A new sliding discrete Fourier transform phase difference measurement method for extreme frequency signals

While there are many ultralow frequency signals and ultrahigh frequency signals in the vibration engineering field, the existing discrete Fourier transform (DFT) spectrum analysis methods bring about significant phase difference errors when measuring these extreme frequency signals. In order to improve the performance of these methods, a new sliding DFT phase difference measurement method for extreme frequency signals is proposed. First, the spectrum of extreme frequency signals is analyzed, which is used to illuminate the contribution of negative frequency. Then, the spectrum leakage is restrained by adopting rectangular self-convolution windows (RSCWs). Finally, the sliding recursive algorithm is introduced to reduce the computational load. The whole processes of formula derivation for phase difference measurement by adopting different RSCWs are described in detail. Simulations show that the proposed method obtains a better real time characteristic and a higher phase difference measurement precision than conventional DFT methods, which is suitable especially for extreme frequency vibration signals.