Extended convolution model for computing the far-field directivity of an amplitude-modulated parametric loudspeaker

The convolution model of the parametric loudspeaker describes the far-field directivity of the difference-frequency wave by the product directivity of two ultrasonic primary frequencies convolved with Westervelt's directivity. This can be extended to the case when the primary wave is amplitude-modulated thus resulting in the harmonic distortion of the self-demodulated wave. This paper proposes the extended convolution model with Westervelt's directivity and Berktay's directivity respectively. The angle-dependent harmonic distortion of the parametric loudspeaker is thereafter investigated, which is a topic not often mentioned in previous literature but is of significance in practice. The measurement, numerical simulation and model results are compared for the case when the double sideband modulation is adopted and the frequency response of the ultrasonic emitter is a known factor. The comparison validates that the extended convolution model provides accurate predictions that are consistent with the measurement results and the extended convolution model is a simpler way to compute the far-field directivity of an amplitude-modulated parametric loudspeaker as compared to the numerical simulation.