¹ National Key Laboratory of Tunable Laser Technology, Harbin Institute of Technology, Harbin, China
² Science Research Center, Research Academy of Science and Technology, Harbin Institute of Technology, Harbin, China

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Abstract—We propose a new method for analysis of the sampling and reconstruction conditions of signals by use of the multiple-parameter fractional Fourier transform (MPFRFT). It is shown that the MPFRFT may provide a novel understanding of sampling process. The proposed sampling theorem generalizes classical Shannon sampling theorem and Fourier series expansion, and provides a fullreconstruction procedure of certain signals that are not bandlimited in the conventional Fourier transform domain. An orthogonal basis for the class of signals which are bandlimited in the MPFRFT domain is also given. Experimental results are proposed to verify the accuracy and effectiveness of the obtained results.

Index Terms—sampling theorem, fractional Fourier transform, multiple-parameter fractional Fourier transform

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Cite: Qiwen Ran, Hui Zhao, Guixia Ge, Jing Ma, and Liying Tan, " Sampling Theorem Associated with Multiple-parameter Fractional Fourier Transform," Journal of Computers vol. 5, no. 5, pp. 695-702, 2010.