Improved algorithm of fractional Fourier transform under condition of oversampling

Zhi Cheng Feng; Jian Ping An

doi:10.3969/j.issn.1001-506X.2012.03.07

Improved algorithm of fractional Fourier transform under condition of oversampling

Zhi Cheng Feng^*, Jian Ping An

^*Corresponding author for this work

School of Cyberspace Science and Technology

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

Abstract

For the weakness that Ozaktas sampling-type fractional Fourier transform (FRFT) has high computational complexity and low resolution, the computation of sampling-type FRFT is investigated under a condition of oversampling, and an improved algorithm of FRFT is presented. By reducing the value range of FRFT under the condition of oversampling, the frequency distribution in time-frequency plane is decreased and the discrete interval keeps the same as samples in time domain. Therefore, the interpolation is avoided and the computation is simplified significantly in the improved algorithm. Moreover, the improved algorithm is invertible. After further improvement, the algorithm has features with adjustable resolution, selectable output region and variable length of output data. The simulation results show the validity of the improved algorithm finally.

Original language	English
Pages (from-to)	467-471
Number of pages	5
Journal	Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics
Volume	34
Issue number	3
DOIs	https://doi.org/10.3969/j.issn.1001-506X.2012.03.07
Publication status	Published - Mar 2012

Keywords

Discretization
Fast calculation
Fractional Fourier transform (FRFT)
High resolution
Sampling-type

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10.3969/j.issn.1001-506X.2012.03.07

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title = "Improved algorithm of fractional Fourier transform under condition of oversampling",

abstract = "For the weakness that Ozaktas sampling-type fractional Fourier transform (FRFT) has high computational complexity and low resolution, the computation of sampling-type FRFT is investigated under a condition of oversampling, and an improved algorithm of FRFT is presented. By reducing the value range of FRFT under the condition of oversampling, the frequency distribution in time-frequency plane is decreased and the discrete interval keeps the same as samples in time domain. Therefore, the interpolation is avoided and the computation is simplified significantly in the improved algorithm. Moreover, the improved algorithm is invertible. After further improvement, the algorithm has features with adjustable resolution, selectable output region and variable length of output data. The simulation results show the validity of the improved algorithm finally.",

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T1 - Improved algorithm of fractional Fourier transform under condition of oversampling

AU - Feng, Zhi Cheng

AU - An, Jian Ping

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N2 - For the weakness that Ozaktas sampling-type fractional Fourier transform (FRFT) has high computational complexity and low resolution, the computation of sampling-type FRFT is investigated under a condition of oversampling, and an improved algorithm of FRFT is presented. By reducing the value range of FRFT under the condition of oversampling, the frequency distribution in time-frequency plane is decreased and the discrete interval keeps the same as samples in time domain. Therefore, the interpolation is avoided and the computation is simplified significantly in the improved algorithm. Moreover, the improved algorithm is invertible. After further improvement, the algorithm has features with adjustable resolution, selectable output region and variable length of output data. The simulation results show the validity of the improved algorithm finally.

AB - For the weakness that Ozaktas sampling-type fractional Fourier transform (FRFT) has high computational complexity and low resolution, the computation of sampling-type FRFT is investigated under a condition of oversampling, and an improved algorithm of FRFT is presented. By reducing the value range of FRFT under the condition of oversampling, the frequency distribution in time-frequency plane is decreased and the discrete interval keeps the same as samples in time domain. Therefore, the interpolation is avoided and the computation is simplified significantly in the improved algorithm. Moreover, the improved algorithm is invertible. After further improvement, the algorithm has features with adjustable resolution, selectable output region and variable length of output data. The simulation results show the validity of the improved algorithm finally.

KW - Discretization

KW - Fast calculation

KW - Fractional Fourier transform (FRFT)

KW - High resolution

KW - Sampling-type

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JF - Xi Tong Gong Cheng Yu Dian Zi Ji Shu/Systems Engineering and Electronics

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Improved algorithm of fractional Fourier transform under condition of oversampling

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