The equations that govern nonlinear acoustics are quite complicated and unfortunately they do not have general analytical solutions. They usually require the use of a computer simulation. However, as early as 1965, Berktay performed an analysis under some simplifying assumptions that allowed the demodulated SPL to be written in terms of the amplitude modulated ultrasonic carrier wave pressure Pc and various physical parameters. Note that the demodulation process is extremely lossy, with a minimum loss in the order of 60 dB from the ultrasonic SPL to the audible wave SPL. A precompensation scheme can be based from Berktay's expression, shown in Equation 1, by taking the square root of the base band signal envelope E and then integrating twice to invert the effect of the double partial time derivative. The analogue electronic circuit equivalents of a square root function is simply an op-amp with feedback, and an equalizer is analogous to an integration function. However these topic areas lie outside the scope of this project.