# Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an 8-bit AtoD from a noise generator (whose description was not provided). I first sampled the noise directly, then I sampled it after passing it through a low-pass filter. I imported the data into MATLAB and used the autocorr function to autocorrelate it. The no-filter data autocorrelated as expected, being just 1 at t=0 (as in Fig 1 in paper); however, the filtered data decays initially as expected but then dips below 0 before coming back up and staying around 0 as in the image below.

My three issues are:

1. I am not really sure what this means physically (is the correlation 'direction' changed so-to-speak?),

2. Why might this be occurring? I know that a description of the noise generator may be important here but I do not have that information myself.

3. Is there any way to correct this issue, and if not, what would be the best compromise?

EDIT:

Here are snapshots of the noise without and with the filter (RC=0.5ms) respectively:

• Quick answer: what you're seeing is normal. The "smearing" of the autocorrelation function in the filtered noise is related to the impulse response of the filter. If you plotted the filter's impulse response, it would look similar to the envelope of the autocorrelation function that you plotted. – Jason R Apr 2 '14 at 22:57
• @JasonR, thank you for the response, but perhaps you could explain a bit more why the impulse response gives that the voltage is more likely to be on the opposite side of the mean, giving a negative autocorrelation. To me, it seems like it should do the opposite. – davly Apr 2 '14 at 23:07