Zoom synchrosqueezing transform and iterative demodulation: Methods with application

Synchrosqueezing is a powerful time-frequency analysis tool for signals with time-varying frequency. However, as it is based on the continuous wavelet transform, its time-frequency representation (TFR) has better time but worse frequency resolution in higher frequency region, while worse time but better frequency resolution in lower frequency region. It makes the synchrosqueezing difficult to accurately estimate IFs with highly oscillating rate but small fluctuation amplitude. To address this issue, a zoom synchrosqueezing transform (ZST) is proposed to generate both excellent time and frequency resolution in a specific frequency region and analyze the mono-component signal in the particular frequency region to obtain accurate IF estimation results. For multi-component signals with nonlinear and close IFs, a ZST based dual iterative demodulation method is proposed, with the inner iteration to gradually refine and accurately extract a concerned mono-component, and the outer iteration to extract all mono-components gradually to alleviate the interference between individual components. Then satisfactory energy concentrated TFRs and accurate IF estimation results of mono-components can be obtained by the proposed ZST. The TFR of the multi-component signal can be gained by superposing the TFRs of all mono-components. The effectiveness of the proposed methods was validated using both simulated signals and a rub-impact signal collected from an engineering machine unit.