  The ability to directly detect gravitational waves has enabled us to
empirically probe the nature of ultra-compact relativistic objects. Several
alternatives to the black holes of classical general relativity have been
proposed which do not have a horizon, in which case a newly formed object (e.g.
as a result of binary merger) may emit echoes: bursts of gravitational
radiation with varying amplitude and duration, but arriving at regular time
intervals. Unlike in previous template-based approaches, we present a
morphology-independent search method to find echoes in the data from
gravitational wave detectors, based on a decomposition of the signal in terms
of generalized wavelets consisting of multiple sine-Gaussians. The ability of
the method to discriminate between echoes and instrumental noise is assessed by
inserting into the noise two different signals: a train of sine-Gaussians, and
an echoing signal from an extreme mass-ratio inspiral of a particle into a
Schwarzschild vacuum spacetime, with reflective boundary conditions close to
the horizon. We find that both types of signals are detectable for plausible
signal-to-noise ratios in existing detectors and their near-future upgrades.
Finally, we show how the algorithm can provide a characterization of the echoes
in terms of the time between successive bursts, and damping and widening from
one echo to the next.
