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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Journal Article
Fractional Fourier transform based key exchange for optical asymmetric key cryptography
TL;DR: A new technique is proposed, based on the Diffie-Hellman protocol, in which the key can be exchanged with high security, and results of computer simulation are presented to verify the proposed idea and analyse the robustness of the proposed technique.
Journal ArticleDOI
Image compression algorithm with reduced blocking artifacts
TL;DR: The novelty of the algorithm is its ability to detect and reduce the blocking artifacts using nonseparable discrete fractional Fourier transform (NSDFrFT) at high compression ratios.
Journal ArticleDOI
A Novel Image Encryption Scheme based on Multiple Parameter Discrete Fractional Fourier Transform
Deepak Sharma,Rajiv Saxena +1 more
TL;DR: A novel method to encrypt an image by using multiple parameters discrete fractional Fourier transform (DFRFT) with random phase matrices with high degree of resistance towards bruteforce attack is proposed.
Journal ArticleDOI
Research of FRFT Rotation Factor Sensitivity and Diffusion Based on Audio
TL;DR: In this article, the authors analyzed the rotation factor sensitivity and diffusion of fractional Fourier transform (FFT) for audio data sources and found that the fractional FFT has a high rotation factor of Δα≥10-3.
Journal ArticleDOI
Heisenberg's uncertainty principle for N-dimensional fractional Fourier transform of complex-valued functions
Zhichao Zhang,Zhichao Zhang,Pu-Yu Han,Yun Sun,An-Yang Wu,Xi-Ya Shi,Sheng-Zhou Qiang,Xian Jiang,Ga Wang,Lu-Bo Liu +9 more
TL;DR: In this paper, the N -dimensional Heisenberg uncertainty principle associated with complex-valued functions' uncertainty product in the Fourier transform domain is extended into two fractional Fourier Transform (FRFT) domains, giving rise to a tighter lower bound on the uncertainty product.