Data from a numerical target scattering model are described in the time and
frequency domains. These echoes are separated into physics-based component
s called wavepackets, which are aspect-dependent. These individual componen
ts are made stochastic by the assumption of random aspect. Each physical co
mponent is then decomposed with a statistically independent basis via the K
arhunen-Loeve Expansion (KLE). It is shown that the echo is well described
by a collection of a feu terms of the KLE, The statistically independent ex
pansion amplitudes are then used to generate detection statistics.