The multiple-parameter fractional Fourier transform

Jun Lang; Ran Tao; Qi Wen Ran; Yue Wang

doi:10.1007/s11432-008-0073-6

The multiple-parameter fractional Fourier transform

Jun Lang, Ran Tao^*, Qi Wen Ran, Yue Wang

^*Corresponding author for this work

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

50 Citations (Scopus)

Abstract

The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ ℤ^M. Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.

Original language	English
Pages (from-to)	1010-1024
Number of pages	15
Journal	Science in China, Series F: Information Sciences
Volume	51
Issue number	8
DOIs	https://doi.org/10.1007/s11432-008-0073-6
Publication status	Published - Aug 2008

Keywords

Multiple-parameter fractional Fourier transform
Multiplicity of the fractional Fourier transform
Signal processing
Weight-type fractional Fourier transform

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10.1007/s11432-008-0073-6

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title = "The multiple-parameter fractional Fourier transform",

abstract = "The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ ℤM. Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.",

keywords = "Multiple-parameter fractional Fourier transform, Multiplicity of the fractional Fourier transform, Signal processing, Weight-type fractional Fourier transform",

author = "Jun Lang and Ran Tao and Ran, {Qi Wen} and Yue Wang",

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AU - Lang, Jun

AU - Tao, Ran

AU - Ran, Qi Wen

AU - Wang, Yue

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N2 - The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ ℤM. Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.

AB - The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ ℤM. Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.

KW - Multiple-parameter fractional Fourier transform

KW - Multiplicity of the fractional Fourier transform

KW - Signal processing

KW - Weight-type fractional Fourier transform

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The multiple-parameter fractional Fourier transform

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