A method of processing an audio signal in a nonlinear acoustic system to reduce distortion in corresponding regenerated audio signals. A first nonlinear processing method includes producing a modeled representation of signal demodulation through a propagation medium, applying an inversion to the modeled representation of signal demodulation, and processing an audio signal using the inverted, modeled signal demodulation representation. A second nonlinear processing method includes applying an inversion to a signal demodulation function, producing a modeled representation of the inverted signal demodulation function, and processing an audio signal using the modeled representation of the inverted signal demodulation function. The processed audio signal is then modulated using an ultrasonic carrier signal, and projected through a propagation medium using an acoustic transducer.