Re: Transfer Function Estimation - Averaging?


<erdinc.saygin@xxxxxxxxx> wrote in message
news:1143468591.878807.199380@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi all,

I have a question about transfer function estimation relating
averaging.


The data that I have is daily records of measurement of earth's noise.
The sample rate is 25 Hz. I have these records from multiple points and
cross-correlating them to get the impulse response between these
points(assuming that the noise has some "white" character). With the
original schema I have created some "respectable" results. But when i
went into the details,I realized that it is not the best way to apply.

Simply, I have segmented the each day with some overlapping and divided
the corresponding part in frequency domain and then added them together
in time domain.

tft_final=ifft(tf(1))+ifft(tf(2))+.......ifft(tf(n)) where tf is the
transfer function between each segments input (u) and output (u)
(YU*/UU*) in frequency domain

This is applied to all individual day records and then I averaged them.


final_estimate=(1/n)(day1+day2+........dayn)


But in terms of transfer function estimation, I don't think I have
applied the right thing. Then I used the same data and tried windowing
and averaging in frequency domain with same amount of segmenting and
overlapping. Then came back to time domain. But the results are simply
too noisy and lacking some information (e.g acausal part of the signal
didn't carry the expected information unlike the first case).

tft_final=ifft(tf(1)+tf(2))+.......tf(n))/n

then
final_estimate=(1/n)(day1+day2+........dayn)


My question is, what might have I have done wrong. By the property of
linearity of DFT, I was expecting the same results for the both cases.

Google on "system identification" to find discussion and methods.

I'm not sure what you're doing. Is this seismic noise?
Assuming that's the case then what are you using for an *input*?
It seems to me that you have a multi-input, multi-output system (really a
distributed system which might more often be represented by partial
differential equations. But, OK, you've got a lumped model and are using
ordinary differential equaations it appears.
Anyway, it looks like you're working with nothing but "outputs" so that's
curious.
How do you separate things out?

I guess this might be a bit like a lumped network model where inputs are
also outputs and outputs are also inputs? I've touched on those things in
school but never used them in practice. How do you separate out the "input"
part of a measurement (e.g. local seismic activity) from the "output" part
(response from distant activity)?

Fred


.

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