Adaptive directional extraction transform for analyzing mixtures of harmonic-like and impulsive-like signals

Many real-world signals are composed of both harmonic-like and impulsive-like components. Accurately characterizing such mixed signals poses a challenge for the conventional time–frequency (TF) analysis methods due to the limitations of the Heisenberg uncertainty principle and current post-processing techniques. In this paper, a novel TF analysis approach called the adaptive directional extracting transform (ADET), is developed. We begin with a theoretical analysis to define an instantaneous frequency (IF) equation for a time-varying model and a group delay (GD) equation for a frequency-varying model within the short-time Fourier transform framework. We then propose to adaptively extract the fixed points of the solutions of these two equations, guided by a novel discrimination criterion. This criterion uses the TF information at the solutions to determine which fixed points to select. Numerical simulations and real-life applications demonstrate that our proposed approach achieves high concentration in both time and frequency while maintaining strong resistance to noise in addressing noisy mixed signals.