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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.

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Journal ArticleDOI

Uncertainty principles for discrete signals associated with the fractional Fourier and linear canonical transforms

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.
Journal ArticleDOI

New Statistics of the Second-Order Chirp Cyclostationary Signals: Definitions, Properties and Applications

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.
Journal ArticleDOI

A pair of linear canonical Hankel transformations and associated pseudo-differential operators

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.
Journal ArticleDOI

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.
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