Results 301 to 310 of about 521,797 (371)

On the extension of the coupled fractional Fourier transform and its properties

Integral transforms and special functions, 2021
The coupled fractional Fourier transform is a two-dimensional fractional Fourier transform that depends on two angles that are coupled in such a way that the transform parameters are and It generalizes the two-dimensional Fourier transform and it serves ...
R. Kamalakkannan, R. Roopkumar, A. Zayed
semanticscholar   +1 more source

Novel Short-Time Fractional Fourier Transform: Theory, Implementation, and Applications

IEEE Transactions on Signal Processing, 2020
As a generalization of the classical Fourier transform (FT), the fractional Fourier transform (FRFT) has proven to be a powerful tool for signal processing and analysis. However, it is not suitable for processing signals whose fractional frequencies vary
Jun Shi, Jiabin Zheng, Xiaoping Liu, W. Xiang, Qinyu Zhang   +4 more
semanticscholar   +1 more source

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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Short time coupled fractional fourier transform and the uncertainty principle

Fractional Calculus and Applied Analysis, 2021
In this paper, we introduce a short-time coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft ).
R. Kamalakkannan, R. Roopkumar, A. Zayed
semanticscholar   +1 more source

Graph Fractional Fourier Transform: A Unified Theory

IEEE Transactions on Signal Processing
The fractional Fourier transform (FRFT) parametrically generalizes the Fourier transform (FT) by a transform order, representing signals in intermediate time-frequency domains.
Tuna Alikaşifoğlu, Bunyamin Kartal, Aykut Koç   +2 more
semanticscholar   +1 more source

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).
E. Koç, Tuna Alikaşifoğlu, A. Aras, Aykut Koç   +3 more
semanticscholar   +1 more source

Fractional fourier transform: photonic implementation

Applied Optics, 1994
The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features.
A W, Lohmann, D, Mendlovic
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Fractional Fourier Transform

2020
This chapter focuses on theory and implementation of fractional Fourier transform (FrFT). FrFT is a wide spread time-frequency tool. The advantages of FrFT domain signal processing has been presented. Various definitions of discrete fractional Fourier transform (DFrFT) has been reviewed and their digital implementation is also explained in detail.
Prajna Kunche, N. Manikanthababu
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Beam analysis by fractional Fourier transform

Optics Letters, 2001
A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed.
X, Xue, H, Wei, A G, Kirk
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Fractional Fourier transformers through reflection

Journal of the Optical Society of America A, 2002
We show that an arbitrary paraxial optical system, compounded with its reflection in an appropriately warped mirror, is a pure fractional Fourier transformer between coincident input and output planes. The geometric action of reflection on optical systems is introduced axiomatically and is developed in the paraxial regime. The correction of aberrations
Kurt Bernardo, Wolf, Guillermo, Krötzsch   +1 more
openaire   +2 more sources