A Characterization of Stockwell Spectra

Signals in real applications are typically finite in duration, dynamic and non-stationary processes with frequency characteristics varying over time. This often requires techniques capable of locally analyzing and processing signals. An integral transform known as the Stockwell transform is a combination of the classic Gabor transform and the current and versatile wavelet transform. It allows more accurate detection of subtle changes and easy interpretation in the time-frequency domain. In this paper, we study the mathematical underpinnings of the Stockwell transform. We look at the Stockwell transform as a stack of simple pseudo-differential operators parameterized by frequencies and give a complete description of the Stockwell spectra.