Modified inverse S transform for filtering in time-frequency spectrum

The S transform is a powerful linear time-frequency representation, and it is especially useful for filter in the time-frequency spectrum. To improve the time resolution of the filter applications, Schimmel and Gallart have proposed a new method for inverse S transform. This new method performs much better than the original in time localization with time-frequency filters. However, there exists some distortion of the inverse transformed signal that it will be enhanced in the positive but suppressed in the negative frequency part. In this paper we will demonstrate the distortion and propose a modified method to derive the correct inverse transformed signal and provide satisfactory time localization in filtering.