Results 251 to 260 of about 2,774 (297)

Fractional finite Fourier transform

Journal of the Optical Society of America A, 2004
We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform.
Kedar, Khare, Nicholas, George
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Fractional Fourier transforms and their optical implementation: I [PDF]

Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1993
Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ...

exaly   +2 more sources

The fractional Fourier transform on graphs

2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), 2017
The emerging field of signal processing on graphs merges algebraic or spectral graph theory with discrete signal processing techniques to process signals on graphs. In this paper, a definition of the fractional Fourier transform on graphs (GFRFT) is proposed and consolidated, which extends the discrete fractional Fourier transform (DFRFT) in the same ...
Yi-Qian Wang, Bing-Zhao Li 0001, Qi-Yuan Cheng   +2 more
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Random fractional Fourier transform

Optics Letters, 2007
We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics.
Zhengjun, Liu, Shutian, Liu
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The Fractional Fourier Transform and Applications

SIAM Review, 1991
This paper describes the “fractional Fourier transform,” which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity $e^{{{ - 2\pi i} / n}} $, the fractional Fourier transform is based on fractional roots of unity $e^{
David H. Bailey, Paul N. Swarztrauber
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On Namias's Fractional Fourier Transforms

IMA Journal of Applied Mathematics, 1987
\textit{V. Namias} [J. Inst. Math. Appl. 25, 241-265 (1980; Zbl 0434.42014)] developed a theory of fractional powers for the Fourier transform and obtained a number of fractional formulae which he used to solve several types of Schrödinger equation. In this paper the authors attempt to provide the necessary mathematical framework for Namias' idea in ...
McBride, A. C., Kerr, F. H.
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Trainable Fractional Fourier Transform

IEEE Signal Processing Letters
Recently, the fractional Fourier transform (FrFT) has been integrated into distinct deep neural network (DNN) models such as transformers, sequence models, and convolutional neural networks (CNNs). However, in previous works, the fraction order $\boldsymbol{a}$ is merely considered a hyperparameter and selected heuristically or tuned manually to find ...
Emirhan Koç, Tuna Alikasifoglu, Arda Can Aras, Aykut Koç   +3 more
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Fractional Fourier transform

Proceedings of the International Conference on Advances in Computing, Communications and Informatics, 2012
The Fractional Fourier transform (FRFT), which provides generalization of conventional Fourier Transform was introduced many years ago in mathematics literature by Namias. In this paper, definition, properties of fractional Fourier transform and its relationship with other transforms is discussed.
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Adaptive harmonic fractional Fourier transform

IEEE Signal Processing Letters, 1999
A novel adaptive harmonic fractional Fourier transform is proposed for analysis of voiced speech signals. It provides a higher concentration than STFT and avoids the cross interference components produced by the Wigner-Ville distribution and other bilinear representation. The proposed method rotates the base tone and harmonics in time-frequency domain.
Feng Zhang, Yan Qiu Chen, Guoan Bi
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Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms [PDF]

Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1994
A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction with the Wigner distribution of a ...
Billur Barşhan, Levent Onural
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