Making Synchrosqueezing Locally Adaptive in The Time-Frequency Plane

In this work, we explore the problem of making synchrosqueezing transform adaptive. To deal with multicomponent signals, existing methods use a fixed order N, thus assuming all the modes making up the signal have order N polynomial phases. To go beyond this limitation, we introduce a new criterion based on the concentration of the representation to locally choose the best order for the synchrosqueezing transform. We study the performance of the proposed approach in terms of the error with respect to the ideal time-frequency representation, both on synthetic and real signals.