Nonlinear noise reduction: A case study on experimental data

Abstract

We apply a recently proposed nonlinear noise-reduction method to time sequences from two different experiments. We demonstrate that it is not difficult to choose the parameters of this algorithm, even though we use no other information about the underlying dynamics than the data themselves. The noise reduction is very robust with respect to changes in the choice of parameters. The reliability of the result is tested by an analysis of the corrections. We discuss the effect of noise reduction on estimates of dimensions, entropies, and Liapunov exponents. For comparison we process one of the sets, densely sampled Taylor-Couette flow data, with a global filter based on singular value decomposition.