Determination to the Confidence Level of PSD Estimation with Given D.O.F. Based on WELCH Algorithm
Xue-Wang Zhu, Si-Jian Zhang, Qinglin Liu · 2015
Approach is proposed for determining the confidence level of the power spectral density (PSD) estimation with give Degree-of-freedom (D.O.F.) based on WELCH algorithm, a modified periodogram estimator for estimating PSD.A relationship between the random error, defined as a ratio of variance and mean value, and the D.O.F. is achieved firstly due to the analysis results of the statistic characteristic quantities.Then a quantitative relation between the confidence level, described as confidence probability and confidence interval, and the D.O.F. is established.Some examples are provided finally to demonstrate the proposed method.It is showed from the results that the PSD WELCH estimation with 128 D.O.F. have probability 68.4% only to ensure the true PSD within 0.88~1.2times the estimation value.