On the class of uncertainty inequalities for the coupled fractional Fourier transform
Journal of Inequalities and Applications, 2022 The coupled fractional Fourier transform F α , β $\mathcal {F}_{\alpha ,\beta}$ is a two-dimensional fractional Fourier transform depending on two angles α and β, which are coupled in such a way that the transform parameters are γ = ( α + β ) / 2 $\gamma
Firdous A. Shah +3 more
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Self Fourier functions and fractional Fourier transforms [PDF]
Optics Communications, 1993 The Fourier transform is perhaps the most important analytical tool in wave optics. Hence Fourier-related concepts are likely to have an important on optics. We will likely recall two novel concepts and then show how they are interrelated. A self-Fourier function (SFF) [1,2] is a function whose Fourier transform is identical to itself.
Mendlovic, D. +2 more
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Low-complexity LSMR equalisation of FrFT-based multicarrier systems in doubly dispersive channels [PDF]
, 2011 The discrete fractional Fourier transform (FrFT) has been suggested to enhance performance over DFT-based multicarrier systems when transmitting over doubly-dispersive channels.
Weiss, Stephan +7 more
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Fractional Fourier transforms of hypercomplex signals [PDF]
Signal, Image and Video Processing, 2012 An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal.
Hendrik De Bie, Nele De Schepper
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Fractional Fourier Transform Aided Computerized Framework for Alcoholism Identification in EEG [PDF]
, 2022 Alcoholism has a detrimental impact on brain functioning. Electroencephalogram (EEG) signals are commonly used by clinicians and researchers to quantify and document alcoholic brain activity.
Akbari, Hesam +5 more
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Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures
Entropy, 2022 The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals.
Hari M. Srivastava +3 more
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Fourier transforming a trapped Bose-Einstein condensate by waiting a quarter of the trap period: simulation and applications [PDF]
, 2006 We investigate the property of isotropic harmonic traps to Fourier transform a weakly interacting Bose–Einstein condensate (BEC) every quarter of a trap period.
Ohberg, Patrik; id_orcid +5 more
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Parseval Relationship of Samples in the Fractional Fourier Transform Domain
Journal of Applied Mathematics, 2012 This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained.
Bing-Zhao Li, Tian-Zhou Xu
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Image Correlation Using Fractional Hermite Transform
IEEE Access, 2020 In this paper, we generalize the Hermite transform into a fractional case using the fractional Fourier transform and the fractional convolution. The new methodology was evaluated using phytoplankton images with different illumination patterns and ...
Alfredo Castro-Valdez +1 more
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The Periodogram of fractional processes [PDF]
, 2007 We analyse asymptotic properties of the discrete Fourier transform and the periodogram of time series obtained through (truncated) linear filtering of stationary processes.
Velasco Gómez, Carlos +2 more
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