Results 231 to 240 of about 1,263,515 (279)

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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Digital computation of the fractional Fourier transform [PDF]

IEEE Transactions on Signal Processing, 1996
An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.
Orhan Arikan, H M Ozaktas
exaly   +4 more sources

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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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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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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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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The fractional Fourier–Jacobi wavelet transform

The Journal of Analysis, 2023
The main objective of this study is to define the fractional Jacobi translation and fractional Jacobi convolution, as well as to analyze the fractional Fourier-Jacobi wavelet transform and its fundamental properties. Additionally, an inversion formula and a Parseval relation for the continuous fractional Fourier-Jacobi wavelet transform are derived.
Othman Tyr, Faouaz Saadi
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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.
openaire   +1 more source

Fractional discrete Fourier transforms

Optics Letters, 1996
Direct calculation of fractional Fourier transforms from the expressions derived for their optical implementation is laborious. An extension of the discrete Fourier transform would have only O(N(2)) computational complexity. We define such a system, offer a general way to compute the fractional discrete Fourier transform matrix, and numerically ...
Z T, Deng, H J, Caulfield, M, Schamschula   +2 more
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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
openaire   +2 more sources