Results 21 to 30 of about 99,067 (287)
Multiweighted-Type Fractional Fourier Transform: Unitarity
Fractal and Fractional, 2021 The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity.
Tieyu Zhao, Yingying Chi
doaj +1 more source
Fractional Fourier Transform Meets Transformer Encoder
IEEE Signal Processing Letters, 2022 Utilizing signal processing tools in deep learning models has been drawing increasing attention. Fourier transform (FT), one of the most popular signal processing tools, is employed in many deep learning models. Transformer-based sequential input processing models have also started to make use of FT.
Furkan Sahinuc, Aykut Koc
openaire +3 more sources
Sampling and series expansion theorems for fractional Fourier and other transforms [PDF]
, 2003 Cataloged from PDF version of article.We present muchbriefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms.
Candan, C., Ozaktas, H. M.
core +1 more source
Fractal and Fractional, 2022 In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, we study the boundary and initial problems of the Laplace and heat equations with chirp functions.
Yinuo Yang +3 more
doaj +1 more source
Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators [PDF]
, 1994 Cataloged from PDF version of article.The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform.
Mendlovic, D., Ozaktas, H. M.
core +1 more source
Novel Fractional Wavelet Transform with Closed-Form Expression [PDF]
, 2014 yesA new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a ...
Abd-Alhameed, Raed A. +4 more
core +2 more sources
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
doaj +1 more source
Nonseparable two-dimensional fractional Fourier transform [PDF]
Applied Optics, 1998 Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented.
Sahin, A., Kutay, M. A., Ozaktas, H. M.
openaire +6 more sources
Uniqueness results for the phase retrieval problem of fractional Fourier transforms of variable order [PDF]
, 2010 In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics.
Jaming, Philippe
core +3 more sources
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
doaj +1 more source