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Outline. Theory IceTop FX for spe events FX for 2-pe events ? Iterative procedure Examples Estimated data volume. Model Waveform. Digitizer sample. Pulse shape. pedestal. noise. gain. baseline. Event ID. Sample period. integer. +/- 0.5. Three parameters for 3 functions.

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Outline

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  1. D. Seckel, Univ. of Delaware

  2. Outline • Theory • IceTop FX for spe events • FX for 2-pe events ? • Iterative procedure • Examples • Estimated data volume

  3. Model Waveform Digitizer sample Pulse shape pedestal noise gain baseline Event ID Sample period integer +/- 0.5 Three parameters for 3 functions

  4. Raw Waveforms 1 = ATWD-0

  5. Extract spe & pedestal

  6. Signal subspace • Construct orthogonal basis functions from linear combination of (phi, phi’, 1) • Project onto these to get coefficients • Invert to get g, dt, b • Reconstruct event from g, dt, b

  7. FX applied to spe With Pedestal • Determine <spe> and pedestal (p) • From <spe> construct basis • Event analysis: • Subtract pedestal • Shift pulse to defined time (ipk) • Use basis to find • Amplitude of pulse, g • time slew between samples, dt • baselne shift, b • Reconstruct event on surface (see red curves) Without Pedestal g0 b0 dt0

  8. Arrival time for SPE events dt distribution ~ 10% too wide

  9. What about multiple-pe events? • In-Ice most events are a few pe at most. • How to reduce data to essentials • Figure shows single pe algorithm picks out largest pe – see red curves in figure

  10. Proposal: keep cutting until there are no trees left • Starting with largest V sample • Use FX algorithm to find pe to fit that peak. • Reconstruct pe • Subtract pe from original waveform • Repeat until fitter returns a good fit, or runs out of trees. First to go Second

  11. Sample 2-pe event in ATWD-0 Note the way the baselines get adjusted. The first baseline gets offset to b>0 to try and resolve the unfit charge. The second baseline goes negative. The sum nicely matches the data.

  12. Sample 3-pe event in ATWD-0 This event shows three cleanly separated photo-electrons.

  13. Sample 3-pe-a This event is well described by 3 pes. It is an open question-at this point if that is really the right number, but is enough to reconstruct the waveform.

  14. Sample mpe This event uses 6-pes. In fact, I chose to stop the fitter at 6, but in this case that seems ok. I suppose there is plenty of room for optimization.

  15. How much data is needed? • g – 10 bits - amplitude • tpe – 7 bits - location of pe • dt - 3 bits - subsample time shift • b - 4 bits - baseline shift 24 bits per photoelectron • 4 byte time stamp • 1 status byte . Total = (5 + 3 Npe) bytes

  16. Gallery Npe Number of bytes

  17. Fixed point arithmetic (in progress)

  18. Summary • Iterative FX process seems to find pe’s efficiently • Reconstructed waveforms with 1-6 pe look good. • Data volume could be as low (5+3 Npe) bytes per event. • 60-25-5-3-2-6 splits would require an average < 11 bytes per event (1/2 of this is clock+status)

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