A Novel Scaling Criterion for Optimal Trade-off Between Time and Frequency Resolution in S-transform

Abstract

S-transform (ST) maps a one-dimensional time domain signal into a two-dimensional time-frequency distribution (TFD). ST uses a scalable Gaussian window for multiresolution analysis. The major drawback of conventional ST is its poor frequency resolution for mid and high frequency voices. This is primarily due to linear scaling in frequency domain. To improve the scaling criterion, various schemes have been proposed in literature such as modified linear scaling, power scaling and sigmoid scaling. The existing criteria are unable to provide fair trade-off between time and frequency resolution for all voices. To this extent, a novel scaling criterion is proposed which can provide proportional window width variation in time and frequency domain. The proposed scaling criterion uses a tangent function to scale the width of the Gaussian window in both time and frequency domain. The performance of proposed scaling approach is examined using a synthetic signal having multiple power quality disturbances. The simulation results indicate the superiority of the proposed scaling approach in terms of the trade-off between time and frequency resolution in TFD.