On the Instantaneous Phase and Frequency Estimation of a Non-Stationary Multicomponent Signal. The JADE Algorithm

TL;DR

This paper introduces the JADE algorithm, a new method for accurately estimating instantaneous frequency, phase, and amplitude of non-stationary mono-component signals, demonstrating robustness to noise.

Contribution

The paper presents the JADE method, combining Dynamic Time Warping with FIF, as a stable alternative for analyzing non-stationary signals.

Findings

JADE is robust to noise in frequency estimation.

Compared to classical methods, JADE captures quick frequency changes more effectively.

JADE improves stability in non-stationary signal analysis.

Abstract

Many real-life signals, such as gravitational wave measurements, biomedical signals, or geophysical data, are strongly non-stationary but can be decomposed into mono-component signals that contain only one active frequency over time. This is made possible thanks to decomposition methods developed in recent years that can handle non-stationary signals. The problem now is how to compute, in an accurate and stable way, the instantaneous frequency, phase, and amplitude of such mono-component signals. Numerous approaches have been developed so far, but they can be unstable in the presence of noise and struggle to capture quick and intrawave changes in frequency. In this work, we present an alternative approach, called the JADE method, which is based on the Dynamic Time Warping algorithm and which we combine with the FIF algorithm to handle and study multicomponent non-stationary signals. We test the robustness of JADE to noise and run comparisons with classical methods used for instantaneous frequency, phase, and amplitude estimation.