An optimization synchrosqueezed fractional wavelet transform for TFF analysis and its applications

To enhance the resolution of synchrosqueezing transform (SST) in non-stationary signal representation, an optimization synchrosqueezed fractional wavelet transform (SSFRWT) is proposed, which possesses rigorous mathematical principle and high resolution. First, the definition, properties, and principles of SSFRWT are presented. On this basis, a time-fractional-frequency (TFF) analysis method is established utilizing SSFRWT. The experimental results demonstrate that SSFRWT is capable of establishing a high-resolution TFF representation for chirp-type signals, surpassing existing methods in terms of noise robustness and energy concentration. Lastly, leveraging the signal TFF representation, SSFRWT is successfully applied to the chirp signal parameter estimation and multi-component signal separation, yielding superior estimation results and reconstructed signal compared to SST. Notably, SSFRWT is also innovatively employed in the field of optical measurement, achieving high-precision measurement of the curvature radius of convex lens.