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Discrete Fourier Transforms of Fractional Processes with Econometric Applications [PDF]

, 2023
Abstract The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process.
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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 E. DeBrunner
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Sliding 2D Discrete Fractional Fourier Transform

IEEE Signal Processing Letters, 2019
The two-dimensional discrete fractional Fourier transform (2D DFrFT) has been shown to be a powerful tool for 2D signal processing. However, the existing discrete algorithms aren't the optimal for real-time applications, where the input signals are stream data arriving in a sequential manner. In this letter, a new sliding algorithm is proposed to solve
Yu Liu 0033, Hongxia Miao, Feng Zhang 0011, Ran Tao 0003   +3 more
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A novel discrete fractional Fourier transform

2001 CIE International Conference on Radar Proceedings (Cat No.01TH8559), 2002
The definition of the fractional Fourier transform (FRFT) is described. Several discrete FRFT methods developed previously are reviewed briefly. A novel discretization method for FRFT is presented in this paper. It has some advantages such as being easily understood and implemented compared with the previous DFRFT methods.
null Tao Ran, null Ping Xianjun, null Shen Yu, null Zhao Xinghao   +3 more
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Discrete fractional Hartley and Fourier transforms

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1998
Summary: This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used
Pei, Soo-Chang, Tseng, Chien-Cheng, Yeh, Min-Hung, Shyu, Jong-Jy   +3 more
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The Fractional Discrete Fourier Transform

1999
A fractional version of the Discrete Fourier Transform or DFT, denoted by the Fractional Discrete Fourier Transform or FDFT for short, is discussed here. First, results of a fractional version of the continuous-time Fourier Transform or CTFT are explored and then parallels are made between the DFT and the CTFT.
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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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Closed-form discrete fractional and affine Fourier transforms

IEEE Transactions on Signal Processing, 2000
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Pei, Soo-Chang, Ding, Jian-Jiun
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On the Grunbaum commuter based discrete fractional Fourier transform

2004 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2004
The basis functions of the continuous fractional Fourier transform (FRFT) are linear chirp signals that are suitable for time-frequency analysis of signals with chirping time-frequency content. Efforts to develop a discrete computable version of the fractional Fourier transform (DFRFT) have focussed on furnishing an orthogonal set of eigenvectors for ...
Balu Santhanam, Juan G. Vargas-Rubio
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A novel method for discrete fractional Fourier transform computation

ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2002
A novel method for the discrete fractional Fourier transform (DFRFT) computation is given in this paper. With the help of this novel method, the DFRFT of any angle can be computed by the weighted summation of the DFRFTs with the special angles. Moreover, the proposed algorithm is suitable for chirp signal detection and the VLSI implementations.
Pei, Soo-Chang, Yeh, Min-Hung
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