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

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.