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 …
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 …
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
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 …
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
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 …
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
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 …
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 …
and powerful analyzing tool for time-frequency analysis, the FRFT has been applied in a lot …
Multidimensional fractional wavelet transforms and uncertainty principles
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 …
RN, namely the multidimensional fractional wavelet transform (MFrWT) and studied some of …
Fractional Fourier Transforms Meet Riesz Potentials and Image Processing
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 …
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 …
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 …
domain, where fractional order can be used to search for the maximum value of fault …