In this paper, we study a special one-dimensional quaternion short-time Fourier transform (QSTFT). Its construction is based on the slice hyperholomorphic Segal–Bargmann transform. We discuss some basic properties and prove different results on the QSTFT such as Moyal formula, reconstruction formula and Lieb’s uncertainty principle. We provide also the reproducing kernel associated with the Gabor space considered in this setting.

中文翻译：

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关于四元离子短时傅立叶和Segal–Bargmann变换

在本文中，我们研究了特殊的一维四元数短时傅立叶变换（QSTFT）。其构造基于切片超全同性Segal–Bargmann变换。我们讨论了一些基本特性，并在QSTFT上证明了不同的结果，例如Moyal公式，重建公式和Lieb的不确定性原理。我们还提供与在此设置中考虑的Gabor空间相关的再现内核。