Biorthogonal Wavelet Packets in $$H^s(\mathbb {K})$$

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Guru P. Singh ◽  
Ashish Pathak
Keyword(s):  
Wavelet Packets ◽  
Biorthogonal Wavelet

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

Constructive Algorithm to Two-Directional Biorthogonal Shortly Supported Wavelets with Poly-Scale Dilation Factor

2010 ◽  
Vol 171-172 ◽  
pp. 113-116
Author(s):  
Yu Min Yu ◽  
Zong Sheng Sheng
Keyword(s):  
Frequency Analysis ◽  
Operator Theory ◽  
Matrix Theory ◽  
New Method ◽  
Wavelet Packets ◽  
Scaling Functions ◽  
Biorthogonal Wavelet ◽  
Time Frequency ◽  
Dilation Factor ◽  
Vector Valued

In this work, the notion of biorthogonal two-directional shortly supported wavelets with poly-scale is developed. A new method for designing two-directional biorthogonal wavelet packets is proposed and their properties is investigated by means of time-frequency analysis methodand, operator theory. The existence of shortly supported biorthogonal vector-valued wavelets associated with a pair of biorthogonal compactly supported vector-valued scaling functions is investigated. A new method for designing a class of biorthogonal shortly supported vector-valued wavelet functions is presented by using multiresolution analysis and matrix theory.

The Description of Two-Direction Biorthogonal Finitely Supported Wavelet Packets with Poly-Scale Dilation

2010 ◽  
Vol 439-440 ◽  
pp. 1171-1176 ◽  
Author(s):  
Shu De Du ◽  
De You Yuan
Keyword(s):  
Wavelet Analysis ◽  
Frequency Analysis ◽  
Operator Theory ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Biorthogonal Wavelet ◽  
Time Frequency ◽  
The Past ◽  
Algebra Theory ◽  
Popular Subject

Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this paper, the notion of biorthogonal two-direction compactly supported wavelet packets with poly-scale is developed. A new method for designing two-direction biorthogonal wavelet packets is proposed and their properties is investigated by algebra theory, means of time-frequency analysis methodand, operator theory. The direct decomposition relationship is provided. Finally, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are derived.

The Research into Biorthogonal Six-Variable Wavelet Packets with Two-Scale and Applications in Material Science

2014 ◽  
Vol 1006-1007 ◽  
pp. 1080-1083
Author(s):  
Shi Heng Wang ◽  
Chun Yi Jiao ◽  
Jian Tang Zhao
Keyword(s):  
Material Science ◽  
Iteration Process ◽  
New Method ◽  
Wavelet Packets ◽  
Riesz Bases ◽  
Constructive Method ◽  
Biorthogonal Wavelet ◽  
Science And Engineering ◽  
Interdisciplinary Field ◽  
Orthogonality Property

Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, the notion of orthogonal nonseparable six-variable wavelet bundles is introduced. A new method for designing them is presented by iteration process. A nice approach for constructing six-variable biorthogonal wavelet bundles is developed. The bi-orthogonality property of six-variable wavelet packets is discussed. Biorthogonality formulas con-cerning these six-variable wavelet packets are obtained. A constructive method for affine frames is presented. Moreover, it is shown how to get new Riesz bases of from the wavelet bundles.

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