Robust S-transform based on L-DFT

Introduction: Time-frequency representations (TFRs) indicate variations of the signal spectral characteristics with time, and they are the natural choice as an analysis tool for the non-stationary signals [1]. The main objectives of the various types of time-frequency distribution functions (e.g. Wigner-Ville distribution (WVD) [1], short-time Fourier transform (STFT) [1], the S-transform [2]) are to obtain time-varying spectral density function with higher resolution, and to overcome any existing interferences [1]. In this Letter, we address the performance of the S-transform for signals contaminated with a–stable noise (e.g. [3]). Previous contributions only addressed the performance of traditional TFRs (e.g. the WVD and STFT in [4]), while the S-transform is a hybrid of shorttime Fourier analysis and wavelet analysis. It employs variable window length producing higher frequency resolution at lower frequencies and sharper time localisation for higher frequencies. This property of the S-transform makes it particularly suitable for analysis of signals with hyperbolic or sinusoidally modulated components. In addition, the phase information provided by the S-transform is referenced to the time origin, and therefore provides supplementary information about spectra which is not available from locally referenced phase information obtained by the continuous wavelet transform [2]. For this reason, the S-transform has already been applied in many fields (e.g. [5]). Nevertheless, the S-transform exhibits very poor performance for signals contaminated with a–stable noise (i.e. impulse noise). To resolve this issue we propose an algorithm for the robust S-transform based on the L-DFT. The results of the numerical analysis show that the proposed scheme achieves significantly enhanced performance.