Phase identification for space charge measurement under periodic stress of an arbitrary waveform based on the Hilbert transform

Data processing (i.e. phase identification) using the instantaneous phase φ ′( t ) defined by the Hilbert transform is discussed to confirm the detecting phase of the space charge observed by the pulsed electroacoustic method under the periodic wave V a ( t ). The discrete voltage V a ( i ) of the periodic wave at the detecting phase φ ( i ) is used for phase identification, and φ ( i ) is equally distributed to obtain N p divisions for the phase within one period. The accuracy of the discrete instantaneous phase φ ′( i ) is significantly determined by the number of samples N for the discrete voltage V a ( i ). The instantaneous phase is consistent with the real phase of pure sine and cosine waves, and this phase linearly varies with time. However, the instantaneous phase non-linearly varies with time under the periodic stress of arbitrary waveforms. This limitation can be resolved using the base wave component, i.e. sine or cosine wave of V a ( t ), which is acquired by the Fourier transform. Finally, the space charge behaviour in low-density polyethylene under square and sine waves with offset is detected to verify the accuracy and effectiveness of the proposed method.