| 朱学旺,刘青林,张思箭.Welch谱估计的随机误差与置信度[J].装备环境工程,2015,12(1):34-38. ZHU Xue-wang,LIU Qing-lin,ZHANG Si-jian.Random Error and Confidence Level of Welch Spectral Estimation[J].Equipment Environmental Engineering,2015,12(1):34-38. |
| Welch谱估计的随机误差与置信度 |
| Random Error and Confidence Level of Welch Spectral Estimation |
| 投稿时间：2014-09-25 修订日期：2015-02-15 |
| DOI：10.7643/issn.1672-9242.2015.01.008 |
| 中文关键词: 功率谱估计 Welch方法 随机误差 置信度 置信概率 置信区间 |
| 英文关键词:PSD estimation Welch PSD estimation random error confidence level confidence probability confidence interval |
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| 中文摘要: |
| 目的 分析Welch谱估计的随机误差及置信度。方法 首先导出Welch谱估计量随机误差的表达式， 然后采用正态标准化处理方法， 将Welch谱估计分量转化为χ2变量。结果 获得了 Welch谱估计的置信度分析方法。结论 以128自由度的Welch谱估计结果的随机误差 （12.5％） 作为相对置信区间， 则其置信概率为68.4％， 若要达到95.5％以上置信概率， 则Welch谱估计的自由度不能小于512， 相应的随机误差为6.25％。 |
| 英文摘要: |
| Objective To analyze the random error and confidence level of Welch estimation for power spectral density (PSD). Methods The expression for Welch PSD estimation random error was firstly deduced, and the Welch spectral estimation component was converted into χ 2 variable by standardizing as a square sum of normal Gaussians. Results An analysis method for the confidence level of Welch spectral estimation was obtained. Conclusion The confidence probability for a 128 DOF Welch PSD estimation was 68.4% when the relative confidence interval described by the random error was 12.5%. To increase the confidence probability to 95.5%, the DOF of Welch PSD estimation must be no less than 512, corresponding to a random error of 6.25%. |
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