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Fri Aug 22 13:58:39 2008
Trend of the Wiener TF
In order to understand if we really need an adaptive filter, I used old data of MC_L and the accelerometers and seismometer to see if the Wiener (ideal) TF between MC_L and the others really changes all the time.
Two tests I made:
Compare the TF after different segments of time, starting from the same point.
Meaning, measuring the TF after 5,10,15,20... minutes, looking when and if the TF stablizes (stops changing).
Compare the TF between same-length segments, from different times.
Meaning, comparing for example 2 segments of 10 minutes taken from different times.
As you can see in the attached PDF, the changes start being minor after 200,000 data points, which correspont to 200,000/256 s, which is approximately 13 minutes.
If you look at the PDF file, it is arranged from shorter times to longer in the order of: 3, 6, 13, 26 and 39 minutes.
As expected, the TF between different segmants of the same length is not completely the same. Again, you can look at the attached PDF.
Sorry the titles are the same. Each 2 consecutive pages represent the same length of segment in different times. The order of segment's lengths is: 3, 13, 26 and 39 minutes
How do I explain what's going on?
Since the Wiener filter finds the correlation matrix between the data and the noise signals, it will maintain some kind of familiar shape when we don't add a significant amount of unusual data. I am assuming that if I had looked at longer time periods, we could see a more significant change in the TF in time. When looking at different times, the average noise is likely to be different which can explain the change in the correlation matrix and the TF.
To sum up
I think we should give adaptive filtering a go.