Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal

Abstract

The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise. The relationship between windowing transform and filtering is analyzed first in the paper. The advantage of adjustable time-frequency window of wavelet transform is introduced. Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed. The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed, and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded. Thirdly, by extending the harmonic wavelet transform, the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper. Then comparing with the Hanning window, the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown, and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented. Finally, the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise, and the satisfactory results are achieved. The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.