To varying degrees, all experimental measurements are corrupted by real-world noise sources including electronic noise in the acquisition system, far-field perturbations in the surrounding environment, and local physical phenomena. This paper presents a grid-based nonlinear analysis technique for causally coupled systems which leverages the availability of a high-fidelity reference signal to effectively denoise a target measurement signal. The foundation of this approach, essentially an ensemble-averaging procedure in multidimensional phase space, is strongly motivated by work from dynamical systems theory. Furthermore, a straightforward extension of this technique allows for recovery of a time-resolved representation from the underresolved measurement signal. Both the nonlinear noise reduction and this temporal deconvolution extension are applied to signals from three different coupled dynamic systems (sine wave system, Lorenz system, and Hall-effect thruster) to demonstrate effectiveness on periodic, chaotic, and experimental systems.

所有实验测量都在不同程度上受到现实世界噪声源的破坏，这些噪声源包括采集系统中的电子噪声，周围环境中的远场扰动以及局部物理现象。本文介绍了一种基于网格的因果耦合系统非线性分析技术，该技术利用了高保真参考信号的可用性来有效地对目标测量信号进行降噪。这种方法的基础（本质上是多维相空间中的整体平均过程）是由动力系统理论的工作大力推动的。此外，该技术的直接扩展允许从欠解析的测量信号中恢复时间解析的表示。