Fractional Fourier analysis of objects with scaling symmetry

The fractional Fourier analysis is used for investigation of fractal structures. As is shown, it reveals the scaling features of deterministic as well as of the random fractals, and allows to determine their main characteristics. As an example we present the fractional Fourier analysis of some self-affine functions. The map of the Radon-Wigner transform of the triadic Cantor set is considered numerically. The application of the fractional Fourier analysis in optical engineering is discussed.

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