class AliFMDDigitizer: public AliFMDBaseDigitizer

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 $Id$ *

 * @file    AliFMDDigitizer.cxx
 *
 * @author  Christian Holm Christensen <cholm@nbi.dk>
 * @date    Mon Mar 27 12:38:26 2006
 * @brief   FMD Digitizers implementation
 *
 * @ingroup FMD_sim



  This class contains the procedures simulation ADC  signal for the
  Forward Multiplicity detector  : SDigits->Digits

  Digits consists of
   - Detector #
   - Ring ID
   - Sector #
   - Strip #
   - ADC count in this channel

  Digits consists of
   - Detector #
   - Ring ID
   - Sector #
   - Strip #
   - Total energy deposited in the strip
   - ADC count in this channel

 As the Digits and SDigits have so much in common, the classes
 AliFMDDigitizer and AliFMDSDigitizer are implemented via a base
 class AliFMDBaseDigitizer.

                 +---------------------+
                 | AliFMDBaseDigitizer |
                 +---------------------+
                           ^
                           |
                +----------+---------+
                |                    |
      +-----------------+     +------------------+
      | AliFMDDigitizer |	| AliFMDSDigitizer |
      +-----------------+	+------------------+
                |
     +-------------------+
     | AliFMDSSDigitizer |
     +-------------------+

 These classes has several paramters:

     fPedestal
     fPedestalWidth
         (Only AliFMDDigitizer)
         Mean and width of the pedestal.  The pedestal is simulated
         by a Guassian, but derived classes my override MakePedestal
         to simulate it differently (or pick it up from a database).

     fVA1MipRange
         The dymamic MIP range of the VA1_ALICE pre-amplifier chip

     fAltroChannelSize
         The largest number plus one that can be stored in one
         channel in one time step in the ALTRO ADC chip.

     fSampleRate
         How many times the ALTRO ADC chip samples the VA1_ALICE
         pre-amplifier signal.   The VA1_ALICE chip is read-out at
         10MHz, while it's possible to drive the ALTRO chip at
         25MHz.  That means, that the ALTRO chip can have time to
         sample each VA1_ALICE signal up to 2 times.  Although it's
         not certain this feature will be used in the production,
         we'd like have the option, and so it should be reflected in
         the code.


 The shaping function of the VA1_ALICE is generally given by

      f(x) = A(1 - exp(-Bx))

 where A is the total charge collected in the pre-amp., and B is a
 paramter that depends on the shaping time of the VA1_ALICE circut.

 When simulating the shaping function of the VA1_ALICe
 pre-amp. chip, we have to take into account, that the shaping
 function depends on the previous value of read from the pre-amp.

 That results in the following algorithm:

    last = 0;
    FOR charge IN pre-amp. charge train DO
      IF last < charge THEN
        f(t) = (charge - last) * (1 - exp(-B * t)) + last
      ELSE
        f(t) = (last - charge) * exp(-B * t) + charge)
      ENDIF
      FOR i IN # samples DO
        adc_i = f(i / (# samples))
      DONE
      last = charge
   DONE

 Here,

   pre-amp. charge train
       is a series of 128 charges read from the VA1_ALICE chip

   # samples
       is the number of times the ALTRO ADC samples each of the 128
       charges from the pre-amp.

 Where Q is the total charge collected by the VA1_ALICE
 pre-amplifier.   Q is then given by

           E S
      Q =  - -
           e R

 where E is the total energy deposited in a silicon strip, R is the
 dynamic range of the VA1_ALICE pre-amp (fVA1MipRange), e is the
 energy deposited by a single MIP, and S ALTRO channel size in each
 time step (fAltroChannelSize).

 The energy deposited per MIP is given by

      e = M * rho * w

 where M is the universal number 1.664, rho is the density of
 silicon, and w is the depth of the silicon sensor.

 The final ADC count is given by

      C' = C + P

 where P is the (randomized) pedestal (see MakePedestal)

 This class uses the class template AliFMDMap<Type> to make an
 internal cache of the energy deposted of the hits.  The class
 template is instantasized as

  typedef AliFMDMap<std::pair<Float_t, UShort_t> > AliFMDEdepMap;

 The first member of the values is the summed energy deposition in a
 given strip, while the second member of the values is the number of
 hits in a given strip.  Using the second member, it's possible to
 do some checks on just how many times a strip got hit, and what
 kind of error we get in our reconstructed hits.  Note, that this
 information is currently not written to the digits tree.  I think a
 QA (Quality Assurance) digit tree is better suited for that task.
 However, the information is there to be used in the future.


 Latest changes by Christian Holm Christensen