Science in China Series F: Information Sciences

, 51:1010

The multiple-parameter fractional Fourier transform


  • Jun Lang
    • Department of Electronic EngineeringBeijing Institute of Technology
    • Department of Electronic EngineeringBeijing Institute of Technology
  • QiWen Ran
    • Department of MathematicsHarbin Institute of Technology
  • Yue Wang
    • Department of Electronic EngineeringBeijing Institute of Technology

DOI: 10.1007/s11432-008-0073-6

Cite this article as:
Lang, J., Tao, R., Ran, Q. et al. Sci. China Ser. F-Inf. Sci. (2008) 51: 1010. doi:10.1007/s11432-008-0073-6


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 transformweight-type fractional Fourier transformmultiplicity of the fractional Fourier transformsignal processing

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© Science in China Press and Springer-Verlag GmbH 2008