Spectrum Recovery Method of Adjacent Harmonic Signals with Extremely Short Sample Time

In some engineering scenarios, detecting harmonics signals with extremely short sample time is necessary but a considerable challenge. Due to the lack of sample points, the insufficient frequency resolution can not separate different harmonic components with adjacent frequencies. In this paper, the sparsity of the harmonic spectrum is considered, and the sine (cosine) basis is adopted to represent the harmonic signal sparsely. Moreover, the group sparsity of the amplitude of the sine (cosine) basis is constrained by the block L1 norm. The simulation results show that the proposed method can effectively separate harmonic components and has high separation accuracy.