Multisynchrosqueezing transform based on local polynomial Fourier transform

The synchrosqueezing transform (SST) is an effective strategy for finely describing nonstationary signals and offers enhanced precision and reconstructability. However, the existing SST methods are unsuitable for addressing polynomial nonstationary signals. Thus, this study proposed the multisynchrosqueezed local polynomial Fourier transform (MSSLPFT) as a solution to mitigate this limitation. First, a new instantaneous frequency (IF) estimator based on the local polynomial Fourier transform (LPFT) was proposed. Furthermore, the corresponding energy reassignment operator synchrosqueezed local polynomial Fourier transform (SSLPFT) in the time–frequency domain was determined, which transformed into MSSLPFT after multiple iterations. To perfectly explain the practicability of the proposed method, examples of monocomponent and multicomponent signals were demonstrated. Subsequently, the discrete implementation was elucidated and its computational complexity was analyzed. Moreover, various time-varying signal experiments were simulated to validate the theoretical derivations. Finally, the formation of a real inverse synthetic aperture radar (ISAR) image was demonstrated to validate the effectiveness and excellence of the proposed method.