Fourier Transform and Reconstruction of Periodic Signal Based on Non-Uniformity Sampling

This paper proposes a non-uniformity synchronous sampling method for periodic signal, establishes the discrete Fourier transform (DFT) algorithm model and derives an interpolation algorithm, which restores the original signal using non-uniformity-sampling value. It has effectively restrained the error during the sampling period and also made the resolution of the time not exceed one T_d (resolution of the timer). And the calculating amount of multiplication about the DFT algorithm is half of general DFT algorithm. The key of the reconstruction is to separate original sampling signal into superposition of several uniformity sampling signals, which make it possible to adopt Shannon theorem. Because there is no time deviation between actual and theoretic sampling point, the precision of interpolating formulae is improved obviously. The accuracy of interpolation algorithm is verified by simulation results. The non-uniform synchronous sampling method, the DFT algorithm and the reconstruction algorithm can be applied extensively in the power supply monitoring system.