约束付立叶光滑方法及其在水文中的应用

阐述了付立叶（Ｆｏｕｒｉｅｒ）光滑方法的最小二乘性质，并据此提出了约束付立叶光滑 法，初步解决了水文变量（流量、雨量等）具有周期性变化规律的统计特征值（均值、方 差等）的最优估计。与建立在等距离离散时间序列上传统的离散付立叶光滑方法不同，提 出了非等距离的离散时间序列的最优付立叶光滑方法以及付立叶系数的递推最小二乘法 估计。

Constrained Fourier Smoothing of Time Series and its Application in Hydrological Analysis

The paper shows that the Fourier smoothing possesses least squares properties and proposes the constrained Fourier smoothing method,applied to estimate the seasonal means of hydrological time series. The traditional discrete Fourier smoothing based on the time series with equal time intervals, while the proposed optimal Fourier smoothing method can solve time series problems with unequal time intervals. The recursive least squares estimation of the Fourier coefficients is also proposed and discussed.