This is a follow-up question to Allan deviation to determine averaging time
I was under the impression that with DC signals I couldn't capture or average a signal forever to get better SNR, because of 1/f or pink noise. I thought the Allan deviation was a good way to determine averaging time.
I have now convinced myself the Allan deviation isn't useful for DC signals like this. It seems like averaging the signal will overcome any extra noise power obtained from a longer capture window. (speaking of white and pink noise)
Here is an example. This is a mixture of white and pink noise.
Here is the associated power spectral density.
I split the signal into 1 second chunks. In each of those chunks, I varied the capture window. On one extreme, I'm taking the first sample and throwing away the rest of the chunk. On the other extreme, I'm taking every sample and averaging them together. This is repeated over many seconds, and the standard deviation taken. Here is the result.
This makes me think I should always make my capture windows as long as possible, and because of averaging I will always get the best noise numbers.
Is this true? Is it because finite capture is a high pass with a cutoff at 1/T, but averaging is also a low pass with cutoff at 1/T?
I repeated the plot for pure pink noise, and it looks like averaging kills the noise.
Thanks for the help.