Hof A L
University of Groningen, Laboratory of Medical Physics, The Netherlands.
IEEE Trans Biomed Eng. 1991 Nov;38(11):1077-88. doi: 10.1109/10.99071.
Frequency shifts in random signals, e.g., EMG or Doppler ultrasound, can be followed by monitoring one or more parameters of the power spectrum. When such a frequency parameter is determined over a finite length of the signal, a random error and sometimes a systematic error or bias are introduced. Approximate expressions, in terms of moments of the power spectrum, have been derived for bias and standard deviation of the estimates for mean frequency, zero-crossing frequency, and fractile frequency (of which the median frequency is a special case). Experimental results from surface EMG recordings of three human muscles in constant force isometric contractions were in agreement with the theoretical predictions. In this case the mean frequency had the smallest random error. It turned out that the measured values of the zero-crossing frequency can deviate considerably from the predictions by the Rice formula when the amplitude distribution is not exactly Gaussian. In the presence of noise, all frequency parameters show a systematic deviation, depending on the signal-to-noise ratio. In addition to known results on this deviation for mean and zero-crossing frequency, an exact and an approximate expression for the fractile frequency are given. In the case of EMG plus wide-band white noise, the median frequency has the best immunity to noise.
随机信号（如肌电图或多普勒超声）中的频率偏移可以通过监测功率谱的一个或多个参数来跟踪。当在信号的有限长度上确定这样一个频率参数时，会引入随机误差，有时还会引入系统误差或偏差。已根据功率谱的矩推导出了平均频率、过零频率和分位数频率（其中中位数频率是一个特殊情况）估计值的偏差和标准差的近似表达式。对人体三块肌肉进行恒力等长收缩时表面肌电图记录的实验结果与理论预测一致。在这种情况下，平均频率的随机误差最小。结果表明，当幅度分布不完全是高斯分布时，过零频率的测量值可能会与莱斯公式的预测有很大偏差。在存在噪声的情况下，所有频率参数都会出现系统偏差，这取决于信噪比。除了关于平均频率和过零频率偏差的已知结果外，还给出了分位数频率的精确表达式和近似表达式。在肌电图加宽带白噪声的情况下，中位数频率对噪声的免疫力最强。
