Synchrosqueezed X-Ray Wavelet-Chirplet Transform for Accurate Chirp Rate Estimation and Retrieval of Modes from Multicomponent Signals with Crossover Instantaneous Frequencies

Recent advances in the chirplet transform and wavelet-chirplet transform (WCT) have enabled the estimation of instantaneous frequencies (IFs) and chirprates, as well as mode retrieval from multicomponent signals with crossover IF curves. However, chirprate estimation via these approaches remains less accurate than IF estimation, primarily due to the slow decay of the chirplet transform or WCT along the chirprate direction. To address this, the synchrosqueezed chirplet transform (SCT) and multiple SCT methods were proposed, achieving moderate improvements in IF and chirprate estimation accuracy. Nevertheless, a novel approach is still needed to enhance the transform's decay along the chirprate direction. This paper introduces an X-ray transform-based wavelet-chirprate transform, termed the X-ray wavelet-chirplet transform (XWCT), which exhibits superior decay along the chirprate direction compared to the WCT. Furthermore, third-order synchrosqueezed variants of the WCT and XWCT are developed to yield sharp time-frequency-chirprate representations of signals. Experimental results demonstrate that the XWCT achieves significantly faster decay along the chirprate axis, while the third-order synchrosqueezed XWCT enables accurate IF and chirprate estimation, as well as mode retrieval, without requiring multiple synchrosqueezing operations.