Characterisation of wave front sets by the Stockwell transform

We characterise the wave front sets via the Stockwell transform defined as a combination of the short-time Fourier transformation and a special class of rotations. The main results of the first part are necessary and sufficient criteria related to the directional smoothness of a tempered distribution in the cases when the space dimension n equals 1, 2, 4 or 8. In the second part, we extend the results to arbitrary n is an element of Z(+). (C) 2020 Elsevier Inc. All rights reserved.