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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 Article
Pseudo-differential operator associated with the fractional Fourier transform
Akhilesh Prasad,Praveen Kumar +1 more
TL;DR: In this paper, the fractional pseudo-differential operators (f.p.d.) associated with the symbol $a(x,\xi) are studied and the boundedness property of f.pd. is studied.
Journal ArticleDOI
Relationship between sampling and multirate filterbanks in the linear canonical transform domain
Feng Zhang,Ran Tao,Yue Wang +2 more
TL;DR: This paper relates the multichannel sampling for bandlimited signals in the LCT domain as well as the corresponding continuous-time LCT filterbank to the discrete- time L CT filterbank, which can lead to new sampling strategies for band limited signals inThe LCTdomain.
Journal ArticleDOI
Discrete fractional Fourier transform computation by adaptive method
Feng Zhang,Ran Tao,Yue Wang +2 more
TL;DR: This work presents the computation method for the DFRFT using the adaptive least-mean-square algorithm and constructs two realization structures of the D FRFT computation with simultaneous multiple-angle parameters for each signal block.
Proceedings ArticleDOI
The Linear Canonical Transform and Its Application to Time-Frequency Signal Analysis
Qiang Xiang,Kai-Yu Qin +1 more
TL;DR: The linear canonical transform (LCT) as mentioned in this paper is a generalization of the classical Fourier transform and fractional Fourier Transform (FRFT) to analyze the signal in between the time and frequency domains.
Journal ArticleDOI
Explicit solutions of a certain class of differential equations by means of fractional calculus
TL;DR: The main object of as mentioned in this paper is to show how several recent contributions on this subject, involving a certain class of ordinary differential equations, can be obtained by suitably applying some general theorems on explicit particular solutions of a family of linear ordinary fractional differintegral equations.