A Statistical Frequency-Chirprate Extractor for Mode Retrieval with Crossover Instantaneous Frequencies

It is challenging to analyze oscillatory signals whose instantaneous frequencies (IFs) are crossover in the time-frequency (TF) domain. Driven by this need, we propose a statistical frequency-chirprate extractor (SFCE) to analyze multi-component non-stationary signals whose IF lines intersect each other at the TF plane. In this paper, an effective sliding real-valued frequency filter is designed to realize the local repre-sentation of the instantaneous attribute value in the linear chirplet transform (LCT) inner product space. On this basis, we obtain SFCE by extracting the fixed-point condition of the statistical frequency-chirprate estimator from the time-frequency-chirprate (TFC) domain. Finally, the TFC information is extracted to the estimated IF and chirprate (CR) trajectories by SFCE, thus providing a novel three-dimension syn-chroextracting chirplet transform (TDSECT), which obtains high precision model retrieval for crossover signals. In addition, we provide a relatively rigorous theoretical analysis of SFCE for multi-component non-stationary signals. Simultaneously error analysis is given. Numerical experiments on two synthetic signals are employed to verify the successfulness of the proposed method.& COPY; 2023 Elsevier B.V. All rights reserved.