A directional audible sound can be generated by amplitude-modulated (AM) into ultrasound wave from a parametric array. To synthesize audio signals produced by the self-demodulation effect of the AM sound wave, a quasi-linear analytical solution, which describes the nonlinear wave propagation, is developed for fast numerical evaluation. The radiated sound field is expressed as the superposition of Gaussian Beams. Numerical results are presented for a rectangular parametric loudspeaker, which are in good agreement with the experimental data published previously.