  The BPM system in Booster only can provide the beam position from the average
of about 15 bunches due to the electronic limitation. Numerically calculating
the difference made by this average can nearly give all the information, which
is needed for extrapolating the BPM data. It is still useful to derive the
analytical expression for the BPM reading, which can be helpful in getting the
insight for the BPM system optimization.
