Commit b93ab70e authored by ignacio's avatar ignacio
Browse files

Corrected typo

parent 74a2244a
Pipeline #85206 failed with stages
in 1 minute and 56 seconds
......@@ -27,7 +27,7 @@ $$
\end{align}
$$
![](figures/1_f.PNG){: style="width:500px"}
![](figures/1_f.PNG)
An interesting feature of pure 1/f noise for this type of "DC" measurement is that the signal to noise ratio is independent of the measurement time, and depends only on the number of data points; measuring more slowly doesn't help. Measuring for a longer time scales both $f_1$ and $f_2$ to lower frequencies. This decreases the bandwidth, and for white noise, would indeed decrease $\sigma_v$. However, with 1/f noise, the averaging window moves to lower frequencies where $S_{vv}$ is larger. For 1/f noise, these two effects exactly cancel (the blue and green bordered areas in the above image have the same area, for the same number of data points).
......@@ -42,7 +42,7 @@ For the "lock-in" measurement, the situation is different. The filter of the lo
$$
\begin{align}
\sigma_v^2 = \int_{f_1}^{f_2} S_vv (f) df \approx S_{vv} (f_0) df
\sigma_v^2 = \int_{f_1}^{f_2} S_vv (f) df \approx S_{vv} (f_0) \Delta f
\end{align}
$$
......
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment