Fractional Fourier transforms on Lp and applications

W Chen, Z Fu, L Grafakos, Y Wu - Applied and Computational Harmonic …, 2021 - Elsevier
This paper is devoted to the L p (R) theory of the fractional Fourier transform (FRFT) for 1≤
p< 2. In view of the special structure of the FRFT, we study FRFT properties of L 1 functions …

Approximation theorems associated with multidimensional fractional Fourier transform and applications in Laplace and heat equations

Y Yang, Q Wu, ST Jhang, Q Kang - Fractal and Fractional, 2022 - mdpi.com
In this paper, we establish two approximation theorems for the multidimensional fractional
Fourier transform via appropriate convolutions. As applications, we study the boundary and …

Riesz transform associated with the fractional Fourier transform and applications in image edge detection

Z Fu, L Grafakos, Y Lin, Y Wu, S Yang - Applied and Computational …, 2023 - Elsevier
The fractional Hilbert transform was introduced by Zayed [30, Zayed, 1998] and has been
widely used in signal processing. In view of its connection with the fractional Fourier …

On the class of uncertainty inequalities for the coupled fractional Fourier transform

FA Shah, WZ Lone, KS Nisar, T Abdeljawad - Journal of Inequalities and …, 2022 - Springer
The coupled fractional Fourier transform F α, β is a two-dimensional fractional Fourier
transform depending on two angles α and β, which are coupled in such a way that the …

Coupled fractional Wigner distribution with applications to LFM signals

AA Teali, FA Shah, AY Tantary, KS Nisar - Fractals, 2023 - World Scientific
The coupled fractional Fourier transform is a much recent ramification of the two-
dimensional fractional Fourier transform, wherein the kernel is not a tensor product of one …

[PDF][PDF] Convolution theorem involving n-dimensional windowed fractional Fourier transform

W Gao, B Li - Science China. Information Sciences, 2021 - scis.scichina.com
The fractional Fourier transform (FRFT) was proposed by Wiener in 1929. As an important
and powerful analyzing tool for time-frequency analysis, the FRFT has been applied in a lot …

Multidimensional fractional wavelet transforms and uncertainty principles

N Kaur, B Gupta, AK Verma - Journal of Computational and Applied …, 2023 - Elsevier
In this paper, we have given a new definition of continuous fractional wavelet transform in
RN, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of …

Fractional Fourier Transforms Meet Riesz Potentials and Image Processing

Z Fu, Y Lin, D Yang, S Yang - SIAM Journal on Imaging Sciences, 2024 - SIAM
Via chirp functions from fractional Fourier transforms, we introduce fractional Riesz
potentials related to chirp functions, which are further used to give a new image encryption …

Uncertainty principles for coupled fractional Wigner–Ville distribution

ATA Nur, M Bahri, N Bachtiar… - Royal Society Open …, 2024 - royalsocietypublishing.org
The coupled fractional Wigner–Ville distribution is a more general version of the fractional
Wigner–Ville distribution. Main properties including boundedness, Moyal's formula and …

Fault diagnosis of rolling bearing based on fractional Fourier instantaneous spectrum

J Cai, Y Xiao, L Fu - Experimental Techniques, 2022 - Springer
Fractional Fourier transform (FRFT) can transform data into the space of the fractional order
domain, where fractional order can be used to search for the maximum value of fault …