A statistical frequency-chirprate extractor for mode retrieval with crossover instantaneous frequencies

Abstract

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 representation 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 synchroextracting 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.