Browsing by Subject "Fractional Fourier transformations"

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    Efficient computation of the ambiguity function and the Wigner distribution on arbitrary line segments
    (IEEE, Piscataway, NJ, United States, 1999) Özdemir, A. K.; Arıkan, Orhan
    Efficient algorithms are proposed for the computation of Wigner distribution and ambiguity function samples on arbitrary line segments based on the relationship of Wigner distribution and ambiguity function with the fractional Fourier transformation. The proposed algorithms make use of an efficient computation algorithm of fractional Fourier transformation to compute N uniformly spaced samples O(N log N) flops. The ability of obtaining samples on arbitrary line segments provides significant freedom in the shape of the grids used in the Wigner distribution or in ambiguity function computations.
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    Fundamental structure of Fresnel diffraction: Longitudinal uniformity with respect to fractional Fourier order
    (Optical Society of America, 2011-12-24) Özaktaş, Haldun M.; Arik, S. O.; Coşkun, T.
    Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.