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Characterize highly oscillating frequency modulation using generalized Warblet transform

机译:使用广义Warblet变换表征高振荡频率调制

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In this paper, in order to characterize highly oscillating time-frequency patterns of signals, whose instantaneous frequency (IF) is periodic or non-periodic, a generalized Warblet transform (GWT) is proposed. By replacing sine function kernel of conventional Warblet transform with Fourier series function, the GWT is able to generate a time-frequency representation (TFR) with satisfying energy concentration for such signals. As any oscillating function can be well approximated by a Fourier series, the GWT is guaranteed to provide an effective way to achieve accurate IF estimation. In addition, a signal-dependent iterative procedure for coefficients estimation is developed to enable the GWT to be applied in practice. Using the Fourier spectrum of the IF, the coefficients of the Fourier series kernel function of the GWT can be estimated and refined adaptively. The effectiveness of the proposed method is verified through comparing with other time-frequency analysis methods on several numerical examples and experimental vibration signal, which is collected from a rotor test rig undergoing speed-up and slow-down stages. Crown Copyright © 2011 Published by Elsevier Ltd. All rights reserved.
机译:为了表征瞬时频率(IF)为周期性或非周期性的信号的高振荡时频模式,提出了一种广义Warblet变换(GWT)。通过用傅立叶级数函数替换常规Warblet变换的正弦函数核,GWT能够生成满足此类信号能量集中的时频表示(TFR)。由于傅立叶级数可以很好地近似任何振荡函数,因此可以保证GWT提供了一种有效的方法来实现准确的IF估计。另外,开发了用于信号估计的依赖信号的迭代过程,以使GWT能够在实践中应用。使用中频的傅立叶谱,可以自适应地估计和细化GWT的傅立叶级数核函数的系数。通过与其他时频分析方法的几个数值示例和实验振动信号进行比较,验证了该方法的有效性。实验振动信号是从经过加速和减速阶段的转子试验台上收集的。冠版权所有©2011 Elsevier Ltd.保留所有权利。

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