Adaptive order synchrosqueezing transform

Abstract

Non-stationary signals are characterized by time-varying amplitudes and frequencies. Tracking them is important for studying the dynamic systems that generate the signals, the synchrosqueezing transform (SST) being a versatile and widely used tool for such a task. In this paper, we address the problem of locally selecting the order for SST, which can be difficult in the presence of strong modulations and noise. We propose to tackle this problem by minimizing the Rényi entropy to maximize the concentration on the time–frequency plane. We do that using coordinate descent, and sparse matrices. Results show superior representations to those obtained with fixed order SST, both in terms of concentration and error with respect to the ideal representation. We illustrate the capabilities of our proposal on real-world signal with strong frequency modulation: bat social vocalization, gibbon song, and voice signal.