these results validate and extend the initial synchronization calibration constants determined from beam tests.

H2 beam test data
-----------------

For test beams in 2004 and 2006, a section of the HCAL barrel was mounted on a table that was adjustable in $\eta$ and $\phi$ coordinates. The unit under test was exposed to pion beams with energies in the 3–300 range. The delivered beam was asynchronous with the 40 MHz integration clock, so all relative sampling phases could be investigated. From these tests the following important timing benchmarks for the HCAL were accurately measured.

[htbp]{} &\

&

\

The HCAL pulse shape was successfully reconstructed from data. Since the pulse is integrated before it is digitized, this required a numerical differentiation technique that utilized the phase between particle arrival and the integration clock, as measured by a time-to-digital converter (TDC) running at 32 times faster than the sample clock rate. This allowed the separation of the data sample into subsamples $S_n$, with $n=$1..32 ordered by TDC phase. These subsamples represent the integration of the pulse $P(t)$ shifted successively by the TDC bit resolution ($\Delta t = 0.78$ ns). Then,

$$\label{eq:recopulse}
\langle I_m \rangle_{S_{n+1}}-\langle I_m \rangle_{S_n} \simeq \int_\tau^{\tau+\Delta t}P(t)dt \simeq P_\mathrm{avg}(\tau)\Delta t\quad,
