Qualitative Uncertainty Principles for the Nonisotropic Angular Stockwell Transforms

ABSTRACT The nonisotropic angular Stockwell transform (NAST) employs an angular, scalable and localized window function, to effectively capture directional characteristics and nonisotropic features presented in the signal. In this paper, our main contributions are to derive three distinct qualitative uncertainty principles (UPs) for the NAST: the Benedicks–Amrein–Berther UP, the logarithmic Sobolev‐type UP, and the Donoho–Stark UP. These uncertainty principles provide rather valuable insights into the behavior and limitations of the NAST regarding localization and concentration properties.