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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
Uncertainty principles for discrete signals associated with the fractional Fourier and linear canonical transforms
Jun Shi,Mo Han,Naitong Zhang +2 more
TL;DR: This paper defines the time spread and the fractional frequency spread for discrete signals and derives an uncertainty relation between these two spreads, which are extended to the linear canonical transform, which is a generalized form of the FRFT.
Journal ArticleDOI
The discrete fractional random cosine and sine transforms
TL;DR: It is demonstrated that the D FRNCT and DFRNST can be regarded as special kinds of D FRNT and thus their mathematical properties are inherited from the DFRNT.
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New Statistics of the Second-Order Chirp Cyclostationary Signals: Definitions, Properties and Applications
Hongxia Miao,Feng Zhang,Ran Tao +2 more
TL;DR: Two new complementary correlation function-based statistics and their basic properties are proposed and discussed and the advantages of the proposed statistics over the classical second-order statistics are examined by the communication signals and the electrocardiogram (ECG) signals.
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A pair of linear canonical Hankel transformations and associated pseudo-differential operators
Akhilesh Prasad,Tanuj Kumar +1 more
TL;DR: In this paper, a pair of linear canonical Hankel transformations and their properties on Zemanian-type spaces have been investigated, and two versions of pseudo-differential operator associated with canonical transformations have been defined and discussed.
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Measuring the complete transverse spatial mode spectrum of a wave field
TL;DR: A method that allows the experimental determination of the entire spatial mode spectrum of any arbitrary monochromatic wave field in a plane normal to its propagation direction is put forward.