1. Mar 20, 2005 Iterative pe finder: IceTop data compression applied to In-ice D. Seckel, Univ. of Delaware

2. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Outline Theory IceTop FX for spe events FX for 2-pe events ? Iterative procedure Examples Estimated data volume

3. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Model Waveform Digitizer sample Event ID Pulse shape gain baseline pedestal noise integer +/- 0.5 Sample period Three parameters for 3 functions

4. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Raw Waveforms 1 = ATWD-0

5. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Extract spe & pedestal

6. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) FX applied to spe g0g0 b0b0 dt 0 Determine and pedestal (p) From 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) With Pedestal Without Pedestal

8. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Arrival time for SPE events dt distribution ~ 10% too wide

9. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Sample 3-pe event in ATWD-0 This event shows three cleanly separated photo-electrons.

13. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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 N pe ) bytes

16. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Gallery Number of bytes N pe

17. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) Fixed point arithmetic (in progress)

18. Iterative pe finder Berkeley, Mar 20, 2005 (Seckel) 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 N pe ) 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)