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Gap filling and noise reduction of unevenly sampled data by means of the Lomb-Scargle periodogram

机译：利用Lomb-Scargle周期图填充和减少不均匀采样数据的噪声

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The Lomb-Scargle periodogram is widely used for the estimation of the power spectral density ofunevenly sampled data. A small extension of the algorithm of the Lomb-Scargle periodogram permitsthe estimation of the phases of the spectral components. The amplitude and phase information issufficient for the construction of a complex Fourier spectrum. The inverse Fourier transform canbe applied to this Fourier spectrum and provides an evenly sampled series (Scargle, 1989).We are testing the proposed reconstruction method by means of artificial time series and realobservations of mesospheric ozone, having data gaps and noise. For data gap filling and noisereduction, it is necessary to modify the Fourier spectrum before the inverse Fourier transform is done.The modification can be easily performed by selection of the relevant spectral components which areabove a given confidence limit or within a certain frequency range. Examples with time series oflower mesospheric ozone show that the reconstruction method can reproduce steep ozone gradients around sunrise and sunset andsuperposed planetary wave-like oscillations observed by a ground-based microwave radiometer at Payerne.The importance of gap filling methods for climate change studies is demonstrated by means of long-termseries of temperature and water vapor pressure at the Jungfraujoch stationwhere data gaps from another instrument have been inserted before the linear trend is calculated.The results are encouraging but the present reconstruction algorithm is far awayfrom being reliable and robust enough for a serious application.
机译：Lomb-Scargle周期图被广泛用于估计不均匀采样数据的功率谱密度。 Lomb-Scargle周期图算法的一个小扩展允许估算频谱分量的相位。振幅和相位信息足以构成复杂的傅立叶频谱。可以将傅立叶逆变换应用于该傅立叶光谱，并提供一个均匀采样的序列（Scargle，1989）。对于数据间隙填充和降噪，必须在进行逆傅立叶变换之前修改傅立叶频谱。通过选择高于给定置信度限制或在特定频率范围内的相关频谱分量，可以轻松进行修改。较低的中层臭氧时间序列的例子表明，该重建方法可以重现出日出和日落附近陡峭的臭氧梯度，以及在Payerne的地面微波辐射计观测到的叠加的行星波状振荡。通过在少女峰站的温度和水蒸气压力的长期序列，在计算线性趋势之前已插入了另一台仪器的数据间隙，结果令人鼓舞，但目前的重建算法远不够可靠和强大认真的应用。

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