Noisy Signal Decomposition by Multiscale Methods

Abstract

The main goals of this study are to propose new approaches of empirical mode decomposition (EMD) that analyze noisy signals efficiently, and to develop synchrosqueezed wavelet transform (SWT) in relation to the component reconstruction problem. EMD has been widely used to decompose nonlinear and nonstationary signals into some components according intrinsic frequency, called intrinsic mode functions (IMFs). However, the conventional EMD may not be efficient in decomposing signals that are contaminated by non-informative noises or outliers. The computational complexity of EMD algorithm also tends to increase as the size of a signal grows because of the repeating process to construct envelopes. This paper presents two new EMD methods that analyze noisy signals as well as is robust to outliers with holding the merits of the conventional EMD. The key ingredient of the first proposed method is to apply a quantile smoothing method to a noisy signal itself instead of interpolating local extrema of the signal when constructing its mean envelope. The key ingredient of the second proposed method is to extract the local oscillation embedded in a signal by utilizing the second derivative. In ad- dition, since EMD algorithm is not easy to analyze mathematically in respect of the theoretical properties, the studies on wavelet-based synchrosqueezing have been developed. The third proposed method is a reconstruction approach for selecting frequency curves on SWT using cross-validation (CV) scheme. Through simulation studies and the real data analysis, it is demonstrated that the proposed methods produce substantially effective results.