The multiple-parameter fractional Fourier transform

  • Jun Lang
  • Ran Tao
  • QiWen Ran
  • Yue Wang


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 \( \mathfrak{M},\mathfrak{N} \in \mathbb{Z}^M \). 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.


multiple-parameter fractional Fourier transform weight-type fractional Fourier transform multiplicity of the fractional Fourier transform signal processing 


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Copyright information

© Science in China Press and Springer-Verlag GmbH 2008

Authors and Affiliations

  1. 1.Department of Electronic EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.Department of MathematicsHarbin Institute of TechnologyHarbinChina

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