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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
Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain
Ran Tao,Bing-Zhao Li,Yue Wang +2 more
TL;DR: A more simple relationship between the discrete fractional spectrum of periodic nonuniformly sampled signals and the continuous spectrum has been obtained and the original continuous spectrum can be reconstructed from periodic non uniformly sampling signals in fractional Fourier domain.
Journal ArticleDOI
Flexible optical encryption with multiple users and multiple security levels
TL;DR: A basic optical encryption architecture that admits several cryptography applications based on multiplexing, where users can decrypt different private images from the same encrypted image, a superuser can have a key that decrypts all encrypted images, and multiplexed images can be encrypted with different levels of security.
Journal ArticleDOI
Image encryption based on the fractional Fourier transform over finite fields
Juliano B. Lima,L. F. G. Novaes +1 more
TL;DR: The transforms constructed are then used as the basis of a novel image encryption scheme, and security aspects of such a scheme are analyzed through computer simulations and specific metrics.
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Fast linear canonical transforms
John J. Healy,John T. Sheridan +1 more
TL;DR: In this paper, a frequency-division fast linear canonical transform algorithm comparable to the Sande-Tukey fast Fourier transform is proposed, and results calculated with an implementation of this algorithm are compared with the corresponding analytic functions.
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Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain
Wen Chen,Xudong Chen +1 more
TL;DR: Numerical results are presented to demonstrate the feasibility and effectiveness of the proposed optical asymmetric cryptosystem for color image encryption.