Calculating standard deviation from power spectral density

Question

I have set of data (x) for power spectral density (Gaussian white noise), and I am trying to find the standard deviation from it. The result looks wrong because I know that the standard deviation must be with a range of 5.

I used below code

sd=std(x)

Data

Thanks

Answer 1

采用逆傅立叶变换，并在零时刻查看元素。请注意，这实际上只是所有值（\int{X(w)e^{iwt}}dw | t=0 = \int X(w) dw）的总和，应用了一些缩放常数，这取决于您在离散频域中定义psd的方式

功率谱密度S_xx(w)等于F{R_xx(tau)}，即自相关的傅立叶变换R_xx(tau) = E[x(t)x(t+tau)]。

由于您需要标准偏差，因此可以获得R_xx(0) = E[x(t)^2]，然后std^2 = E[x(t)^2] - E[x(t)]^2。

不幸的是，您似乎无法恢复E[x(t)]。也许你已经知道这是0？