The generalized stockwell transform associated with the spherical mean operator and uncertainty principles

Stockwell theory is often seen as an alternative to time-frequency analysis, and it has many roots and becomes an interdisciplinary field combining harmonic analysis, applied mathematics and signal and data processing. In this paper, we will prove several uncertainty principles for the generalized Stockwell transform associated with the spherical mean operator, which set restrictions on the time-frequency behavior of a signal, such as Heisenberg-type, Shannon-type and local uncertainty principles. As a side result, by following the Donoho–Stark criterion, we will derive a sufficient condition by means of which one can recover a signal from the knowledge of a truncated version.