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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 of a higher-order cosh–Gaussian beam
TL;DR: In this paper, the authors derived an analytical expression for a higher-order cosh-Gaussian beam passing through a fractional Fourier transform (FRFT) system and illustrated its properties with numerical examples.
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Fast and accurate algorithm for the computation of complex linear canonical transforms.
TL;DR: A space-bandwidth product tracking formalism is developed to ensure that the number of samples is information-theoretically sufficient to reconstruct the continuous transform, but not unnecessarily redundant.
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Fully phase-based encryption using fractional order Fourier domain random phase encoding: error analysis
TL;DR: The tolerance to data loss and binarization of theencrypted data/image and the effects of noise perturbations on the encrypted data are studied to evaluate the quality of the recovered image.
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Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum
TL;DR: A new asymmetric cryptosystem based on coherent superposition and equal modulus decomposition of fractional Fourier spectrum is proposed, which can resist known-plaintext and known-public key attacks (specific attack).
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Novel convolution and correlation theorems for the fractional Fourier transform
TL;DR: In this article, the authors proposed a new convolution as well as correlation structure for the fractional Fourier transform (FRFT) which have similar time domain to frequency domain mapping results as the classical FT.