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Discrete Pseudo-Fractional Fourier Transform and Its Fast Algorithm [PDF]

Electronics (Switzerland), 2021
In this article, we introduce a new discrete fractional transform for data sequences whose size is a composite number. The main kernels of the introduced transform are small-size discrete fractional Fourier transforms. Since the introduced transformation
Dorota Majorkowska-Mech, Aleksandr Cariow, Cariow Aleksandr   +2 more
exaly   +2 more sources

Digital computation of the fractional Fourier transform [PDF]

IEEE Transactions on Signal Processing, 1996
An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time.
Orhan Arikan, H M Ozaktas
exaly   +3 more sources

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Fractional discrete Fourier transforms

Optics Letters, 1996
Direct calculation of fractional Fourier transforms from the expressions derived for their optical implementation is laborious. An extension of the discrete Fourier transform would have only O(N(2)) computational complexity. We define such a system, offer a general way to compute the fractional discrete Fourier transform matrix, and numerically ...
Z T, Deng, H J, Caulfield, M, Schamschula   +2 more
openaire   +2 more sources

Research progress on discretization of fractional Fourier transform

Science in China Series F: Information Sciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ran Tao 0003, Feng Zhang 0011, Yue Wang 0001   +2 more
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The generalized discrete fractional fourier transforms

IEEE International Conference on Acoustics Speech and Signal Processing, 2002
In this paper, we develop the generalized discrete fractional Fourier transform (GDFRFT) by factorizing the generalized discrete Fourier transform (GDFT) matrix. Specifically, the eigenvalues and eigenvectors are presented and then used to define the GDFRFT.
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The analysis of the discrete fractional Fourier transform algorithms

2009 Canadian Conference on Electrical and Computer Engineering, 2009
The discrete formal FRFT is difficult to obtained by the directly sampling the continuous FRFT because the kernel function of the continuous fractional Fourier transform (FRFT) exhibits drastic oscillation and the oscillation amplitude has the distinct difference from the different order of the FRFT.
Qi-Wen Ran, Hai-Ying Zhang, Zhongzhao Zhang, Xuejun Sha   +3 more
openaire   +1 more source

The Analysis of Resolution of the Discrete Fractional Fourier Transform

First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06), 2006
The fractional Fourier transform (FRFT) is a unified time-frequency transform that does not suffer from the cross terms and is suitable for processing the non stationary signal. It is required to define the corresponding analysis range and discrete resolution in the FRFT domain in order to apply the FRFT to digital signal processing field.
Bing Deng, Ran Tao 0003
openaire   +1 more source

Discrete and finite fractional Fourier transforms

Frontiers in Optics, 2003
Finite models for oscillator or waveguide systems provide corresponding fractional Fourier-type transforms between finite arrays of ‘sensor’ points. The kernel matrices are unitary and are well-known in group theory; they involve the discrete polynomials of Kravchuk, q-Kravchuk, Meixner and Hahn.
openaire   +1 more source

Geometry and dynamics in the fractional discrete Fourier transform

Journal of the Optical Society of America A, 2007
The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its ...
Kurt Bernardo, Wolf, Guillermo, Krötzsch   +1 more
openaire   +2 more sources

On the effects of windowing on the discretization of the fractional Fourier transform

2017 51st Asilomar Conference on Signals, Systems, and Computers, 2017
The eigenvalue degeneracy problem inherent in the discrete Fourier transform (DFT) matrix operator and the development of a full basis of orthogonal eigenvectors have been addressed via a commuting matrix, devoid of the aforementioned eigenvalue degeneracy problem, that also serves as a discrete version of the Gauss-Hermite (G-H) differential operator.
Balu Santhanam, Thalanayar S. Santhanam, Satish Mandai   +2 more
openaire   +1 more source