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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
Nonlinear optical security system based on a joint transform correlator in the Fresnel domain
TL;DR: The security system proposed in this paper preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of the key random mask in the decryption process.
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Three uncertainty relations for real signals associated with linear canonical transform
TL;DR: In this article, three novel results of uncertainty principle in the LCT domains are obtained, in which one is connected with parameters a and b, and the other two are connected with c and d; the last one was connected with the four transformation parameters a, b, c, d and d. The effects of time scaling on these results' bounds are also involved.
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Shifted Fourier Matrices and Their Tridiagonal Commutors
Stuart Clary,Dale H. Mugler +1 more
TL;DR: In this paper, it was shown that the n × n Fourier matrices can commute with a nonscalar tridiagonal matrix for all values of the shift parameter, provided that the base of the base matrix q = e^{2π{text{\textit{\r{\i}}}}} \tau} determined by q is an n$th root of unity.
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Finite two-dimensional oscillator: II. The radial model
TL;DR: In this paper, a finite two-dimensional radial oscillator of (N + 1)2 points is proposed, with the dynamical Lie algebra so(4) = su(2)x⊕su(2y)y examined in part I of this work, but reduced by a subalgebra chain.
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New Wigner distribution and ambiguity function based on the generalized translation in the linear canonical transform domain
TL;DR: The results show that the new WD and AF applied to the parameters estimation for LFM signals are very useful and effective and achieve better detection performance than the LCWD and LCAF, respectively, as well as the WDL and AFL, respectively.