Calculating standard deviation from power spectral density

0
votes

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

1
matlabsignal-processing
That code works, my guess: your knoledge of the range of std is wrong. – Ander Biguri
std(x) will give you the standard deviation of the spectrum amplitude. But it sounds like you want the standard deviation of the time-series signal. This questions is a math/statistics question, not a programming one. – Eric

1 Answers

2
votes

Take the inverse fourier transform, and look at the element at time zero. Note that this is actually just the sum of all the values (\int{X(w)e^{iwt}}dw | t=0 = \int X(w) dw), with some scaling constant applied which depends on how you defined the psd in a discrete frequency domain

The power spectral density, S_xx(w), is equal to F{R_xx(tau)}, the fourier transform of the autocorrelation, R_xx(tau) = E[x(t)x(t+tau)].

Since you want the standard deviation, you can get R_xx(0) = E[x(t)^2], and then std^2 = E[x(t)^2] - E[x(t)]^2.

Unfortunately, it seems you have no way to recover E[x(t)]. Perhaps you already know this is 0?