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Message ID: 6029     Entry time: Mon Nov 28 18:53:35 2011
Author: Den 
Type: Summary 
Category: WienerFiltering 
Subject: seismic noise substraction 

There is still a problem why GUR, STS signals are poorly coherent to MC_L.  But at least we can see coherence at 2-5 Hz. It might be useful to do something with adaptive filtering because it does not work at all for a long time. We start with Wiener filtering. I still doubt that static filtering is useful. Adaptive filter output is linear to its coefficients, so why not to provide adaptive filter with a zero approximation equal to calculated Wiener filter coefficients. Then you automatically have Wiener filter ouput + adaptively control coefficients. But if Wiener filter is already present in the model, I tried to make it work. Then we can compare performance of the OAF with static filter and without it.

I started with GUR1_X and MC_F signals recorded 1 month ago to figure out how stable TF is. Will the same coefficients work now online? In the plot below offline Wiener filtering is presented.



This offline filtering was done with 7500 coefficients. This FIR filter was converted to IIR filter with the following procedure:

1. Calculate frequency responce of the filter. It is presented below.


2. Multiply this frequency response by a window function. This we need because we are interested in frequencies 0.1-20 Hz at this moment. We want this function to be > 1e-3 at ~0Hz, so that the DC component is filtered out from seismometer signal. From the other hand we also do not want huge signal at high frequenies. We know that this signal will be filtered with aggresive low-pass filterd before going to the actuator but still we want to make sure that this signal is not very big to be filtered out by the low-pass filter.

The window function is done in the way to be a differential function to be easier fitted by the vectfit3. Function is equal to 1 for 0.5 - 20 Hz and 1e-5 for other frequencies except neighbouring to the 0.5 and 20 where the function is cosine.


3. I've used vectfit3 software to approximate the product of the frequency response of the filter and window fucntion with the rational function. I've used 10 complex conjugate poles. The function was weighted in the way to make deviation as small as possible for interesting frequencies 0.5 - 10 Hz. The approximation error is big below 20 Hz where the window function is 1e-5 but at least obtained rational function does not increase as real function do at high frequencies.


I tried to make a foton filter out of this approximation but it turns out that this filter is too large for it. Probably there is other problem with this approximation but once I've split the filter into 2 separate filters foton saved it. Wiener21 and Wiener22 filters are in the C1OAF.txt STATIC_STATMTX_8_8 model.

I've tested how the function was approximated. For this purpose I've downloaded GUR and MC_F signals and filtered GUR singla with rational approximation of the Wiener filter frequency response. From power spectral density and coherence plots presented below we can say that approximation is reasonable.


Next, I've approximated the actuator TF and inverted it. If TF measured in p. 5900 is correct then below presented its  rational approximation. We can see deviation at high frequencies - that's because I used small weights there using approximation - anyway this will not pass through 28 Hz low-pass filter before the actuator.


I've inverted this TF p->z , z->p, k->1/k. I've also added "-" sign before 1/k because we subtract the signal, not add it. I placed this filter 0.5Actuator20 to the C1OAF.txt SUS-MC2_OUT filter bank.

The next plot compares online measured MC_L without static filtering and with it. Blue line - with online Wiener filtering, red line - without Wiener filtering.


We can see some subtraction in the MC_L due to the static Wiener filtering in the 2-5 Hz where we see coherence. It is not that good as offline but the effect is still present. Probably, we should measure the actuator TF more precisely. It seems that there some phase problems during the subtraction. Or may be digital noise is corrupting the signal. 

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