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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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Proceedings ArticleDOI
Fractional Fourier Transforms and Wigner Distribution Functions for Stationary and Non-Stationary Random Process
Jian-Jiun Ding,Soo-Chang Pei +1 more
TL;DR: The relations among the random process, the Wigner distribution function, the ambiguity function, and the fractional Fourier transform (FRFT) are discussed and many interesting properties are found.
Journal ArticleDOI
Fractional Fourier Transform Meets Transformer Encoder
TL;DR: FrFNet as discussed by the authors introduces the fractional Fourier transform (FrFT) into the transformer architecture, which provides an opportunity to access any intermediate domain between time and frequency and find better transformation domains.
Posted Content
Distance function wavelets - Part II: Extended results and conjectures
TL;DR: It is found that the translation invariant monomial solutions of the high-order Laplace equations can be used to make very simple harmonic polynomial DFW series.
Journal ArticleDOI
An interplay between parameter (p, q)-Boas transform and linear canonical transform
TL;DR: In this article, the generalized Boas transform product theorem was proved in the linear canonical transform domain and a linear combination of a signal and its parameter (p, q)-Boas transform was studied.
Journal ArticleDOI
Extending Murty interferometry to the Terahertz part of the spectrum
TL;DR: In this paper, the authors discuss some novel technologies that enable the implementation of shearing interferometry at the terahertz part of the spectrum, including direct measurement of lens parameters, determination of homogeneity of samples, measurement of optical distortions and non-contact evaluation of thermal expansion coefficient of materials buried inside media that are opaque to optical or infrared frequencies but transparent to THz frequencies.