Authors: Qing Jiang Chen, Yu Ying Wang

Abstract: Wavelet analysis has become a popular subject in scientific research during the past twenty years. In this work, we introduce the notion of vector-valued multiresolution analysis and vector-valued multivariate wavelet packets associated with an integer-valued dilation matrix. A novel method for constructing multi-dimen-
-sional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are established. Orthogonality decomposition relation formulas of the space are derived by constructing a series of subspaces of wavelet packets. Finally, one new orthonormal wavelet packet bases of are constructed from these wavelet packets.

896

Authors: Jin Cang Han, Yang Li

Abstract: The notion of matrix-valued multiresolution analysis. A procedure for designing orthogonal matrix-valued univariate wavelet packets is presented and their orthogonality properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal basis of are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.

1147

Authors: Jian Tang Zhao, Jie Li

Abstract: In this paper, the notion of orthogonal vector-valued bivariate wavelet packets, which is a generalization of uni-wavelet packets, is introduced. A procedure for constructing them is presented. Their characteristics is investigated by using time-frequency analysis method, matrix theory and finite group theory. Orthogonality formulas are established. Orthonormal wavelet packet bases are obtained.

1184

Abstract: In this article, the notion of orthogonal nonseparable four-dimensional wavelet packets which is the generalizaion of orthogonal univariate wavelet packets is introduced. A new approach for constructing them is presented by iteration method. The orthogonality properties of five-dimensional wavelet packets are discussed. Three orthogonality formulas concerning these wavelet packets are estabished.

1377

Authors: Can Yang Hu, Qing Jun Chen, Qing Yang Xu

Abstract: Simulation of nonstationary processes has become an indispensable tool in study and prevention of natural disasters. A new method of simulation of nonstationary random processes is presented based on the orthogonal HHT spectra of sample observations and random phase. It takes advantage of orthogonal EMD, the instantaneous frequency, amplitude of the Hilbert transform and independent random phase angle, thus overcoming difficulties in the estimation of the frequency modulation and interdependence of frequency and amplitude modulation functions faced by most currently available methods. The new method extracts and preserves the true physical features of the process. The examples of earthquake ground motion and subway vibration, as low frequency and high frequency nonstationary process respectively, were simulated in the paper. The time history of sample, Fourier amplitude spectrum of sample, arithmetic average of sample, variance of sample, Wavelet time-frequency distribution of sample amd autocorrelation coefficient of sample compare well with those of the records. Scattering extent of the peaks of the sample processes is also analyzed in the paper. We can conclude that the method has great potential for engineering applications when dealing with nonstationary, nonlinear random peocesses exist in natural disasters, such as earthquake wave, vibration wave , wind wave and ocean wave.

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