Signal Optimal Smoothing Techniques

Producing high- and low-resolution smoothers by means of Spectral Analysis

TB in support of chapter "Signal Optimal Smoothing by Means of Spectral Analysis" in "Advances in Statistical Methodologies and their Application to Real Problems", Tsukasa Hakimoto ed., INTECH, April 2017, DOI: 10.5772/66150. This chapter introduces two new empirical methods for obtaining optimal smoothing of noise‐ridden stationary and nonstationary, linear and nonlinear signals. Both methods utilize an application of the spectral representation theorem (SRT) for signal decomposition that exploits the dynamic properties of optimal control. The methods respectively produce a low‐resolution and a high‐resolution smoothing filter, which may be utilized for optimal long‐ and short‐run tracking as well as forecasting devices. Monte Carlo simulation applied to three broad classes of signals enables comparing the dual SRT methods with a similarly optimized version of the well‐known and reputed empirical Hilbert‐Huang transform (HHT).