Water probe: signal processing now ok

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Denicolai, Marco" <Marco.Denicolai@xxxxxxxxxxx>

Hello all,

I'm finally through with the signal processing from the water probe.
Here is what I do, in a nutshell:

1. I measure with the probe a 250V-to-zero falling step with very small
fall time.
2. To calculate the probe freq. response I compare the measured step
with an ideal one. Here

         http://www.iki.fi/dncmrc/scratch/input_steps.jpg

  you can see measured and ideal steps, suitable squeezed to facilitate
their processing with FFT.
4. After some basic processing I get the probe freq. response in
amplitude and phase

         http://www.iki.fi/dncmrc/scratch/fresp_amp.jpg
         http://www.iki.fi/dncmrc/scratch/fresp_phase.jpg

 Note that I have cut away all freq. response over 12 MHz. The impulse
response of the probe looks like this

         http://www.iki.fi/dncmrc/scratch/iresp.jpg

5. Knowing the probe response I can now "compensate" for it and get from
each measurement a "clean" signal as I should see it if the probe were
ideal. To test this idea I feed my "compensation" algoritm with the
measured step and I get a cleaned up step.

         http://www.iki.fi/dncmrc/scratch/rebuilt.jpg

I can now use the same algorithm to clean up all measurements of tesla
stuff done with my probe.

For who is interested (?) the reconstrution algorithm was the only
difficult part of the whole thing. After a lot of head banging I came up
with this solution:

- convolution in the frequency space: FFT of input divided by FFT of
probe, then IFFT to get back to time space
- overlap-add algorithm: the input is sliced to avoid circular
convolution problems
- Hanning windowing to cut the slices: avoids spikes at the slice
boundaries, 50% overlap to achieve a gain of 1

Every other solution fails for one or another reason. Inverse
convolution in the time domain is very unstable.

Paul,
We also measured the step (and calculated the probe fresponse) with the
bottom of the secondary grounded

         http://www.iki.fi/dncmrc/scratch/fresp_amp1.jpg

and with the secondary TOP turn grounded

         http://www.iki.fi/dncmrc/scratch/fresp_amp.jpg

In this last case you can easily notice that the 100 kHz resonance has
shifted to about 200 kHz. This means that you were right: the secondary
is indeed responsible for that peak. Note that the responses are so
clean now because we have been averaging (within the o-scope) 200
readings of the step.

It seems to me like the next step is to switch Thor on and to make some
measurements at full operation.

Best Regards
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