标题： SigSpec - I. 傅里叶空间中的频率和相位解析显著性 显示英文标题

标题： SigSpec - I. Frequency- and Phase-Resolved Significance in Fourier Space

摘要： 在恒星测光和光谱的时间序列中识别具有低信噪比的频率，并准确测量其振幅比和峰值宽度，是星震学的关键目标。 这些也是对于存在间隙的时间序列或数据采样率不恒定的时间序列的挑战，即使使用现代离散傅里叶变换（DFT）软件也是如此。 此外，Lomb和Scargle引入的虚警概率是一种近似值，在数据间隙较长的时间序列中，这种近似值变得不够可靠。 本文提出了一种严格的统计方法，称为SigSpec，用于确定DFT中峰值显著性的方法。 SigSpec基于一个解析解，即给定振幅的DFT峰值并非由非等间距数据集中的白噪声引起的概率。 如果同时考虑频率和相位，则可以显式推导出由白噪声生成的振幅谱的基本概率密度函数（PDF）。 本文定义并评估了一个无偏统计估计量——“频谱显著性”，它取决于DFT中的频率、振幅和相位，并且考虑了时域采样。 我还比较了该估计量与其他已确立技术的结果，并通过地面和空间测光数据的一些例子展示了SigSpec的有效性，说明了SigSpec如何处理噪声和时域采样对确定显著频率的影响。 显示英文摘要

摘要： Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also challenges for time series with gaps or whose data are not sampled at a constant rate, even with modern Discrete Fourier Transform (DFT) software. Also the False-Alarm Probability introduced by Lomb and Scargle is an approximation which becomes less reliable in time series with longer data gaps. A rigorous statistical treatment of how to determine the significance of a peak in a DFT, called SigSpec, is presented here. SigSpec is based on an analytical solution of the probability that a DFT peak of a given amplitude does not arise from white noise in a non-equally spaced data set. The underlying Probability Density Function (PDF) of the amplitude spectrum generated by white noise can be derived explicitly if both frequency and phase are incorporated into the solution. In this paper, I define and evaluate an unbiased statistical estimator, the "spectral significance", which depends on frequency, amplitude, and phase in the DFT, and which takes into account the time-domain sampling. I also compare this estimator to results from other well established techniques and demonstrate the effectiveness of SigSpec with a few examples of ground- and space-based photometric data, illustratring how SigSpec deals with the effects of noise and time-domain sampling in determining significant frequencies.