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I'm working to understand some noise on some of our analog-to-digital converter signals. I've analyzed a log of 2^18 samples in MATLAB, and can make the following observations:

  • the noise consists of large single-sample spikes on top of my expected signal
  • the FFT spectrum of the noise looks white (hard to say since there is some signal there as well, but all the peaks seem to be at the fundamental + harmonics of my signal)
  • amplitude of the spikes seems equally likely to be positive or negative
  • the distribution of spike amplitudes seems to be approx exp(-K*|x|): that is, if I do either an ascending or descending sort of the data, and plot it on a semilog scale (log-x, linear y) then at the low end of the sort (i.e. the outliers) the distribution looks linear on the semilog plot.

Do any of you know of a random process that might meet/approximate the above criteria? I am looking for some insight into what type of noise this is, so I might better guess where it is coming from.

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This seems to be Laplace noise. Have a look at:

which is handy for modeling such spikey, sparse noise.

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