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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
Resolution enhancement of low resolution wavefields with POCS algorithm
TL;DR: In this article, the problem of enhancing the resolution of wavefield or beam profile measurements obtained using low-resolution sensors is addressed by interpolating signals from partial fractional Fourier transform information in several domains.
Proceedings ArticleDOI
An overview of fractional order signal processing (fosp) techniques
TL;DR: A brief overview of existing fractional order signal processing (FOSP) techniques where the developments in the mathematical communities are introduced; relationship between the fractional operator and long-range dependence is demonstrated, and fundamental properties of each technique and some of its applications are summarized.
Journal ArticleDOI
On uncertainty principle for signal concentrations with fractional Fourier transform
TL;DR: The uncertainty principle for signal concentrations associated with the FRFT is investigated and it is shown that if the fraction of a nonzero signal's energy on a finite interval in one fractional domain with a certain angle @a is specified, then it must remain below a certain maximum.
Journal ArticleDOI
A simple fractional-calculus approach to the solutions of the Bessel differential equation of general order and some of its applications
TL;DR: In this paper, a simple fractional-calculus approach to the solutions of the classical Bessel differential equation of general order would lead naturally to several interesting consequences which include an alternative investigation of the power-series solutions obtainable usually by the Frobenius method, which is based largely upon some of the general theorems on (explicit) particular solutions of a certain family of linear ordinary fractional differintegral equations.
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Perspective projections in the space-frequency plane and fractional Fourier transforms
TL;DR: Perspective projections in the space-frequency plane are analyzed, and it is shown that under certain conditions they can be approximately modeled in terms of the fractional Fourier transform.