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Determinism Test, Noise Estimate and Hidden E'requency Recognition: The Singular Value Decomposition Approach
並列摘要
Given a scalar time series, the trajectory matrix of a system can be constructed by the Takens' delay-coordinate map theorem. We employ the method of singular value decomposition (SVD) to derive the eigenvalue spectrum of the trajectory matrix. It is shown that when the embedding dimension of the trajectory matrix is very large, the SVD eigenvalue spectrum could be utilized to test the determinism and estimate the strength of noise in time series. On the other hand, we show that the dynamically connected frequency components hidden in chaotic time series can be detected by the SVD method. Finally, three kinds of circuit experiments are presented as demonstrations.
並列關鍵字
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