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 ArticleDOI
Approximations to the Solution of R - L Space Fractional Heat Equation in Terms of Kummers Hyper Geometric Functions by Using Fourier Transform Method: A New Approach
S.D. Manjarekar,A.P. Bhadane +1 more
TL;DR: In this article, Fourier transform was used to solve the Riemann - Liouville Space Fractional Heat equation by using Fourier Transform Method approximated by Kummers Hyper geometric functions.
Dissertation
La fonction d'appareil en spectrométrie par transformation de Fourier: de la modélisation à l'algorithmique
TL;DR: In this paper, the authors introduce a methode de controle flexible du profil spectral des fonctions d'apodisation, which permet d'integrer numeriquement the fonction d'appareil.
Journal ArticleDOI
Noise and Interference Suppression in Sonar Echoes Using the Fractional Fourier Transform
TL;DR: This paper presents a simple FrFT-based algorithm that separates sonar echoes of a desired SOI from the cluttered background, and exploits the fact that it can find the best time axis ‘t a ’ in which the SOI becomes a tone with the FrFT, enabling easy notching (zeroing) of the clutter.
Journal ArticleDOI
Uncertainty Principle for a Kind of Quaternionic Linear Canonical Transform
TL;DR: Based on the properties of the left-sided quaternionic linear canonical transform (QLCT), an uncertainty principle is established in this article, which states that the product of the variances of quaternionvalued signals in the spatial and frequency domains has a lower bound and only a 2D Gaussian signal minimizes the uncertainty principle.
Proceedings ArticleDOI
The reality-preserving multiple-parameter fractional fourier transform and its application to image encryption
TL;DR: A new approach for image encryption based on the real-value and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission is proposed.