I'm interested in estimating the mean and standard deviation of a signal that was sampled non-uniformly. Assuming I have an estimate of the signal bandwidth, what algorithms would provide estimates of these quantities?

I imagine simply weighting the values by their relative frequencies could work. But is this actually a good approach? Does it have some theoretical guarantee like how the sample mean is an unbiased estimator of the population mean?

I'd appreciate any insight or references I could turn to. Thank you.

  • $\begingroup$ I would use the sample mean for the mean. the sample variance needs to be divided by the degrees of freedom which is the tricky part. $\endgroup$ – Stanley Pawlukiewicz Feb 14 at 20:54
  • $\begingroup$ @StanleyPawlukiewicz, won't the vanilla sample mean bias the estimate toward those parts of the signal where the sampling frequency is higher? $\endgroup$ – hhquark Feb 14 at 21:02
  • $\begingroup$ it depends on what you are developing statistics on. perhaps you can elaborate on what your goal is. a mean , a spectral mean? a histogram of amplitudes? $\endgroup$ – Stanley Pawlukiewicz Feb 14 at 21:30
  • $\begingroup$ I'm looking for the mean of the signal. I suppose I'm implicitly modeling the signal as a continuous time signal that was sampled. In that case, I'm looking for an estimate of the mean of the continuous time signal. $\endgroup$ – hhquark Feb 14 at 22:54
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    $\begingroup$ Hi! Why don't you first convert those samples to uniform ones ? $\endgroup$ – Fat32 Feb 15 at 9:55

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