Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis

TLDR

The authors propose the matching demodulation transform (MDT), an iterative algorithm that generates a time‑frequency representation with improved energy concentration. MDT iteratively matches the signal’s instantaneous frequency through partial demodulation and stepwise refinement based on an FM model, and a synchrosqueezing variant further sharpens the time‑frequency representation. Compared to conventional TF methods, MDT eliminates the need for ad‑hoc dictionaries, and theoretical analysis demonstrates bounded IF estimation error and convergence, with simulations and real data confirming its validity and practical utility.

Abstract

The authors introduce an iterative algorithm, called matching demodulation transform (MDT), to generate a time-frequency (TF) representation with satisfactory energy concentration. As opposed to conventional TF analysis methods, this algorithm does not have to devise ad-hoc parametric TF dictionary. Assuming the FM law of a signal can be well characterized by a determined mathematical model with reasonable accuracy, the MDT algorithm can adopt a partial demodulation and stepwise refinement strategy for investigating TF properties of the signal. The practical implementation of the MDT involves an iterative procedure that gradually matches the true instantaneous frequency (IF) of the signal. Theoretical analysis of the MDT's performance is provided, including quantitative analysis of the IF estimation error and the convergence condition. Moreover, the MDT-based synchrosqueezing algorithm is described to further enhance the concentration and reduce the diffusion of the curved IF profile in the TF representation of original synchrosqueezing transform. The validity and practical utility of the proposed method are demonstrated by simulated as well as real signal.