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.

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:
> 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. ( 
>> shows the fit results covering some parts of the signal, 
>> 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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