Efficient Discrete S-Transform Based on Optimally Concentrated Window

Abstract

S-transform (ST) is a well-known tool for time–frequency analysis. However, the long taper of the Gaussian window (GW) and the scaling criterion lead to poor time resolution at lower frequencies and poor frequency resolution at higher frequencies. This letter proposes a novel optimally concentrated discrete window (OCDW) based on a constraint optimization problem of maximization of the product of time- and frequency-domain energy concentrations in given time and frequency intervals. Furthermore, it is extended to design an OCDW-based ST for multiresolution analysis. A new scaling criterion is also presented for the OCDW-based ST, which prevents unnecessary deterioration in frequency resolution at higher frequencies and time resolution at lower frequencies. The efficacy of the proposed approach is examined using a synthetic signal having multiple power quality disturbances. Simulation results show that the proposed OCDW-based ST provides higher energy concentration in time–frequency distribution (TFD) than that of the GW-based ST. The simulation results also illustrate the superiority of the proposed scaling criterion in terms of the tradeoff between time and frequency resolution in TFD.