论文标题
加性高斯白噪声下功率光谱子带能量比的统计特征
The Statistical Characteristics of Power-Spectrum Subband Energy Ratios under Additive Gaussian White Noise
论文作者
论文摘要
功率光谱子带能量比（PSER）已应用于各种领域，但有关其统计特性的报告受到限制。因此，本研究在存在纯噪声和混合信号的加性高斯白噪声的情况下研究了这些特征。通过分析功率谱箱的概率和独立性以及F和beta分布之间的关系，我们为PSER开发了概率分布。结果表明，在纯噪声的情况下，PSER遵循β分布。另外，概率密度函数和分位数与噪声方差没有任何关系，仅与功率谱中的线数，也就是说，PSER不受噪声的影响。当高斯白噪声与已知信号混合时，所得的PSER遵循双中心β分布。在这种情况下，很难识别分位数，因为概率密度和累积分布函数由无限序列表示。但是，当光谱箱不包含已知信号的功率谱时，发现了近似的分位数。在纯噪声的情况下，严格证明该分位数与分位数一致，并为识别有效信号提供了方便的方法。
The power-spectrum subband energy ratio (PSER) has been applied in a variety of fields, but reports on its statistical properties have been limited. As such, this study investigates these characteristics in the presence of additive Gaussian white noise for both pure noise and mixed signals. By analyzing the probability and independence of power spectrum bins, and the relationship between the F and beta distributions, we develop a probability distribution for the PSER. Results showed that in the case of pure noise, the PSER follows a beta distribution. In addition, the probability density function and the quantile exhibited no relationship with the noise variance, only with the number of lines in the power spectrum, that is, PSER is not affected by noise. When Gaussian white noise was mixed with the known signal, the resulting PSER followed a doubly non-central beta distribution. In this case, it was difficult to identify the quantile, as the probability density and cumulative distribution functions were represented by infinite series. However, when a spectral bin did not contain the power spectrum of the known signal, an approximated quantile was found. This quantile is strictly proved to be in agreement with the quantile in the case of pure noise and offers a convenient methodology for identifying valid signals.
