The self-demodulation property of a parametric array loudspeaker (PAL) system can peel off audible sound modulated on ultrasonic waves and deliver it with high directivity, but also introduces nonlinear distortion. The PAL system can be modeled by the Volterra series expansion to circumvent heavy calculation owing to numerical sound field solutions. However, most of the Volterra filter based models are vague in terms of the applicable region and the theoretical foundation. In this work, we extand the discrete Berktay far field solution to propose a new differential Volterra filter (Diff-VF). Integrated with Kalman algorithm, our proposed structure outperforms current VF-based models using the NLMS algorithm, exhibiting superior performance in ablation experiments. Moreover, the kernel relationship between the existing and proposed VF-based models is also verified.

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