Abstract：A novel method using the regular distributed partial data for the periodic signal analysis is proposed. Differential measurement of the non-sinusoidal voltage signal based on a staircase waveform is discussed, where the first and last parts of each step are discarded to overcome the transient effect and Gibbs phenomenon. In Fourier transformation of higher frequency components the significant deviations will be caused. When the base functions are divided with same mode, the relevant influence matrix will be derived; its inverse matrix can then recover the original Fourier coefficients. The key point here is to simplify calculation of the inverse matrix. The condition of this simplification is proposed in which the influence matrix becomes sparse. The limiting amplitude condition required in the differential sampling based on the staircase waveform is investigated. Simulations and demonstration experiments show an acceptable workload and a very high accuracy. This method can be applied to spectrum analysis when partial samples are regularly lost.
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2019, Vol. 40 
