论文标题
中心高斯工艺中单个设备光谱密度的噪声与信号比率
Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes
论文作者
论文摘要
我们讨论了一个任意实现的中心高斯流程$ x（t）$的单个设备功率频谱密度$ s（ω，\ mathcal {t}）$的统计属性，其中$ω$是角度频率，$ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ mathcal {t} $。我们以其噪声与信号比率得出了双面不等式，并获得$ s（ω，\ Mathcal {t}）$的完整概率密度函数。我们的发现表明，$ s（ω，\ Mathcal {t}）$的波动超过其平均值$μ（ω，\ Mathcal {t}）$。这意味着使用$μ（ω，\ rathcal {t}）$描述这些过程的行为可能是有问题的。我们最终评估了$ s（ω，\ mathcal {t}）$的典型行为，并发现在大多数情况下，它与平均$μ（ω，\ Mathcal {t}）$显着偏离。
We discuss the statistical properties of a single-trajectory power spectral density $S(ω,\mathcal{T})$ of an arbitrary real-valued centered Gaussian process $X(t)$, where $ω$ is the angular frequency and $\mathcal{T}$ the observation time. We derive a double-sided inequality for its noise-to-signal ratio and obtain the full probability density function of $S(ω,\mathcal{T})$. Our findings imply that the fluctuations of $S(ω,\mathcal{T})$ exceed its average value $μ(ω,\mathcal{T})$. This implies that using $μ(ω,\mathcal{T})$ to describe the behavior of these processes can be problematic. We finally evaluate the typical behavior of $S(ω,\mathcal{T})$ and find that it deviates markedly from the average $μ(ω,\mathcal{T})$ in most cases.
