ABSTRACT
This chapter develops illustrative nonlinear techniques to effect processing in difficult channels and relates the results to the preceding techniques, that is, autocorrelation, cepstrum. In specific applications, the metrics or distance measures within the channel are featured a priori by appropriate sets of time delays. The total channel space is divided into subspaces, each characterized by a known set of time delays. The applications address problems in passive source localization, restoration of cancelled peaks, identification, distortion in lumped parameter networks, and seismic echo sounding. For passive localization in a multipath environment, the relative range and depth of the source to the receiver may be estimated from the extracted time delays in the complex cepstrum. Properties of homomorphic filtering and their application to reverberant, distortional, and dispersive channels are delineated. While processing based on peak detection and estimation can be sustained in reverberant and distortional channels, breakdown occurs in the presence of dispersion.
