论文标题
韦尔奇方法无偏见的两翼方法
Unbiased two-windows approach for Welch's method
论文作者
论文摘要
周期图方法广泛用于估计功率和跨光谱，其中韦尔奇的方法是最受欢迎的。先前的研究已经分析了功率谱估计的方差，并开发了分析概率函数，表明该方法在应用于白噪声信号或无限窗口长度的极限时无偏见。但是，当使用有限窗口时，没有针对更复杂的信号的估计偏差表达式。在这项研究中，我们表明，对于有限的窗口长度，Welch的方法对白色信号以外的所有信号都有偏差。提出了一种新颖的两窗口方法，该方法是将应用于具有界相关长度的信号时无偏的。数值实验用于说明新方法的优势。
Periodogram methods are widely used for the estimation of power- and cross-spectra, of which Welch's method is the most popular. Previous studies have analyzed the variance of the power spectra estimates and developed analytical probability functions, showing that the approach is unbiased when applied to white-noise signals or in the limit of infinite window lengths. However, no explicit expression for the estimation bias is available for more complex signals when finite windows are used. In this study, we show that, for finite window lengths, Welch's method is biased for all signals other than the white-noise signal. A novel two-window approach that is unbiased when applied to signals with bounded correlation lengths is proposed. Numerical experiments are used to illustrate the advantages of the novel approach.
