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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
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Journal ArticleDOI
Compact Fractional Fourier Domains
TL;DR: A coarse-to-fine grid search strategy is adopted to find the optimum fractional Fourier transform angle that makes the transformed signal minimum with low computational cost.
Journal ArticleDOI
Uncertainty Relations for coarse-grained measurements: an overview
TL;DR: A review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks can be found in this article.
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Hierarchically optical double-image correlation using 3D phase retrieval algorithm in fractional Fourier transform domain
TL;DR: The results illustrate that when the extracted phase-only patterns are compressed, optical double-grayscale-image correlation can be effectively conducted without the visualization of input information at each hierarchical level in 3D space.
Journal Article
Fractional Waveguide with Impedance Walls
TL;DR: In this paper, two distinct ranges of wall impedance have been found in which fractional impedance behaves in opposite ways for 0 < α < 1, and for 1 > α < 2, the fractional wall impedance is capacitive in range 1 and inductive in range 2, where α is fractional parameter.
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Mutually unbiased coarse-grained measurements of two or more phase-space variables
TL;DR: In this article, it was shown that mutual unbiasedness can be recovered between periodic coarse graining of any two non-parallel phase-space operators, such as position and momentum.