Sampling Theorem Associated with Multiple-parameter Fractional Fourier Transform

We propose a new method for analysis of the sampling and reconstruction conditions of signals by use of the multiple-parameter fractional Fourier transform ( MP FRFT). It is shown that the MP FRFT may provide a novel understanding of sampling process. The proposed sampling theorem generalizes classical Shannon sampling theorem and Fourier series expansion, and provides a full-reconstruction 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 i n the MPFRFT domain is also given. Experimental results are proposed to verify the accuracy and effectiveness of the obtained results.

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