Propagation-invariant classification of sounds in channels with dispersion and absorption

In a previous paper [G. Okopal et al., J. Acoust. Soc. Am. 123, 832-841 (2008)], a method to obtain features of a wave that are unaffected by dispersion, per mode, was developed for improving classification of underwater sounds (e.g., sonar backscatter). The current paper builds on this work and presents additional contributions. First, it is shown that the dispersion-invariant moments developed previously are not invariant to frequency-dependent attenuation (absorption); consequently, their classification performance degrades in such channels. Second, a feature extraction method is developed to obtain features that are invariant to dispersion, and to two forms of absorption (known a priori): namely, absorption that yields spectral magnitude attenuation (in dB) that is linear with frequency, and linear with log-frequency. Third, the relationship of these absorption- and dispersion-invariant moment (ADIM) features to the cepstrum of the wave is examined, and it is shown that cepstral moments are also invariant to dispersion, and to the first form of absorption for odd-order moments. Finally, simulations are conducted to illustrate the performance of the ADIMs and cepstral moments on classifying the backscatter from steel shells in a dispersive channel with absorption. Receiver operator characteristic curves quantify the superior discriminability of the ADIMs and cepstral moments compared to ordinary moments.