A Method to Enhance Noise Reduction for Data Generated from a Known Differential Equation

Abstract

In this paper we propose a method to enhance noise reduction for data generated from a known differential equation. We develop a theoretical basis for the procedure and then illustrate it in the case of some data generated using Duffing's equation. This method consists of embedding the data in higher dimensions and then transforming the data into a lower dimension using a singular matrix. We show that the singular matrix squeezes out some of the noise and leaves the true signal intact. Finally, using a nonlinear function, we reverse the effect of the singular matrix to get closer to the original data.