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The Characteristics Concerning a Class of Orthogonal Multivariate Matrix-Valued Scaling Functions and Frame Packets

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Abstract:

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. In this work, the notion of matrix-valued multiresolution analysis of space is introduced. A method for constructing orthogonal matrix-valued ternary wavelet packs is developed and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are provided. Finally, new orthonormal wavelet pack bases of space are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

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Periodical:

Applied Mechanics and Materials (Volumes 321-324)

Pages:

1317-1320

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.321-324.1317

Citation:

Cite this paper

Online since:

June 2013

Authors:

Hong Yun Liu, Jie Li

Keywords:

Filter Functions, Frame Packets, Iteration Approach, Matrix-Valued Scaling Function, Matrix-Valued Wavelet Transform, Multivariate

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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