Iterative SVD Method for Noise Reduction of LowDimensional Chaotic Time Series
Abstract
A new simple method using singular value decomposition (SVD) is presented for reducing noise from a sampled signal where the deterministic signal is from a lowdimensional chaotic dynamical system. The technique is concerned particularly with improving the reconstruction of the phase portrait. This method is based on time delay embedding theory to form a trajectory matrix. SVD is then used iteratively to distinguish the deterministic signal from the noise. Under certain conditions, the method can be used almost blindly, even in the case of a very noisy signal (e.g. a signal to noise ratio of 6 dB). The algorithm is evaluated for a chaotic signal generated by the Duffing system, to which white noise is added.
 Publication:

Mechanical Systems and Signal Processing
 Pub Date:
 January 1999
 DOI:
 10.1006/mssp.1998.9999
 Bibcode:
 1999MSSP...13..115S