Two New Sliding DTFT Algorithms for Phase Difference Measurement Based on a New Kind of Windows

For the ultra-low frequency signals or adjacent Nyquist frequency signals, which exist in the vibration engineering domain, the traditional DTFT-based algorithm shows serious bias for phase difference measurement. It is indicated that the spectrum leakage and negative frequency contribution are the essential causes of the bias. In order to improve the phase difference measurement accuracy of the DTFT-based algorithm, two new sliding DTFT algorithms for phase difference measurement based on a new kind of windows are proposed, respectively. Firstly, the new kind of windows developed by convolving conventional rectangular windows is introduced, which obtains a stronger inhibition of spectrum leakage. Then, with negative frequency contribution considered, two new formulas for phase difference calculation under the new kind of windows are derived in detail. Finally, the idea of sliding recursive is proposed to decrease the computational load. The proposed algorithms are easy to be realized and have a higher accuracy than the traditional DTFT-based algorithm. Simulations and engineering applications verified the feasibility and effectiveness of the proposed algorithms.