Noise Corruption of Empirical Mode Decomposition and Its Effect on Instantaneous Frequency

TL;DR

This paper investigates how noise affects Empirical Mode Decomposition (EMD), revealing that noise-induced modes impair accurate instantaneous frequency estimation, and analyzes the underlying mechanisms through theoretical and synthetic data analysis.

Contribution

It identifies the cause of poor IF estimation in noisy EMD, detailing the extraction of mixed modes and the influence of spectral leak and phase, advancing understanding of EMD's noise sensitivity.

Findings

Noise causes extraction of modes containing both signal and noise.

Spectral leak and phase influence mode extraction in noisy EMD.

Analysis on synthetic seismic data demonstrates the impact of noise on EMD performance.

Abstract

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.