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The Fractional Fourier Transform: with Applications in Optics and Signal Processing
TLDR
The fractional Fourier transform (FFT) as discussed by the authors has been used in a variety of applications, such as matching filtering, detection, and pattern recognition, as well as signal recovery.Abstract:
Preface. Acknowledgments. Introduction. Signals, Systems, and Transformations. Wigner Distributions and Linear Canonical Transforms. The Fractional Fourier Transform. Time-Order and Space-Order Representations. The Discrete Fractional Fourier Transform. Optical Signals and Systems. Phase-Space Optics. The Fractional Fourier Transform in Optics. Applications of the Fractional Fourier Transform to Filtering, Estimation, and Signal Recovery. Applications of the Fractional Fourier Transform to Matched Filtering, Detection, and Pattern Recognition. Bibliography on the Fractional Fourier Transform. Other Cited Works. Credits. Index.read more
Citations
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Journal ArticleDOI
Propagation of Lorentz and Lorentz-Gauss beams through an apertured fractional Fourier transform optical system
TL;DR: By expanding the hard-aperture function into a finite sum of complex Gaussian functions, the authors in this paper derived approximate analytical formulae for Lorentz and Gauss beams propagating through an apertured fractional Fourier transform (FRT) optical system.
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In vivo O-Space imaging with a dedicated 12 cm Z2 insert coil on a human 3T scanner using phase map calibration.
TL;DR: The first experimental proof‐of‐concept O‐Space images on in vivo and phantom samples are shown, paving the way for more in‐depth exploration of O‐ Space and similar imaging methods.
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Sampling reconstruction of N-dimensional bandlimited images after multilinear filtering in fractional Fourier domain
Deyun Wei,Yuan-Min Li +1 more
TL;DR: In this article, the generalized sampling expansion is investigated for the case where the fractional bandlimited input depends on N real variable, i.e., f ( t ) = f (t 1, ⋯, t N ) and is used as a common input to a parallel bank of m independent N dimensional linear fractional Fourier filters.
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Some fractional-calculus results for the $$\bar H$$ -function associated with a class of Feynman integrals
TL;DR: In this article, the authors present, in a unified manner, a number of key results for fractional-calculus operators such as the Riemann-Liouville, the Weyl, and other fractional calculus operators based on the Cauchy-Goursat Integral Formula.
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The discrete fractional Fourier transform based on the DFT matrix
Ahmet Serbes,Lutfiye Durak-Ata +1 more
TL;DR: It is shown that this DFrFT definition based on the eigentransforms of the DFT matrix mimics the properties of continuous fractional Fourier transform (FrFT) by approximating the samples of the continuous FrFT.