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We propose a new method for analysis of the sampling and reconstruction conditions of signals by use of the weighted fractional Fourier transform (WFRFT). It is shown that the WFRFT domain 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 band-limited in the traditional Fourier sense. An orthogonal sampling basis for the class of band-limited signals in the sense of WFRFT is also given. Experimental results are proposed to verify the accuracy and effectiveness of the obtained results.