Adaptive Dolph–Chebyshev window-based S transform in time-frequency analysis

The S transform is widely used in time-frequency analysis (TFA). However, the standard S transform suffers from the poor energy concentration in time-frequency distribution (TFD). In this study, an adaptive Dolph-Chebyshev window instead of the Gaussian window-based S transform and its fast realisation strategy are introduced for non-stationary signal TFA. By controlling the shape of the Dolph-Chebyshev window adaptively to signal, the new TFA method is able to achieve a high energy concentration in TFD. In addition, the new method is superior to other classical methods for instantaneous frequency estimation. Several examples are presented to illustrate its behaviour on different signals and demonstrate its validity.