间隔时间序列的傅立叶分析：太阳和恒星振荡参数的改进估计
Fourier Analysis of Gapped Time Series: Improved Estimates of Solar and Stellar Oscillation Parameters
摘要：
定量的日震和星震学需要非常精确地测量恒星振荡全球模式的频率、振幅和寿命。众所周知，这些测量的精度取决于观测的总长度（T）、质量和完整性。除了在一些简单的情况下，在测量精度的数据的差距的影响是知之甚少，特别是在傅立叶空间中，可观察的卷积与观察窗口引入不同的频率之间的相关性。在这里，我们描述并实现了一个相当一般的方法来检索振荡参数的极大似然估计，同时考虑到适当的统计观测。我们的拟合方法适用于复傅立叶空间，并利用相位信息。我们考虑了类太阳随机振荡和长寿命的谐波振荡，加上随机噪声。使用数值模拟，我们证明了存在的情况下，我们的改进的拟合方法是更少的偏见，并具有更高的精度比忽略频率相关性。对于低信噪比的类太阳振荡来说尤其如此。例如，我们讨论的情况下，模式频率估计的精度增加了五倍，占空比为15%。在长寿命的正弦振荡的情况下，适当的治疗的频率相关性并没有提供任何显着的改善，但我们确认，模式频率可以测量从间隙数据在一个更好的精度比1/T瑞利分辨率。
英文摘要：
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on the total length (T), quality, and completeness of the observations. Except in a few simple cases, the effect of gaps in the data on measurement precision is poorly understood, in particular in Fourier space where the convolution of the observable with the observation window introduces correlations between different frequencies. Here we describe and implement a rather general method to retrieve maximum likelihood estimates of the oscillation parameters, taking into account the proper statistics of the observations. Our fitting method applies in complex Fourier space and exploits the phase information. We consider both solar-like stochastic oscillations and long-lived harmonic oscillations, plus random noise. Using numerical simulations, we demonstrate the existence of cases for which our improved fitting method is less biased and has a greater precision than when the frequency correlations are ignored. This is especially true of low signal-to-noise solar-like oscillations. For example, we discuss a case where the precision on the mode frequency estimate is increased by a factor of five, for a duty cycle of 15%. In the case of long-lived sinusoidal oscillations, a proper treatment of the frequency correlations does not provide any significant improvement; nevertheless we confirm that the mode frequency can be measured from gapped data at a much better precision than the 1/T Rayleigh resolution.
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