Reassigning and synchrosqueezing the Stockwell Transform: Complementary proofs
Dominique Fourer, François Auger, Jiabin Hu · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
The S-transform is an efficient tool for time-frequency analysis that gained interest in many signal processingapplication fields. This is due to its ability to produce an analysis with a frequency dependent resolution, as for the wavelettransform, while keeping a direct relation with the Short-Time Fourier Transform (STFT). In this paper, the S-transform is firstbriefly recalled with its properties and its relationships with the STFT and the Continuous Wavelet Transform (CWT). Then, wepropose to enhance the S-transform using the reassignment and the synchrosqueezing methods, which have been already successfullyapplied to the STFT and the CWT. Thanks to these methods, we provide a “sharpen” time-frequency representation from theS-transform while allowing a signal reconstruction thanks to the synchrosqueezing method. The Levenberg-Marquardt algorithmis also used to provide reassignment and synchrosqueezing operators for the S-transform that allow a user to adjust thestrength of the resulting time-frequency distribution. We also derive for the S-transform a second-order synchrosqueezingoperator that improves the time-frequency localization of the synchrosqueezed S-transform by considering signals with frequency-modulatedcomponents. Finally, numerical results obtained with the reassigned and synchrosqueezed S-transforms are comparedwith the Gabor STFT and the Morlet CWT.