Reassigning and synchrosqueezing the Stockwell Transform: Complementary proofs

Dominique Fourer (1) , François Auger (1) , Jiabin Hu (1)

1 IREENA - Institut de Recherche en Energie Electrique de Nantes Atlantique EA4642

The S-transform is an efficient tool for time-frequency analysis that gained interest in many signal processing application fields. This is due to its ability to produce an analysis with a frequency dependent resolution, as for the wavelet transform, while keeping a direct relation with the Short-Time Fourier Transform (STFT). In this paper, the S-transform is first briefly recalled with its properties and its relationships with the STFT and the Continuous Wavelet Transform (CWT). Then, we propose to enhance the S-transform using the reassignment and the synchrosqueezing methods, which have been already successfully applied to the STFT and the CWT. Thanks to these methods, we provide a “sharpen” time-frequency representation from the S-transform while allowing a signal reconstruction thanks to the synchrosqueezing method. The Levenberg-Marquardt algorithm is also used to provide reassignment and synchrosqueezing operators for the S-transform that allow a user to adjust the strength of the resulting time-frequency distribution. We also derive for the S-transform a second-order synchrosqueezing operator that improves the time-frequency localization of the synchrosqueezed S-transform by considering signals with frequency-modulated components. Finally, numerical results obtained with the reassigned and synchrosqueezed S-transforms are compared with the Gabor STFT and the Morlet CWT.

Mots clés: Time-frequency analysis; Stockwell transform; reassignment; synchrosqueezing

Domaines: Traitement du signal et de l'image [eess.SP]; Mathématiques [math]; Informatique [cs]

Dominique Fourer, François Auger, Jiabin Hu. Reassigning and synchrosqueezing the Stockwell Transform: Complementary proofs. 2015. ⟨hal-01467244⟩