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

Abstract

The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> transform is useful in time-frequency analysis. Many inverse <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> transform algorithms have been proposed with different filtering properties in the time-frequency spectrum. In this paper, the transformation matrices of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> 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.