Vibration Signal Extraction Based on FFT and Least Square Method

Fast Fourier Transform (FFT), widely used in spectrum analysis, is a powerful processing vibration signal to obtain the signal amplitude, frequency, and phase. However, the discrepancy between the FFT derived values and the real values could be introduced due to spectral leakage and spectral interference. This inconsistency is prohibited in some applications, for example, the extraction of vibration characteristics for power machinery and failure diagnostics. Therefore, the methodology to obtain the frequency domain's exact characteristics becomes one of the most concerning topics in vibration and signal processing. In this paper, a newly developed iterative method is presented in detail for high-accuracy characteristic extraction of multiple frequencies periodic vibration signals based on FFT and least square method. In the situation where the attenuation signal is superposed onto the periodic signal, the accurate characteristics of these two signals are also obtainable. Besides, simulation examples are provided, showing that the proposed method can be applied to the single-frequency signal, multiple frequency signals (including the signals of which the adjacent frequencies are close), and attenuation signal. The experimental results show that using the data processing method in this paper to extract the attenuation signals' characteristics, and the fitted attenuation curves are in good agreement with the actual attenuation signals. The method shown in this paper can be used for precisely extracting the characteristics of the periodic signal and attenuation signals in engineering.