In this paper, we introduce a short-time coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft ). We then prove that it satisfies Parseval’s relation, derive its inversion and addition formulas, and characterize its range on ℒ 2 (ℝ 2 ). We also study its time delay and frequency shift properties and conclude the article by a derivation of an uncertainty principle for both the coupled fractional Fourier transform and short-time coupled fractional Fourier transform.

中文翻译：

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短时耦合分数傅立叶变换和测不准原理

在本文中，我们使用耦合分数阶傅里叶变换 ( cfrft ) 的核来介绍短时耦合分数阶傅里叶变换 ( scfrft )。然后我们证明它满足Parseval 关系，推导出它的求逆和加法公式，并刻画它在ℒ 2 (ℝ 2 ) 上的范围。我们还研究了它的时间延迟和频移特性，并通过推导耦合分数阶傅里叶变换和短时耦合分数阶傅里叶变换的不确定性原理来结束本文。