A novel discrete fractional Fourier transform

Ran Tao; Xianjun Ping; Yu Shen; Xinghao Zhao

A novel discrete fractional Fourier transform

Ran Tao^*, Xianjun Ping, Yu Shen, Xinghao Zhao

^*Corresponding author for this work

School of Information and Electronics

Beijing Institute of Technology

Research output: Contribution to conference › Paper › peer-review

8 Citations (Scopus)

Abstract

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 easily understood and implemented compared with the previous DFRFT methods. Especially, it need small computation amount because of only a diagonal matrix should be recomputed when the rotational angle is changed. In addition, it need not consider the match between eigenvalues and eigenvectors. And it doesn't need to orthogonalize the DFT Hermite eigenvectors, either. A few simulation results for some typical signals are provided to verify the correctness of the proposed method.

Original language	English
Pages	1027-1030
Number of pages	4
Publication status	Published - 2001
Event	2001 CIE International Conference on Radar Proceedings - Beijing, China Duration: 15 Oct 2001 → 18 Oct 2001

Conference

Conference	2001 CIE International Conference on Radar Proceedings
Country/Territory	China
City	Beijing
Period	15/10/01 → 18/10/01

Keywords

Discrete fractional Fourier transform
Fractional Fourier transform
Hermite function
Time-frequency analysis

Cite this

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title = "A novel discrete fractional Fourier transform",

abstract = "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 easily understood and implemented compared with the previous DFRFT methods. Especially, it need small computation amount because of only a diagonal matrix should be recomputed when the rotational angle is changed. In addition, it need not consider the match between eigenvalues and eigenvectors. And it doesn't need to orthogonalize the DFT Hermite eigenvectors, either. A few simulation results for some typical signals are provided to verify the correctness of the proposed method.",

keywords = "Discrete fractional Fourier transform, Fractional Fourier transform, Hermite function, Time-frequency analysis",

author = "Ran Tao and Xianjun Ping and Yu Shen and Xinghao Zhao",

year = "2001",

language = "English",

pages = "1027--1030",

note = "2001 CIE International Conference on Radar Proceedings ; Conference date: 15-10-2001 Through 18-10-2001",

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TY - CONF

T1 - A novel discrete fractional Fourier transform

AU - Tao, Ran

AU - Ping, Xianjun

AU - Shen, Yu

AU - Zhao, Xinghao

PY - 2001

Y1 - 2001

N2 - 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 easily understood and implemented compared with the previous DFRFT methods. Especially, it need small computation amount because of only a diagonal matrix should be recomputed when the rotational angle is changed. In addition, it need not consider the match between eigenvalues and eigenvectors. And it doesn't need to orthogonalize the DFT Hermite eigenvectors, either. A few simulation results for some typical signals are provided to verify the correctness of the proposed method.

AB - 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 easily understood and implemented compared with the previous DFRFT methods. Especially, it need small computation amount because of only a diagonal matrix should be recomputed when the rotational angle is changed. In addition, it need not consider the match between eigenvalues and eigenvectors. And it doesn't need to orthogonalize the DFT Hermite eigenvectors, either. A few simulation results for some typical signals are provided to verify the correctness of the proposed method.

KW - Discrete fractional Fourier transform

KW - Fractional Fourier transform

KW - Hermite function

KW - Time-frequency analysis

UR - http://www.scopus.com/inward/record.url?scp=0035719721&partnerID=8YFLogxK

M3 - Paper

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SP - 1027

EP - 1030

T2 - 2001 CIE International Conference on Radar Proceedings

Y2 - 15 October 2001 through 18 October 2001

ER -

A novel discrete fractional Fourier transform

Abstract

Conference

Keywords

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