Closed-Form Analytical Expression of Fractional Order Differentiation in Fractional Fourier Transform Domain

In this paper, a closed-form analytical expression for fractional order differentiation in the fractional Fourier transform (FrFT) domain is derived by utilizing the basic principles of fractional order calculus. The reported work is a generalization of the differentiation property to fractional (noninteger or real) orders in the FrFT domain. The proposed closed-form analytical expression is derived in terms of the well-known confluent hypergeometric function. An efficient computation method has also been derived for the proposed algorithm in the discrete-time domain, utilizing the principles of the discrete fractional Fourier transform algorithm. An application example of a low-pass finite impulse response (FIR) fractional order differentiator in the FrFT domain has also been investigated to show the practicality of the proposed method in signal processing applications.