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Re: System identification...

 From: Doug Stewart Subject: Re: System identification... Date: Wed, 19 Jan 2011 13:16:56 -0500

On Wed, Jan 19, 2011 at 1:10 PM, Rudolf Widmer-Schnidrig wrote:
On 19.01.11 16:00, Doug Stewart wrote:

On Wed, Jan 19, 2011 at 9:38 AM, Rudolf Widmer-Schnidrig wrote:
On 19.01.11 13:32, Doug Stewart wrote:

On Wed, Jan 19, 2011 at 3:19 AM, Rudolf Widmer-Schnidrig wrote:
Dear List,

I have measured (in the time domain) input and output of a mechanical system (a seismometer) and would like to derive a filter model B(s)/A(S) based on this data.

I see the path via the frequency domain:
[H, F] = pwelch(input,output,.....'trans')
[B, A] = invfreqs(H,F,nA,nB)

Question: is there a way to find A and B without going first into the Fourier domain?

many cheers           - Ruedi

--
+---------------------------------------------------------------+
Rudolf Widmer-Schnidrig

What Input did you use?
If it was an impulse then Yes
if it was a step then yes
and maybe more.

Doug
Dear Doug, I have used both a sweep and a random telegraph signal.         -Ruedi

OK
A sweep is inherently a frequency domain type of test so maybe you can use Bode type analysis to find the corner freq. and gain and type of role off etc.

Dear Doug,

Since my input sweep has constant amplitude the amplitude variation with frequency of the output signal shows immediately how the gain of the instrument varies with frequency.  From a comparison of input and output signals in the time domain one can - at least qualitatively - also see the phase delay and how it varies with frequency. What  I am after is a precise estimation of the poles and zeros to within hopefully 1% or better.
is the    random telegraph signal   a white noise type of signal??

The random telegraph signal is band limited white noise.

Doug
My seismometer can be modeled as a band-pass filter. I also have a good idea on the number of poles and zeros (nA and nB) needed for a description in the s- or z-plane.  So maybe I'll just have to do a grid search and perturb the locations of the A and B values until

norm(output - H(z)*input)

is minimal.  Fortunately in the case of the z-transform the serach is limited to the real axis.

-Ruedi
```--
+---------------------------------------------------------------+
Rudolf Widmer-Schnidrig

```
Ok we are now understanding each other.

What I have done is used an optimization method where I give it the starting poles and zeros and then let the computer minimize the sum of squared differences as it plays with the pole and zero locations. I am sure that you can use complex poles for this method.

If you want more help on this maybe we should go private emails from here.

Doug