Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Fractal signal processing <s> The effect of the fractional Fourier transform on homogeneous functions is discussed. The fractional Fourier transform is used for the determination of the main parameters of fractals. An application is made to the Mandelbrot–Weierstrass cosine fractal. The results are applied to describe the propagation of a fractal field through quadratic refractive-index media and to determine its fractal dimension. <s> BIB001 </s> Fractional Fourier transform as a signal processing tool: An overview of recent developments <s> Fractal signal processing <s> A fractional Fourier transform (FrFT) based estimation method is introduced in this paper to analyze the long range dependence (LRD) in time series. The degree of LRD can be characterized by the Hurst parameter. The FrFT-based estimation of Hurst parameter proposed in this paper can be implemented efficiently allowing very large data set. We used fractional Gaussian noises (FGN) which typically possesses long-range dependence with known Hurst parameters to test the accuracy of the proposed Hurst parameter estimator. For justifying the advantage of the proposed estimator, some other existing Hurst parameter estimation methods, such as wavelet-based method and a global estimator based on dispersional analysis, are compared. The proposed estimator can process the very long experimental time series locally to achieve a reliable estimation of the Hurst parameter.Copyright © 2007 by ASME <s> BIB002
The FRFT also found its application in processing of fractal signals. For example, the FRFT was used for the determination of the main parameters of fractals in BIB001 . In BIB002 , a FRFT based estimation method was introduced to analyze the long range dependence in time series. In particular, the FRFT was used for estimation of the Hurst exponent. The results have shown that the FRFT estimator can achieve a reliable estimation of the Hurst exponent when compared to some other existing estimation methods, such as wavelet-based method and a global estimator based on dispersional analysis.