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Let's take it to the limit: Signal0: infinite SNR. Signal1: anything less. I just don't see how the output of averaging these would improve over Signal0. I do
by bobmcnamara 2y ago
Let's take it to the limit:
Signal0: infinite SNR.
Signal1: anything less.
I just don't see how the output of averaging these would improve over Signal0. I don't think it can.
- xvedejas 2y agoThey're thinking about when you sample from the same noise distribution, averaging gives an unbiased estimator of the mean. But when you know one SNR is higher than the other, maybe this doesn't hold? But maybe if you transform the distributions to look the same, thus taking a weighted average? I'm not sure.
- pkolaczk 2y agoIt does hold, it is just weaker. You can improve the SNR of a better signal by adding another signal with worse SNR to it. But you need to normalize the signals the way their noise floors are the same amplitude before addition.
- pkolaczk 2y agoWe’re not talking about signals with different SNRs. Where did you get the assumption from?