Dispersion-invariant features for classification

In dispersive propagation, waves from the same source will generally differ depending on how far they have traveled. Accordingly, it is desirable for classification in such environments to either account for propagation effects, or to obtain features that are invariant to such effects. The latter approach is taken in this paper, and features are derived that are unaffected by channel dispersion, per mode. A "local" view of pulse propagation in time-frequency phase space is considered. It is shown that the local duration of a wave, obtained from its time-frequency Wigner distribution, is invariant to dispersion. While higher moments of the Wigner distribution are not invariant to dispersion, the phase space considerations suggest an approach for defining "dispersion-invariant moments" (DIMs) of any order. This approach is also used to define a dispersion-invariant correlation coefficient that can be used for classification. The classification utility of the DIMs, and of the dispersion-invariant correlation coefficient, is evaluated via simulations of acoustic scattering from steel shells in a dispersive channel model (Pekeris waveguide). Receiver operating characteristic curves quantify the improved discriminability of the DIMs versus ordinary temporal moments, and of the dispersion-invariant correlation coefficient versus the ordinary correlation coefficient.