Merriam G R, Wachter K W
Am J Physiol. 1982 Oct;243(4):E310-8. doi: 10.1152/ajpendo.1982.243.4.E310.
There is no generally accepted procedure for identifying ultradian pulsations in hormonal time series. We suggest an approach based on removing long-term trends, such as diurnal rhythms, from the series of observations; identifying peaks in the residual series; and resolving each peak, if appropriate, into overlapping secretory episodes. The first step uses a robust smoothing technique to generate a smoothed series that omits peaks or trends with time constants less than 6--12 h. The smoothed series is subtracted from the original, and in the second step their difference, the residual series, is examined for the presence of peaks. The standard deviation of the assay is calculated at each point, and the residuals are rescaled in terms of this unit. Peaks are identified as individual subseries elevated above the base line of duration n, all the points in which have magnitude at least G(n), where the values of G are cut-off criteria based on the width of the peak. Thus the algorithm selects both narrow high peaks and broader peaks that may be lower. The user selects the G(n) for each hormone based on theoretical considerations or a set of calibration data series. Points that meet these criteria are identified as belonging to peaks and flagged. To assure that the smoothing process is not influenced by runs of closely spaced peaks, these flagged points are then assigned a reduced weight, and the smoothing is repeated; the revised residuals are then reexamined. After these two steps are iterated until there are no further changes, each peak is examined once more to determine whether it can be resolved into more than one overlapping peak. Finally, the process collects statistics on the average frequency and amplitude of the peaks. We have developed computer programs to carry out these algorithms.
在激素时间序列中，目前尚无普遍接受的识别超日波动的程序。我们提出一种方法，该方法基于从观测序列中去除长期趋势，如昼夜节律；识别残差序列中的峰值；并在适当情况下将每个峰值分解为重叠的分泌事件。第一步使用稳健的平滑技术生成一个平滑序列，该序列省略了时间常数小于6 - 12小时的峰值或趋势。将平滑序列从原始序列中减去，在第二步中，检查它们的差值即残差序列中是否存在峰值。在每个点计算测定的标准差，并根据该单位对残差进行重新缩放。峰值被识别为高于持续时间为n的基线的单个子序列，其中所有点的幅度至少为G(n)，其中G的值是基于峰值宽度的截止标准。因此，该算法既选择窄的高峰值，也选择可能较低的宽峰值。用户根据理论考虑或一组校准数据序列为每种激素选择G(n)。满足这些标准的点被识别为属于峰值并进行标记。为确保平滑过程不受紧密间隔峰值序列的影响，然后为这些标记点分配较小的权重，并重复平滑过程；然后重新检查修订后的残差。重复这两个步骤，直到没有进一步变化，然后再次检查每个峰值，以确定它是否可以分解为多个重叠的峰值。最后，该过程收集有关峰值平均频率和幅度的统计数据。我们已经开发了计算机程序来执行这些算法。
