Open AccessBook
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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Wigner distribution in optics
TL;DR: The Wigner distribution was introduced by Dolin and Walther in the sixties to relate partial coherence to radiometry as discussed by the authors, and it has been used in many applications in the field of first-order optics.
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Recovery of Bandlimited Signals in Linear Canonical Transform Domain from Noisy Samples
Hui Zhao,Ruyan Wang,Daiping Song +2 more
TL;DR: This paper shows that the generalized Shannon-type reconstruction scheme for bandlimited signals in LCT domain cannot be directly applied in the presence of noise since it leads to an infinite mean integrated square error, and proposes a reconstruction algorithm based on the oversampling theorem.
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Image and video processing using discrete fractional transforms
Neeru Jindal,Kulbir Singh +1 more
TL;DR: Comparison of performance states that discrete fractional Fourier transform is superior in compression, while discrete fractionsal cosine transform is better in encryption of image and video.
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Linear canonical ambiguity function and linear canonical transform moments
TL;DR: In this paper, a linear canonical ambiguity function (LCAF) based on the linear canonical transform (LCT) was proposed, and the properties and physical meaning of the LCAF were given.
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On uncertainty principles for linear canonical transform of complex signals via operator methods
TL;DR: A much briefer and more transparent derivation is presented to obtain a general uncertainty principle of the LCT for arbitrary signals via operator methods and it is proved that the derived results hold for arbitrary LCT parameters.