In the framework of higher-dimensional time-frequency analysis, we propose a novel Clifford-valued Stockwell transform for an effective and directional representation of Clifford-valued functions. The proposed transform rectifies the windowed Fourier and wavelet transformations 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 investigated 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 directional uncertainty principles for the Clifford-valued Stockwell transform. To validate the acquired results, illustrative examples are given.

在高维时频分析的框架中，我们提出了一种新颖的 Clifford 值 Stockwell 变换，用于有效和定向地表示 Clifford 值函数。所提出的变换通过采用角度、可缩放和局部化的窗口来校正加窗傅里叶和小波变换，这在 Clifford 域中的多尺度信号分析中提供了方向灵活性。使用算子理论和克利福德傅里叶变换的机制研究了所提出变换的基本性质，例如内积关系、重构公式和范围定理。此外，对于在 Clifford Fourier 域中提出的变换，推导出了著名的 Heisenberg 型不等式的几个扩展。我们通过推导克利福德值斯托克韦尔变换的方向不确定性原理来结束我们的研究。为了验证获得的结果，给出了说明性示例。