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Entry  Mon Dec 14 16:46:42 2015, ericq, Update, WienerFiltering, Noise Subtraction Puzzler subpuzz.pdf
    Reply  Thu Jan 7 15:29:54 2016, ericq, Update, WienerFiltering, Noise Subtraction Puzzler subpuzz2.pdfpuzzle.zip
       Reply  Thu Jan 14 15:08:37 2016, ericq, Update, WienerFiltering, Noise Subtraction Puzzler subpuzz_resolved.pdf
          Reply  Thu Jan 14 18:41:36 2016, rana, Update, WienerFiltering, Noise Subtraction Puzzler 
Message ID: 11880     Entry time: Mon Dec 14 16:46:42 2015     Reply to this: 11918
Author: ericq 
Type: Update 
Category: WienerFiltering 
Subject: Noise Subtraction Puzzler 

Here's something to ponder.

Our online MCL feedforward uses perpendicular vertex T240 seismometer signals as input. When designing a feedforward filter, whether FIR Wiener or otherwise, we posit that the PSD of the best linear subtraction one can theoretically achieve is given by the coherence, via Psub = P(1-C). 

If we have more than one witness input, but they are completely uncorrelated, then this extends to Psub = P(1-C1)(1-C2). However, in reality, there are correlations between the witnesses, which would make this an overestimate of how much noise power can be subtracted. 

Now, I present the actual MCL situation. [According to Ignacio's ELOG (11584), the online performance is not far from this offline prediction]

Somehow, we are able to subtract much more noise at ~1Hz than the coherence would lead you to believe. One suspicion of mine is that the noise at 1Hz is quite nonstationary. Using median [C/P]SDs should help with this in principle, but the above was all done with medians, and using the mean is not much different.

Thinking back to one of the metrics that Eve and Koji were talking about this summer, (std(S)/mean(S), where S is the spectrogram of the signal) gives an answer of ~2.3 at that peak at 1.4Hz, which is definitely in the nonstationary regieme, but I don't have much intution into just how severe that value is.

So, what's the point of all this? We generally use coherence as a heuristic to judge whether we should bother attempting any noise subtraction in the first place, so I'm troubled by a circumstance in which there is much more subtraction to be had than coherence leads us to believe. I would like to come up with a way of predicting MISO subtraction results of nonstationary couplings more reliably.

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