A noise reduction method using singular value decomposition

A method to reduce noise in experimental data with nonlinear time evolution is presented. The measured digital data are assumed to be a single point scalar measurement taken at the correct sampling rate. The N scalar data will be vectorized by embedding them into a m dimensional space. A singular value decomposition (SVD) technique will then be applied to the N × m matrix. The dynamical system to be investigated are the Lorenz equations. Gaussian random noise is added to the simulated system as measurement error, and the SVD technique is applied to the data. The results are displayed using time histories, phase plane plots and the correlation integral to determine the effects of noise and the noise reduction method.