Abstract
In this paper, we consider the deformed Stockwell transform. Knowing the fact that the study of the time-frequency analysis are both theoretically interesting and practically useful, we investigated several problems for this subject on the setting of the deformed Stockwell transform. Firstly, we study the boundedness and compactness of localization operators associated with the deformed Stockwell transforms on R. Next, we present typical examples of localization operators. Finally, the scalogram for the deformed Stockwell transform are introduced and studied at the end.