  Classical (quasinormal) and quantum (Hawking) radiations are investigated for
test fields in the background of a four dimensional, spherically symmetric and
asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB)
theory. The geometry of the EdGB black hole deviates from the Schwarzschild
geometry only slightly. Therefore, here we observe that the quasinormal
spectrum also deviates from its Schwarzschild limit at most moderately,
allowing for a $9\%$ decrease in the damping rate and up to a $6\%$ decrease in
the real oscillation frequency. However, the intensity of Hawking radiation of
an electromagnetic field turned out to be much more sensitive characteristic
than its quasinormal spectrum, allowing for a $54\%$ increase of the energy
emission rate. The analytical formula for the eikonal regime of quasinormal
modes is derived for test fields and it is shown that the correspondence
between the eikonal quasinormal modes and null geodesics is indeed fulfilled
for test fields, but is not expected for the gravitational one.
