Results 131 to 140 of about 2,662 (145)

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
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On the multiangle centered discrete fractional Fourier transform

IEEE Signal Processing Letters, 2005
Existing versions of the discrete fractional Fourier transform (DFRFT) are based on the discrete Fourier transform (DFT). These approaches need a full basis of DFT eigenvectors that serve as discrete versions of Hermite-Gauss functions. In this letter, we define a DFRFT based on a centered version of the DFT (CDFRFT) using eigenvectors derived from the
J.G. Vargas-Rubio, B. Santhanam
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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.
Tao, Ran, Zhang, Feng, Wang, Yue
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Discrete fractional Fourier transform computation by adaptive method

Optical Engineering, 2013
The continuous fractional Fourier transform (FRFT) can be interpreted as a rotation of a signal in the time-frequency plane and is a powerful tool for analyzing and processing nonstationary signals. Because of the importance of the FRFT, the discrete fractional Fourier transform (DFRFT) has recently become an important issue. We present the computation
Feng Zhang, Ran Tao, Yue Wang
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Improved spectrograms using the discrete Fractional Fourier transform

2013 IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE), 2013
The conventional spectrogram is a commonly employed, time-frequency tool for stationary and sinusoidal signal analysis. However, it is unsuitable for general non-stationary signal analysis [1]. In recent work [2], a slanted spectrogram that is based on the discrete Fractional Fourier transform was proposed for multicomponent chirp analysis, when the ...
Oktay Agcaoglu, Balu Santhanam, Majeed Hayat   +2 more
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Sparse Discrete Fractional Fourier Transform and Its Applications

IEEE Transactions on Signal Processing, 2014
The discrete fractional Fourier transform is a powerful signal processing tool with broad applications for nonstationary signals. In this paper, we propose a sparse discrete fractional Fourier transform (SDFrFT) algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional Fourier ...
Shengheng Liu, Tao Shan, Ran Tao, Yimin D. Zhang, Guo Zhang, Feng Zhang, Yue Wang   +6 more
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Closed-form discrete fractional and affine Fourier transforms

IEEE Transactions on Signal Processing, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pei, Soo-Chang, Ding, Jian-Jiun
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A Discrete Fractional Fourier Transform

2019
Some properties of the XFT as a discrete fractional Fourier transform and as a linear canonical transform are given in this chapter. The eigenvectors of the discrete fractional Fourier transform are obtained and the discrete canonical coherent states are studied.
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Discrete fractional Fourier transform based on orthogonal projections

IEEE Transactions on Signal Processing, 1999
Summary: The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been recently developed by \textit{B. Santhanam} and \textit{J. H.
Pei, Soo-Chang, Yeh, Min-Hung, Tseng, Chien-Cheng   +2 more
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Hirschman uncertainty with the discrete fractional fourier transform

2013 Asilomar Conference on Signals, Systems and Computers, 2013
The Hirschman Uncertainty [1] is defined by the average of the Shannon entropies of a discrete-time signal and its Fourier transform. The optimal basis for the Hirschman Uncertainty has been shown to be the picket fence function, as given in a previous paper of ours [2].
Kirandeep Ghuman, Victor DeBrunner
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