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| Random Error and Confidence Level of Welch Spectral Estimation |
| Received:September 25, 2014 Revised:February 15, 2015 |
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| DOI：10.7643/issn.1672-9242.2015.01.008 |
| KeyWord:PSD estimation Welch PSD estimation random error confidence level confidence probability confidence interval |
| Author | Institution |
| ZHU Xue-wang |
Institute of Systems Engineering，CAEP，Mianyang ，China |
| LIU Qing-lin |
Institute of Systems Engineering，CAEP，Mianyang ，China |
| ZHANG Si-jian |
Institute of Systems Engineering，CAEP，Mianyang ，China |
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| Abstract: |
| 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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