The method of matched pursuits is an algorithm by which a waveform is parsed into its fundamental constituents here, in the context of short-pulse electromagnetic scattering, wavefronts, and resonances (constituting what we have called wave-based matched pursuits). The wave-based matched-pursuits algorithm is used to develop a codebook of features that are representative of time-domain scattering from a target of interest, accounting for the variability of such as a function of target-sensor orientation. This codebook is subsequently used in the context of a hidden Markov model (HMM) in which the probability of measuring a particular codebook element is quantified as a function of target-sensor orientation. We review the wave-based matched-pursuits algorithm and its use in the context of an HMM (for target identification). Finally, this new wave-based signal processing algorithm is demonstrated with simulated scattering data, with additive noise.