I have a system consisting of 32 horizontal plus 32 vertical charge sensitive wires. They are part of a particle detector and each one is coupled to a charge amplifier consisting of preamp stage followed by several pulse shaping stages (5th order filter, here the link). In short each time a wire detect a "cloud" of electrons a quasi-gaussian pulse is produced by the amplifier corresponding to the specific wire and the X-Y positions are determined by the time overlap of pulses in the different set of wires. Unfortunately, the two groups of signals are affected by a strong common-mode noise (actually I believe that the name noise is not really correct as it looks like that it comes from some sort of undesired positive feedback on the channels). Of course the experiment has already been performed and there is no way to improve the electronic setup.

In the attached figure I selected from each group only 5 out of the 32 channels in order you can observe their features. Please note that I have manually shifted the baseline of each waveform only for visualisation purposes. Also note that the time is expressed in time samples, as the data comes from a fast ADC which samples every 50 nsec the signal in each channel. In addition, there are some channels that I have plotted with the red color as I believe the gain of those channels is quite poor.

Waveforms of 5 selected channels out of 32 in each group of charge sensitive wires. For proper visualisation the channels are shifted vertically. The channels plotted in red are those that might be featured by low gain of the corresponding charge amplifier.

At the moment the only way I could find to mitigate this strong common-mode is by computing the mean waveform across all the channels in the same group and subtracting it from the channels themselves. This produces a little improvement as I can observe a general reduction of the RMS (this is calculated in a region at large times, where I know there are not pulses from electron detection). Of course the RMS increases for all those channels that suffer of low gain. I believe that this is called Common Average Reference (CAR), but I am not sure as I have not a background in signal processing.

Now the question I would like to submit to this community is multiple:

  1. Can I use the cross-correlation between channels in order to perform a better common-mode suppression optimised per channel?
  2. Can I understand from these data some kind of multiplication factor (or equalisation factor) that can be used produce a uniform response across all the channels (of course not a uniform SNR as it depends also on the actual gain for each channel)?

I understand that the entire problem I have might be an entire university course on signal processing, hence also some references to proper literature (either papers or textbooks) are very welcome. Also, I looked around, especially in this community, but I could not spot anything but this other question, similar but not really fitting my needs. Most likely this is because I am not expert of the field and I have used wrong wordings in searching for an answer.

  • $\begingroup$ Is it the sinusoidal-ish signal present in all the time-series that you would classify as the common mode disturbance? $\endgroup$ – Arnfinn Aug 6 '18 at 21:30
  • $\begingroup$ One item is that it seems sure that you have "ringing" and this would be due to poor amplifier compensation or perhaps the inductance/capacitance of the wires. In the second case an appropriate "loading" would be needed; a term from the telephone industry and Heavyside :) The DC common mode would probably have to be killed by time wise sampling/autocalibration. This works fine as long as you mind your p's&q's. You can calculate how often the system would be diverted very fully but it does require some time set aside. I have referred your real question to a friend. $\endgroup$ – rrogers Aug 7 '18 at 19:23
  • $\begingroup$ @Arnfinn Yes it is and I am trying to analyse it in the frequency domain. But I guess that the time scale of the "sinusoidal-ish" disturbance is about the same as the integration signal. Hence, if this is the case using an hard cut on the frequency domain and going back to the time domain might result in a distortion of the signal. $\endgroup$ – frappesco Aug 13 '18 at 15:16
  • $\begingroup$ @rrogers I guess you are right, but when we could figure out the issue only after we cosed all the setup and unfortunately we could not repeat the experiment with improved electronics. So the only way is to try to apply some offline (software) technique to reduce as much as possible the unwanted disturbance on the time series. Thanks a lot for the support and to forward my issue to your friend. $\endgroup$ – frappesco Aug 13 '18 at 15:22
  • $\begingroup$ @frappesco I would suggest you do a fit to a sinusoidal function, and subtract it from the data. This is pretty common practice when estimating signal-to-noise ratios, for example. I have done this using the MATLAB optimisation toolbox, and Stephen Boyd's toolbox (cvxpy.org). If you need references I can look for them and send it to you. $\endgroup$ – Arnfinn Aug 14 '18 at 17:21

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