I have a 10 second recorded signal band pass filtered from 100-500 Hz. The original sampling rate is 10 kS. Now I run a moving window RMS with a window length: 10 ms on the signal (10/1000 * sampling rate). I then find the samples of the RMS signal that are greater than 2 SD from mean. I get a total number of, say, 4894 samples that satisfy this condition.
Now I down sample the signal to 2 kS, and do the same process with the recalculated window length also of 10 ms (but different sample length due to the sampling rate). When I apply the same >2 SD criteria I get 974 samples.
I then use the sample indices from the two different cases to see if they are indeed the same samples by normalizing the indices by sampling rate times 1000 to get ms precision.
Then I compute the intersection of these two sets of times when s.d > 2 for both the sampling rates.
I get a value of around 700. I am trying to understand why. Shouldn't all the samples times in the set corresponding to the 2 kS sampling rate actually be a subset of the sampling times seen in the 5 kS sampling rate for the > 2 SD criteria?