Elimination of the discretization side-effect in the S transform using folded windows

The S transform, which is one of the time-frequency transforms, has been shown to be useful in time frequency analysis and many signal processing applications. The discrete counterpart of the S transform (DST) can be implemented in both the time and the frequency domains, i.e., the Time DST and the Freq DST. However, previous studies found that the conventional Time DST and the conventional Freq DST are not consistent, which may result in unreliable time-frequency information. In this paper, a new DST that adopts the folded window is proposed to eliminate the side effects of discretizing. The consistence of the time and the frequency versions is an important property of the continuous S transform and the proposed DST inherits this property. The proposed folded window can also be applied to the DST whose window is not a Gaussian function and the short-time Fourier transform.

Research Highlights
► The discrete S transform (DST) with the folded window is proposed.
► Both Gaussian and non-Gaussian windows can be converted into the folded form.
► With the folded window, the Time DST and the Freq DST can be consistent.
► The folded window can also be applied for the short time Fourier transform.