The inverse S-transform in filters with time-frequency localization

The S-transform provides a framework for data-adaptive filters which take advantage of time-frequency localized spectra. These filters basically consist in a data transformation to the time-frequency domain, the data-adaptive weighting of the localized spectra, and a back transformation. We illustrate that the inverse S-transform of manipulated spectra not necessarily transforms the localized signals as expected from the imposed weighting. The time localization is not directly translated and spurious signals and noise can be generated. We discuss this problem and suggest a new inverse S-transform, which may be helpful to many applications to take more advantage of the time-frequency localization.