On the range of Stockwell transforms

The structure of the range of Stockwell transforms for a signal from L2(R)L2(R) is obtained using the Vasilevski scheme. The paper completes the full picture of structural results for the four commonly used transforms of signal analysis: continuous wavelet transform, short-time Fourier transform, continuous shearlet transform and the Stockwell transform. Applications of this new characterization are discussed in connection with time–frequency signal localization.