D. Seckel, Univ. of Delaware

Mar 20, 2005

Iterative pe finder: IceTop data compression applied to In-ice

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Outline

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

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Model Waveform

wia gita i bi pa i

a

Digitizer sample

Event ID

Pulse shape

gain baseline

pedestal

noise

wiai gia i 'a 1

2 i

2 ''a … bi piai ia

ta i ta i iinteger +/- 0.5

Sample period

Three parameters for 3 functions

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Raw Waveforms

1 = ATWD-0

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Extract spe & pedestal

20 40 60 80 100 120

180

185

190

195

200

205

20 40 60 80 100 120-0.1

00.10.20.30.40.50.6

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Signal subspace

0 20 40 60 80 100 120

-0.4

-0.2

0

0.2

0.4

0.6

Threeout of 128orthonormal basis functions

• 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

wiai gia i 'a 1

2 i

2 ''a … bi piai ia

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FX applied to spe

g0

b0

dt0

• 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)

With Pedestal Without Pedestal

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Arrival time for SPE events

ipk and dt histograms from atwd0 for spe events

5 10 15

100

200

300

400

500

600

-0.5 0 0.5 1

100

200

300

400

Arrival time distribution for spe events

6 8 10 12 14 16

20

40

60

80

100

dt distribution~ 10% too wide

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What about multiple-pe events?

0 204060801001207550250255075 0.646

0.2680.105

cx 0.707V 13.36

0 2040608010012020020406080100

0.9570.256

0.060

cx 0.125V 2.52

0 204060801001200255075100125150 0.955

0.2450.004

cx 0.165V 3.34

0 204060801001207550250255075 0.736

0.1290.128

cx 0.652V 22.45

0 20406080100120250255075100125 0.969

0.1270.045

cx 0.205V 4.17

0 2040608010012050250255075100

0.8200.0230.244

cx 0.517V 9.60

0 2040608010012050250255075100125

0.8570.0570.096

cx 0.504V 10.26

0 2040608010012020020406080100 0.966

0.2480.013

cx 0.077V 1.68

0 20406080100120604020020406080 0.777

0.1070.011

cx 0.621V 9.65

0 204060801001207550250255075 0.690

0.1870.274

cx 0.643V 11.56

0 20406080100120250255075100125 0.984

0.1200.055

cx 0.118V 3.75

0 2040608010012050050100 0.792

0.0910.197

cx 0.570V 12.46

0 2040608010012040200204060 0.796

0.0480.130

cx 0.590V 6.95

0 204060801001204020020406080 0.836

0.0630.059

cx 0.542V 8.32

0 20406080100120604020020406080

0.7130.1000.240

cx 0.651V 10.97

0 204060801001204020020406080 0.868

0.1580.054

cx 0.467V 6.73

0 204060801001207550250255075100

0.7870.1020.163

cx 0.587V 14.21

0 2040608010012050250255075100

0.7870.115

0.011

cx 0.606V 10.17

0 20406080100120250255075100125

0.9440.2180.023

cx 0.247V 4.67

0 2040608010012020020406080100120 0.963

0.2420.012

cx 0.116V 2.72

• 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

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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.

0 204060801001207550250255075 0.646

0.2680.105

cx 0.707V 13.36

0 2040608010012020020406080100

0.9570.256

0.060

cx 0.125V 2.52

0 204060801001200255075100125150 0.955

0.2450.004

cx 0.165V 3.34

0 204060801001207550250255075 0.736

0.1290.128

cx 0.652V 22.45

0 20406080100120250255075100125 0.969

0.1270.045

cx 0.205V 4.17

0 2040608010012050250255075100

0.8200.0230.244

cx 0.517V 9.60

0 2040608010012050250255075100125

0.8570.0570.096

cx 0.504V 10.26

0 2040608010012020020406080100 0.966

0.2480.013

cx 0.077V 1.68

0 20406080100120604020020406080 0.777

0.1070.011

cx 0.621V 9.65

0 204060801001207550250255075 0.690

0.1870.274

cx 0.643V 11.56

0 20406080100120250255075100125 0.984

0.1200.055

cx 0.118V 3.75

0 2040608010012050050100 0.792

0.0910.197

cx 0.570V 12.46

0 2040608010012040200204060 0.796

0.0480.130

cx 0.590V 6.95

0 204060801001204020020406080 0.836

0.0630.059

cx 0.542V 8.32

0 20406080100120604020020406080

0.7130.1000.240

cx 0.651V 10.97

0 204060801001204020020406080 0.868

0.1580.054

cx 0.467V 6.73

0 204060801001207550250255075100

0.7870.1020.163

cx 0.587V 14.21

0 2040608010012050250255075100

0.7870.115

0.011

cx 0.606V 10.17

0 20406080100120250255075100125

0.9440.2180.023

cx 0.247V 4.67

0 2040608010012020020406080100120 0.963

0.2420.012

cx 0.116V 2.72

First to go

Second

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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.

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Sample 3-pe event in ATWD-0

This event shows three cleanly separated photo-electrons.

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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.

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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.

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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

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Gallery

Number of bytesNpe

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Fixed point arithmetic (in progress)

Comparison of spe waveform with 8,12,16,20 bit arithmetic

0 20 40 60 80 100 12016 bit sample

-0.2

0

0.2

0.4

0.6

dezilamroneps

014

0 20 40 60 80 100 12020 bit sample

-0.2

0

0.2

0.4

0.6

dezilamroneps

015

0 20 40 60 80 100 1208 bit sample

-0.2

0

0.2

0.4

0.6

dezilamroneps

012

0 20 40 60 80 100 12012 bit sample

-0.2

0

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0.6

dezilamroneps

013

nbit r.r sumfloatfifloatfi floatsumfifi format of sumfifi8 1. 0.998062 0.96875 num161,1, 1, 1, 1, 1, 0, 0, 0, 012 1. 1.0001 0.995361 num161,1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 016 1. 0.999992 0.999237 num161,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 020 1. 1. 0.99994 num161,1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0

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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)