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Instantaneous frequency tracking of a sinusoidally frequency-modulated signal with low modulation index: application to laser measurements in acoustics

机译:具有低调制指数的正弦频率调制信号的瞬时频率跟踪:在声学中的激光测量中的应用

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摘要

In this paper, the problem of the instantaneous frequency (IF) estimation of sinusoidally frequency-modulated signals has been addressed, especially when small modulation indices are involved. Such a problem is encountered when laser-Doppler velocity measurements are carried out in acoustics. The amplitude and phase of the sine-wave IF law are then the searched parameters. A new time-frequency transform, specifically designed for tracking sine wave IF variations has been developed, using as a starting point the formalism of the Polynomial Wigner-Ville distributions. The computation of this transform, quick and simple, followed by an amplitude and phase estimation of the IF law, is the so-called Time-Frequency Synchronous Detector (TFSD). After a derivation of the Cramer-Rao bounds for the estimation of the searched parameters, the performances of the detector are studied and compared to those of the Cross Wigner-Ville-based estimator (CWV) and those of a parametric estimator based on the maximum likelihood (ML), For moderate SNR, the TFSD represents a better compromise in terms of bias, variance and computational time than the CWV. The ML performances are slightly better for synthesized signals than those of the time-frequency methods, but the latter provide significantly better estimates for experimental signals.
机译:在本文中,正弦频率调制信号的瞬时频率(IF)估计问题已得到解决,特别是在涉及小的调制指数时。当在声学中进行激光多普勒速度测量时会遇到这样的问题。然后,搜索到的参数是正弦波IF律的幅度和相位。已经开发了一种新的时频变换,专门设计用于跟踪正弦波IF变化,使用多项式Wigner-Ville分布的形式主义作为起点。这种转换的计算既快速又简单,随后是IF律的幅度和相位估计,即所谓的时频同步检测器(TFSD)。在推导用于估计搜索参数的Cramer-Rao边界后,研究了检测器的性能,并将其与基于Cross Wigner-Ville的估计器(CWV)以及基于最大值的参数估计器的性能进行了比较。对于中等SNR,TFSD在偏差,方差和计算时间方面表现出比CWV更好的折衷。合成信号的ML性能比时频方法的ML性能稍好,但是后者为实验信号提供了更好的估计。

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