Clifford-Valued Stockwell Transform and the Associated Uncertainty Principles

In the framework of higher-dimensional time-frequency anal- ysis, we propose a novel Clifford-valued Stockwell transform for an ef- fective and directional representation of Clifford-valued functions. The proposed transform rectifies the windowed Fourier and wavelet transfor- mations by employing an angular, scalable and localized window, which offers directional flexibility in the multi-scale signal analysis in Clifford domains. The basic properties of the proposed transform such as inner product relation, reconstruction formula, and the range theorem are in- vestigated using the machinery of operator theory and Clifford Fourier transforms. Moreover, several extensions of the well-known Heisenberg- type inequalities are derived for the proposed transform in the Clifford Fourier domain. We culminate our investigation by deriving the direc- tional uncertainty principles for the Clifford-valued Stockwell transform. To validate the acquired results, illustrative examples are given. Mathematics Subject Classification. 42B10, 42C40, 15A66, 15A67, 44A05, 47G10, 94A12.