Moments of a wave propagating with dispersion and damping

When a wave propagates in a medium with dispersion and damping, different frequencies propagate at different velocities and are attenuated at different rates. Accordingly, the wave changes as it propagates. These propagation effects can negatively impact automatic classification, since what is observed changes from location to location. We examine various moments of a wave, such as duration and bandwidth, which are often used as features for classification, and quantify the effects of dispersion and damping on these moments. We also identify moment-like features that are invariant to dispersion and damping, and thus may offer advantages over ordinary moments as features for classification.