Riesz fractional order derivative in Fractional Fourier Transform domain: An insight

摘要

This paper presents a novel closed-form analytical expression for Riesz fractional order derivative in the Fractional Fourier domain. The expression is obtained in the terms of higher transcendental functions such as Parabolic Cylinder Function as well as Confluent Hypergeometric Function. The presented work is analyzed in the discrete domain by using the properties of Discrete Fractional Fourier Transform (DFrFT). The proposed algorithm is capable of preserving the texture and edge information without any phase distortion. The design example discussed in the paper shows the efficacy of the proposed algorithm for a signal with high frequency chirp noise. The design flexibility of the proposed approach is confirmed due to the fact that it provides an optimal value of performance metrics such as Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) corresponding to the variation of the fractional order of Riesz derivative and fractional parameter in the rotation angle of Fractional Fourier Transform (FrFT). The proposed algorithm provides better results in terms of minimum RMSE of 0.115136 and MAE of 0.094223 for the optimal fractional order of 0.43 at a rotation angle of 0.45 pi. (C) 2019 Elsevier Inc. All rights reserved.