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From the sampling theory, if the bandwidth of a signal is small, then the sampling interval can be very large. In this paper, a higher order modulation scheme is proposed to minimize the bandwidth of a signal. Then, combining the proposed high order modulation with the fractional Fourier transform and time-frequency analysis, a new sampling algorithm is presented. The proposed sampling algorithm can minimize the area of a signal in the time-frequency domain and much reduce the number of sampling points. Simulation results show that, when using the proposed sampling algorithm, the amount of data required for recording a signal can be much less. The proposed sampling algorithm is especially efficient for sampling a time variant signal, such as the voice of an animal and the speech signal.