Least-Squares Signal Synthesis from Modified S-Transform

The S-transform (ST) is a linear time-frequency representation containing characteristics from the short-time Fourier transform and the wavelet transform with a frequency-dependent localizing window. As other linear time-frequency representations, one of the main applications of the ST is time-frequency filtering, which necessitates devising efficient methods for signal reconstruction from modified representations. In this paper, an algorithm for least-squares synthesis from modified ST is presented, requiring the same computational complexity as the forward transform. Additionally, for the same purpose, another faster and more flexible method is developed by means of which the signal is reconstructed by using only part of the modified representation whose size is similar to that of the original signal and contains almost no redundant information.