Mean chisq/DOF is 0.56 for 3-pole, 0.68 for double-Gaussian.

http://www.slac.stanford.edu/~meeg/ecalpulsefit/3pole/rchisq.png

http://www.slac.stanford.edu/~meeg/ecalpulsefit/2gaus/rchisq.png

I think that in every fit the 2-Gaussian shape overestimates the rising 
edge; 3-pole looks better. As Andrea says, the pulse peak is definitely 
better fit by 3-pole.

On Thu, 3 Apr 2014, Sho Uemura wrote:

> chisq/dof plot attached - I'm using TGraph to fit, which assumes errors of 1 
> mV per data point. I use the time range (-200, 60).
>
> On Thu, 3 Apr 2014, Gabriel CHARLES wrote:
>
>> Could you both provide an average value of chi square that the different 
>> parametrization can be compared easily, please ?
>> 
>> Also, from the simulation it appears that the rising edge could be present. 
>> In attachment you will find a picture with two plots. The top one 
>> corresponds to the signal after the crystal and the APD, that is the input 
>> of the preamplifier.
>> It is obtained by the convolution of the signal of the crystal and the APD. 
>> The crystal response is composed of the sum of two decreasing exponential 
>> governed by different time constants. The APD transfert function is given 
>> by the bottom plot (sorry for the wrong Y axis units).
>> 
>> There is no reason for the preamplifier to reduce the tail.
>> 
>> I think that if there is no huge difference between the chi square it would 
>> be better to keep the two gaussian function.
>> 
>> ---
>> Gabriel CHARLES
>> Institut de Physique Nucléaire d'Orsay
>> 
>> On Thu, 3 Apr 2014 13:15:00 -0700 (PDT), Sho Uemura wrote:
>>> I tried two more parametrizations. These are parametrizations
>>> commonly used for the APV25 preamp that we use in the SVT.
>>> 
>>> CR-RC: t*exp(-t/tp)
>>> 3-pole, or CR-RC-RC: t^2*exp(-t/tp)
>>> 
>>> 3-pole seems to fit well, I think better than the asymmetric
>>> Gaussian. CR-RC seems no better than the Gaussian. Other
>>> parametrizations I tried (variations on CR-RC or 3-pole using more
>>> than one time constant) were degenerate with CR-RC or 3-pole, so I
>>> didn't include those plots.
>>> 
>>> Plots attached are for 3-pole function. All plots for 3-pole and
>>> CR-RC, and the pyroot scripts I used, are online:
>>> 
>>> http://www.slac.stanford.edu/~meeg/ecalpulsefit/
>>> 
>>> I also see what you see, where there are 2 clusters in the
>>> distribution of shape parameters. I chose the center of the larger
>>> cluster (with the faster time constant) and refit all the events with
>>> this time constant fixed; those plots are named "fit2" and as expected
>>> they fit the faster pulses well and the slower pulses poorly.
>>> 
>>> More data will help.
>>> 
>>> I plotted the three parametrizations we have, see plot4.pdf attached.
>>> If we agree that the Gaussian has an unphysical rising edge, I think
>>> we should use 3-pole.
>>> 
>>> On Tue, 1 Apr 2014, Andrea Celentano wrote:
>>> 
>>>> Dear all,
>>>> here are some results about HPS Ecal signals parametrization.
>>>> I took data with the crystal placed vertically, APD gain 150, room 
>>>> temperature. I put a threshold ~ 20 mV to keep only big enough signals, 
>>>> out of the noise.
>>>> I acquired data with a 2.5Gs/s oscilloscope, 1 GHz bandwidth, 50 Ohm 
>>>> input impedance.
>>>> 
>>>> I used the same* configuration employed at JLab for cabling: 8m 3M cable 
>>>> ---> passive splitter ---> 3m lemo cable.
>>>> 
>>>> *actually I employed an 8 meters 3M cable instead of 7m because the 
>>>> latter is not available here in Genova.
>>>> 
>>>> Attached you find a postcript file with the results. (outGood.ps shows 
>>>> the fit results covering some parts of the signal, outGood1.ps no)
>>>> 
>>>> - Neglect first blank page
>>>> - Pages from 2 to 32 are the 31 signals I got, with superimposed the fit 
>>>> performed with the two-gaussians parametrization. Each chi2 fit is 
>>>> performed independently.
>>>> Signals are in mV and ns.
>>>> Note that near ~ 100 ns there is probably a reflection due to some 
>>>> impedance mismatch in the cables chain.
>>>> However,  I am not using those points to fit. I am fitting the data in 
>>>> between -200 ns and +80 ns. The function is then plotted in the full time 
>>>> range.
>>>> 
>>>> - Last page is a summary of the fits performed. Two 1d-histograms are the 
>>>> distributions of the two time constants used in the parametrization. Then 
>>>> I am plotting also their correlation, as well as the correlation of the 
>>>> rise-time (par[1]) with the signal amplitude (from the fit).
>>>> 
>>>> I noted that the fit parameters Trise, Tfall are not distributed as two 
>>>> gaussians. In particular, for Trise there is an accumulation of events at 
>>>> ~ 5 ns and ~ 7 ns, correlated with corresponding Tfall at ~ 15 and ~20 
>>>> ns. Actually, I see that, other than the amplitude, signals do not have 
>>>> always the same shape: look, for example, at signals n.5 and n.6 (ps 
>>>> pages n.5 and n.6).
>>>> 
>>>> Attached you find also the C implementation of the signal 
>>>> parametrization, in form of a "double fun(double *x,double  *par)" used 
>>>> by ROOT when fitting trough TF1.
>>>> Finally, I am attaching also the raw data for the 31 signals I got, so if 
>>>> you're interested you can play with different signal parametrizations.
>>>> 
>>>> I am planning to take more data these days.
>>>> 
>>>> 
>>>> Bests,
>>>> 
>>>> Andrea
>>>> 
>> 
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