We explore the subtleties that may emerge if mass accretion events increase
significantly the mass of a black hole horizon during its: gravitational w
ave (GW) emission. We find that horizon growth extends the phenomenology of
black hole ring-down in a well defined manner. The resulting GW signals ar
e best described as amplitude and frequency (AM-FM) modulated versions of t
he simple damped sinusoidal wave forms. Any appreciable increase in the hor
izon mass during emission reflects on the instantaneous signal frequency, w
hich shows a prominent negative branch in the f(f) evolution diagram. The f
eatures of the frequency evolution pattern reveal key properties of the acc
retion event, such as the rural accreted mass and the accretion rate. For s
low accretion rates the frequency evolution follows verbatim the accretion
rate, as expected from dimensional arguments.