  We have performed an extensive numerical study of coalescing black-hole
binaries to understand the gravitational-wave spectrum of quasi-normal modes
excited in the merged black hole. Remarkably, we find that the masses and spins
of the progenitor are clearly encoded in the mode spectrum of the ringdown
signal. Some of the mode amplitudes carry the signature of the binary's mass
ratio, while others depend critically on the spins. Simulations of precessing
binaries suggest that our results carry over to generic systems. Using Bayesian
inference, we demonstrate that it is possible to accurately measure the mass
ratio and a proper combination of spins even when the binary is itself
invisible to a detector. Using a mapping of the binary masses and spins to the
final black hole spin, allows us to further extract the spin components of the
progenitor. Our results could have tremendous implications for gravitational
astronomy by facilitating novel tests of general relativity using merging black
holes.
