Discrete Inverse $S$ Transform With Least Square Error in Time-Frequency Filters

The S transform is useful in time-frequency analysis. Many inverse S transform algorithms have been proposed with different filtering properties in the time-frequency spectrum. In this paper, the transformation matrices of the S transform and two novel least square inverse algorithms are proposed. The first one minimizes the global mean square error of the entire time-frequency spectrum, and the second one considers only the specific interesting time-frequency regions and is more flexible. The proposed inverse algorithms can provide more stable and better performance than the existing ones.