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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
An Extrapolation Algorithm for $(a,b,c,d)$ -Bandlimited Signals
TL;DR: An iterative (a, b, c, d)-bandlimited signal extrapolation algorithm is proposed and by use of the interesting properties of generalized prolate spheroidal wave functions, the convergence of the proposed algorithm is proved.
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A discrete linear chirp transform (DLCT) for data compression
TL;DR: This paper proposes an orthogonal linear-chirp transform, the discrete linear chirP transform (DLCT), to represent any signal in terms oflinear chirps, with modulation and dual properties, in data compression.
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Hybrid Watermarking Algorithm using Finite Radon and Fractional Fourier Transform
TL;DR: A watermarking scheme based on finite radon transform (FRAT), fractional Fourier Transform (FRFT) and singular value decomposition is proposed, which provides additional degree of freedom in security, robustness, payload capacity and visual transparence.
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Linear transformations and aberrations in continuous and finite systems
TL;DR: In this article, the authors quantize the geometric optical model into discrete, finite-dimensional systems based on the Lie algebra, whose wavefunctions are N-point signals, phase space is a sphere and transformations are represented by the N × N unitary matrices that form the group.