Laguna P, Moody G B, Mark R G
Departamento de Ingeniería Electrónica y Comunicaciones, Universidad de Zaragoza, Spain.
IEEE Trans Biomed Eng. 1998 Jun;45(6):698-715. doi: 10.1109/10.678605.
This work studies the frequency behavior of a least-square method to estimate the power spectral density of unevenly sampled signals. When the uneven sampling can be modeled as uniform sampling plus a stationary random deviation, this spectrum results in a periodic repetition of the original continuous time spectrum at the mean Nyquist frequency, with a low-pass effect affecting upper frequency bands that depends on the sampling dispersion. If the dispersion is small compared with the mean sampling period, the estimation at the base band is unbiased with practically no dispersion. When uneven sampling is modeled by a deterministic sinusoidal variation respect to the uniform sampling the obtained results are in agreement with those obtained for small random deviation. This approximation is usually well satisfied in signals like heart rate (HR) series. The theoretically predicted performance has been tested and corroborated with simulated and real HR signals. The Lomb method has been compared with the classical power spectral density (PSD) estimators that include resampling to get uniform sampling. We have found that the Lomb method avoids the major problem of classical methods: the low-pass effect of the resampling. Also only frequencies up to the mean Nyquist frequency should be considered (lower than 0.5 Hz if the HR is lower than 60 bpm). We conclude that for PSD estimation of unevenly sampled signals the Lomb method is more suitable than fast Fourier transform or autoregressive estimate with linear or cubic interpolation. In extreme situations (low-HR or high-frequency components) the Lomb estimate still introduces high-frequency contamination that suggest further studies of superior performance interpolators. In the case of HR signals we have also marked the convenience of selecting a stationary heart rate period to carry out a heart rate variability analysis.
本文研究了一种用于估计非均匀采样信号功率谱密度的最小二乘法的频率特性。当非均匀采样可以建模为均匀采样加上一个平稳随机偏差时，该频谱会在平均奈奎斯特频率处导致原始连续时间频谱的周期性重复，并且存在一个影响高频段的低通效应，该效应取决于采样离散度。如果离散度与平均采样周期相比很小，则基带处的估计是无偏的，且几乎没有离散度。当非均匀采样通过相对于均匀采样的确定性正弦变化来建模时，所获得的结果与小随机偏差情况下的结果一致。在心率（HR）序列等信号中，这种近似通常能很好地满足。理论预测的性能已经通过模拟和实际HR信号进行了测试和验证。将 Lomb 方法与包括重采样以获得均匀采样的经典功率谱密度（PSD）估计器进行了比较。我们发现，Lomb 方法避免了经典方法的主要问题：重采样的低通效应。此外，只应考虑高达平均奈奎斯特频率的频率（如果心率低于60次/分钟，则低于0.5赫兹）。我们得出结论，对于非均匀采样信号的PSD估计，Lomb方法比具有线性或三次插值的快速傅里叶变换或自回归估计更合适。在极端情况下（低心率或高频成分），Lomb估计仍然会引入高频污染，这表明需要对性能更优的插值器进行进一步研究。对于HR信号，我们还指出了选择一个平稳心率周期来进行心率变异性分析的便利性。
