Controlled-coverage discrete S-transform (CC-DST): Theory and applications

The S-transform (ST) is a popular linear time-frequency (TF) transform with hybrid characteristics from the short-time Fourier transform (STFT) and the wavelet transform. It enables a multi-resolution TF analysis and returns globally referenced local phase information, but its expensive computational requirements often overshadow its other desirable features. In this paper, we develop a fully discrete ST (DST) with a controllable TF sampling scheme based on a filter-bank interpretation. The presented DST splits the analyzed signal into subband channels whose bandwidths increase progressively in a fully controllable manner, providing a frequency resolution that can be varied and made as high as required, which is a desirable property for processing oscillatory signals lacked by previously presented DSTs. Thanks to its flexible sampling scheme, the behavior of the developed transform in the TF domain can be adjusted easily; with specific parameter settings, for example, it samples the TF domain dyadically, while by choosing different settings, it may act as a STFT. The spectral partitioning is performed through asymmetric raised-cosine windows whose collective amplitude is unitary over the signal spectrum to ensure that the transform is easily and exactly invertible. The proposed DST retains all the appealing properties of the original ST, representing a local image of the Fourier transform; it requires low computational complexity and returns a modest number of TF coefficients. To confirm its effectiveness, the developed transform is utilized for different applications using real-world and synthetic signals.