Determinism test, noise estimate and hidden frequency recognition: The singular value decomposition approach

Given a scaler time series, the trajectory matrix of a system can be constr ucted 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 tr ajectory matrix is very large, the SVD eigenvalue spectrum could be utilize d to test the determinism and estimate the strength of noise in time series . On the other hand, we show that the dynamically connected frequency compo nents hidden in chaotic time series can be detected by the SVD method. Fina lly, three kinds of circuit experiments are presented as demonstrations.