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首页> 外文期刊>Emerging and Selected Topics in Circuits and Systems, IEEE Journal on >Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain
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Caputo-Based Fractional Derivative in Fractional Fourier Transform Domain

机译：分数阶傅里叶变换域中基于Caputo的分数阶导数

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摘要

This paper proposes a novel closed-form analytical expression of the fractional derivative of a signal in the Fourier transform (FT) and the fractional Fourier transform (FrFT) domain by utilizing the fundamental principles of the fractional order calculus. The generalization of the differentiation property in the FT and the FrFT domain to the fractional orders has been presented based on the Caputo's definition of the fractional differintegral, thereby achieving the flexibility of different rotation angles in the time—frequency plane with varying fractional order parameter. The closed-form analytical expression is derived in terms of the well-known higher transcendental function known as confluent hypergeometric function. The design examples are demonstrated to show the comparative analysis between the established and the proposed method for causal signals corrupted with high-frequency chirp noise and it is shown that the fractional order differentiating filter based on Caputo's definition is presenting good performance than the established results. An application example of a low-pass finite impulse response fractional order differentiating filter in the FrFT domain based on the definition of Caputo fractional differintegral method has also been investigated taking into account amplitude-modulated signal corrupted with high-frequency chirp noise.
机译：本文利用分数阶微积分的基本原理，提出了信号在傅里叶变换（FT）和分数傅里叶变换（FrFT）域中的分数导数的新型闭式解析表达式。基于Caputo对分数微积分的定义，提出了FT和FrFT域中微分性质对分数阶的一般化，从而在分数阶参数变化的情况下实现了时频平面上不同旋转角度的灵活性。闭合形式的分析表达式是根据众所周知的更高先验函数（合流超几何函数）得出的。设计实例证明了所建立方法与拟议方法对因高频线性调频噪声而损坏的因果信号的比较分析，并且表明基于Caputo定义的分数阶微分滤波器表现出比所建立结果更好的性能。考虑到高频线性调频噪声对幅度调制信号的破坏，基于Caputo分数微分积分方法的定义，研究了FrFT域中低通有限脉冲响应分数阶微分滤波器的应用实例。

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