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. Negative autocorrelation

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?


Here are snapshots of the noise without and with the filter (RC=0.5ms) respectively: Noise before without filter Noise going through RC=0.5ms low-pass filter

  • $\begingroup$ 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. $\endgroup$ – Jason R Apr 2 '14 at 22:57
  • $\begingroup$ @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. $\endgroup$ – davly Apr 2 '14 at 23:07

If the impulse response of the low pass filter goes negative, that means that the filter is adding an inverted or negative image of the input signal to the output at that delay. Which the autocorrelation is finding it as it is, negative. The impulse response goes negative as one way of canceling out some of the input spectrum in the filter's stopband.

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  • $\begingroup$ Ok so you're saying it's down to the filter then. Would you recommend a compromise to account for it? $\endgroup$ – davly Apr 3 '14 at 15:17

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