Open AccessBook
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
On function spaces with fractional Fourier transform in weighted Lebesgue spaces
Erdem Toksoy,Ayşe Sandıkçı +1 more
TL;DR: In this article, the authors defined the sum norm of the vector space of the fractional Fourier transform of a weight function in the space of weight functions and showed that it is invariant under time-frequency shifts.
Proceedings ArticleDOI
Matched Filtering in Fractional Fourier Domain
Feng Zhang,Ran Tao,Yue Wang +2 more
TL;DR: The theory introduced in this paper is validated by simulations and the response of the matched filter in fractional Fourier domain to chirp signals is analyzed, and the sidelobe suppression method for matched filtering in the fractional fourier domain is considered.
Posted Content
XFT: Extending the Digital Application of the Fourier Transform
TL;DR: In this article, a Gaussian-like quadrature of the continuous fractional Fourier transform is derived in terms of the Hermite polynomials and their zeros, which can be solved by a diagonal congruence transformation equivalent to a chirp-FFTchirp transformation.
Journal ArticleDOI
Convolution with the linear canonical Hankel transformation
Tanuj Kumar,Akhilesh Prasad +1 more
TL;DR: In this paper, translation and convolution for linear canonical Hankel transformations are introduced and some inequalities for linear time-invariant filters are studied. And some applications of linear canonical transformations to a generalized non-linear parabolic equation and a canonical convolution integral equation are given.
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Classical and Quantum Light: Versatile tools for quantum foundations and quantum information
TL;DR: A redefinition of the quantum nonlocal correlation called steering in the multipartite scenario, based on an inconsistency in the previous definition, namely the creation of this correlation from scratch using operations that supposedly would not be able to do so.