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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
Fractional Fourier transform for beams generated by Gaussian mirror resonator
Bin Tang,Minghua Xu +1 more
TL;DR: In this article, the propagation properties of beams generated by Gaussian mirror resonator passing through FRFT optical systems have been studied in detail, and some typical numerical examples are given to compare the results obtained by the approximate analytical method with those by the numerical integral method.
Journal ArticleDOI
Weak fault diagnosis of rolling bearing based on FRFT and DBN
TL;DR: A fault diagnosis method based on fractional Fourier transform and deep belief networks can effectively detect the weak fault of rolling bearing.
Posted Content
Explicit Hermite-type eigenvectors of the discrete Fourier transform
TL;DR: In this article, an explicit basis of non-orthogonal eigenvectors of the discrete Fourier transform (DFT) was constructed by applying the Gramm-Schmidt orthogonalization procedure.
Journal ArticleDOI
Two-dimensional nonseparable discrete linear canonical transform based on CM-CC-CM-CC decomposition.
Soo-Chang Pei,Shih-Gu Huang +1 more
TL;DR: A new decomposition called CM-CC-CM-CC decomposition is proposed, which decomposes the 2D NsLCT into two 2D CMs and two2D chirp convolutions, which have a perfect reversibility property, meaning that one can reconstruct the input signal/image losslessly from the output.
Journal ArticleDOI
Phase-space window and degrees of freedom of optical systems with multiple apertures
Haldun M. Ozaktas,Figen S. Oktem +1 more
TL;DR: It is shown how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space.