Orthogonal analysis and accurate reconstruction method of one-dimensional signal

An orthogonal analysis and signal technology, applied in the field of one-dimensional signal processing, can solve problems such as incomplete orthogonality of inherent modal functions, and achieve the effect of low reconstruction error and accurate reconstruction.

CN106096236AInactive Publication Date: 2016-11-09GUANGDONG UNIV OF TECH
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Patent Information

Authority / Receiving Office
CN · China
Current Assignee / Owner
Publication Date
2016-11-09
Estimated Expiration
Not applicable · inactive patent

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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.
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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...

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Embodiment Construction

[0019] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

[0020] See figure 1 , a one-dimensional signal orthogonal analysis and accurate reconstruction method of the present invention, comprising steps:

[0021] S1: Perform empirical mode decomposition on the original signal x to obtain the corresponding M intrinsic mode functions, standardize the intrinsic mode functions, and arrange them into a matrix in the form of column vectors

[0022] S2: Establishing an optimization problem P of the matrix;

[0023] S3: set p...