dimensions py = γy ρ. The scale factor duality in this case is that when γx = 0 the duality transformation acts on the four-dimensional scale factor and the dilaton with the extra dimensions intact while when γy = 0 it acts on the extra six dimensions and the dilaton with four dimensions intact.

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