Orthogonal analysis and accurate reconstruction method of one-dimensional signal

Abstract

The invention discloses an orthogonal analysis and accurate reconstruction method of a one-dimensional signal. The orthogonal analysis and accurate reconstruction method comprises the following steps: carrying out empirical mode decomposition on an original signal x to obtain M corresponding intrinsic mode functions, carrying out standardization on the intrinsic mode functions, arranging to obtain one matrix in a column vector form, and establishing the optimization problem P of the matrix; setting an orthogonal matrix and a diagonal matrix obtained by singular value decomposition as follows, and solving an optimal solution of the optimization problem P, i.e., obtaining accurate orthonormal approximation U; finding the optimal projection of the signal x in a vector space which is formed by expansion of U; and reconstructing the signal x. By use of the orthogonal analysis and accurate reconstruction method, an optimized method is used for solving the accurate orthonormal approximation of the intrinsic mode function, an approximate vector can be efficiently obtained in real time, meanwhile, the approximate vector can retain the property of an original intrinsic mode function to a maximum extent, the optimal projection from the original signal to the approximate vector is obtained, and therefore, the approximate vector can be guaranteed to have a low reconstruction error so as to guarantee the accurate reconstruction of the one-dimensional signal.

Description

technical field [0001] The invention belongs to the field of one-dimensional signal processing, in particular to a one-dimensional signal orthogonal analysis and accurate reconstruction method. Background technique [0002] If a one-dimensional signal is reconstructed through a part of the intrinsic mode function, there are still some components in the reconstructed signal that leak into the removed intrinsic mode function, such as the intrinsic mode obtained by the empirical mode decomposition in the Hilbert-Huang transform. The mode function has the problem of incomplete orthogonality, which will lead to serious energy leakage. Therefore, it is very meaningful to orthogonalize the intrinsic mode function obtained by empirical mode decomposition. [0003] Currently, Tian-li Huang, Wei-xin Ren and Meng-lin Lou proposed to use the Gram-Schmidt orthogonalization method to solve this problem in "The orthogonal Hilbert-Huang transform and its application in earthquake motion rec...

AI Technical Summary

Problems solved by technology

[0005] Aiming at the problem of incomplete orthogonality of the inherent mode functions obtained by the experimental mode decomposition in the prior art, the present invention proposes a one-dimensional signal orthogonal analysis and accurate reconstruction method, and obtains the intrinsic mode functions through the method of singular value decomposition Exact Orthogonal Approximation of State Functions

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