改进谐波小波及其在振动信号时频分析中的应用

针对谐波小波在时域衰减速度慢的缺点，对其在频域进行光滑化处理，得到了性质更好的改进谐波小波。由于采用光谱化方法只能得到改进小波在频域的表达式，因而采用基于FFT的算法对它进行计算。针对振动信号一般舸样点较多的特点，采用计算等间隔小波系数的方法以减少计算量。以改进谐波小波对某新型导弹空中点火试验的振动信号进行了时频分析，并采用计算时频图等高图的方法以消除大部分无用的信息，得到了振动信号的高清晰时频图。

Application of Improved Harmonic Wavelets on Time-Frequency Analysis of Vibration Signal

The disadvantage of harmonic wavelets is that the rate of decay is so low (proportional to x -1 ) that localization is not very precise. This is because the Fourier transform of the wavelets is restricted to a specified frequency band. This paper gives a method smoothing the boxcar spectrum of harmonic wavelets to improve localization in time domain. The paper presents a method which improves the harmonic wavelets so that the improved wavelets have simpler structure and adjustable decay rates in time domain.The improved harmonic wavelets are found to be more suitable than the conventional harmonic wavelets for vibration analysis because their rate of decay in time domain is much higher. The improved wavelets can also be computed by a numerically efficient algorithm based on the FFT. In this paper, the improved harmonic wavelets are used to analyze the dynamical behavior of a missile.Then a time frequency map is obtained, which can trace how the missile vibration signal changes with time.Finally the physical cause represented by the signal is interpreted.