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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
A review of optical image encryption techniques
TL;DR: This overview allows the numerical simulations of the corresponding optical encryption systems, and the extra degree of freedom (keys) provided by different techniques that enhance the optical encryption security, to be generally appreciated and briefly compared and contrasted.
Journal ArticleDOI
Double image encryption based on random phase encoding in the fractional Fourier domain
TL;DR: A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution that can be recovered without cross-talk.
Journal ArticleDOI
Airy-Gauss beams and their transformation by paraxial optical systems.
TL;DR: The generalized Airy-Gauss (AiG) beams are introduced and their propagation through optical systems described by ABCD matrices with complex elements in general is analyzed to describe in a more realistic way the propagation of the Airy wave packets.
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Short-time Fourier transform: two fundamental properties and an optimal implementation
Lutfiye Durak,Orhan Arikan +1 more
TL;DR: By extending the time-bandwidth product concept to fractional Fourier domains, a generalized time- bandwidth product (GTBP) is defined and it is shown that GTBP provides a rotation independent measure of compactness.
Journal ArticleDOI
Double image encryption based on iterative fractional Fourier transform
Zhengjun Liu,Shutian Liu +1 more
TL;DR: An image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders is presented, independent of additional random phases as the encryption/ decryption keys.