Comparative analysis of phase difference estimation methods based on Hilbert transform with or without endpoint effect

The Hilbert transform method has its own particular superiority in phase difference estimation, but endpoint effect limits its precision when data record is short. We firstly analyze endpoint effect of Hilbert transform and point out its reason is spectrum leakage. Then, an all phase Hilbert transform method is proposed to solve this problem. In this method, a pretreatment is carried out at the first place that data record is recomposed with all cases of truncation been considered. In succession, Hilbert transform of the pretreated data is calculated. Phase difference is estimated by triangle operation of the pretreated data and its Hilbert transform. Comparative analysis of phase difference estimation methods based on Hilbert transform with or without endpoint effect is carried out. Theoretical analysis, simulation and experimental results collaborate to prove the validity of the proposed method. Comparative studies demonstrate that the proposed method suppresses endpoint effect effectively and improves the precision significantly when calculational points are deficiency.