In this paper, the two-sided fractional Clifford–Fourier transformation (FrCFT) is defined and some of its properties are given. First, we give the definition of the two-sided FrCFT and discuss the relationship between the two-sided Clifford–Fourier transformation (CFT) and the two-sided FrCFT. Then, the inverse transformation of the two-sided FrCFT is given and the time–frequency properties are discussed. Finally, we study differential properties and the Plancherel identity of the two-sided FrCFT.

中文翻译：

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双边分数 Clifford-Fourier 变换

在本文中，定义了双边分数克利福德-傅里叶变换（FrCFT）并给出了它的一些性质。首先，我们给出了双边 FrCFT 的定义，并讨论了双边 Clifford-Fourier 变换（CFT）和双边 FrCFT 之间的关系。然后，给出了双边FrCFT的逆变换，并讨论了时频特性。最后，我们研究了两侧 FrCFT 的微分特性和 Plancherel 恒等式。