  We present an analysis of gravitational wave (GW) predictions from five
two-dimensional Core Collapse Supernova (CCSN) simulations that varied only in
the Equation of State (EOS) implemented. The GW signals from these simulations
are used to produce spectrograms in the absence of noise, and the emergent
high-frequency feature (HFF) is found to differ quantitatively between
simulations. Below 1 kHz, the HFF is well approximated by a first-order
polynomial in time. The resulting slope was found to vary between 10-50% across
all models. Further, using real interferometric noise we investigated the
current capabilities of GW detectors to resolve these differences in HFF slope
for a Galactic CCSN. We find that for distances up to 1 kpc, current detectors
can resolve HFF slopes that vary by at least 30%. For further Galactic
distances, current detectors are capable of distinguishing the upper and lower
bounds of the HFF slope for groupings of our models that varied in EOS. With
the higher sensitivity of future GW detectors, and with improved analysis of
the HFF, our ability to resolve properties of the HFF will improve for all
Galactic distances. This study shows the potential of using the HFF of CCSN
produced GWs to provide insight into the physical processes occurring deep
within CCSN during collapse, and in particular its potential to further
constrain the EOS through GW detection.
