Range‐distributed targets are often characterized as arrays of point scatterers. This conceptualization corresponds to a target impulse response that is a sequence of impulses. A physically meaningful generalization of this description is obtained by modeling an impulse response in terms of pulse doublets, impulses, step functions, ramp functions, etc., i.e., as a superposition of delayed impulsesanddifferentiated or integrated impulses. A sonar system for generalized target characterization is derived in this paper. Signals and receivers are specified for (1) optimum estimation of reflector parameters and (2) detection of a known target in clutter. The derived signals correspond closely with some of the waveforms that are used by dolphins and bats for echolocation. The corresponding echo analyzers are similar to psychoacoustic models of the mammalian hearing system.Subject Classification: [43]60.20, [43]60.50; [43]30.82; [43]80.50.