A new optimized Stockwell transform applied on synthetic and real non-stationary signals

Abstract

International audienceThe aim of this paper is to improve the energy concentration of the Stockwell transform (S-transform) in the time–frequency domain. Amodified S-transform is proposed with several parameters to control the width of ahybrid Gaussian window. Aconstrained optimization problem is proposed based on an energy concentration measure as objective function and inequalities constraints to define the bounds of the Gaussian window. An active-set algorithm is applied to resolve the optimization problem. The optimization of the energy concentration in the time–frequency plane can lead to more reliable applications for non-stationary signals. The simulation results show a significant improvement of the proposed methodology most notably in the presence of noise comparing with the standard S-transform and existing modified S-transform in the literature. Moreover, comparisonwith other knowntime–frequency transforms such as Short-time Fourier transform (STFT) and smoothed-pseudo Wigner–Ville distribution (SPWVD) is also performed and discussed. The proposed S-transform is tested also on real non-stationary signals through an example of split detection in heart sound