Worthmann Brian M, Dowling David R
Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.
Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA.
J Acoust Soc Am. 2020 Mar;147(3):1863. doi: 10.1121/10.0000953.
The autoproducts are nonlinear mathematical constructs developed from acoustic fields with non-zero bandwidth. When averaged through the field's bandwidth, the autoproducts may mimic a genuine acoustic field at frequencies that are lower or higher than the original field's bandwidth. The resulting opportunity to extend signal processing to user-selectable below- or above-band frequencies is intriguing for many signal processing algorithms. Based on prior work, the limitations of the autoproducts' mimicry of out-of-band fields are understood when the in-band acoustic field is well-represented by ray acoustics. Thus, the focus in this study is on autoproducts in acoustic shadow zones behind barriers containing only diffracted acoustic fields where a sum of ray-path contributions is not an adequate field description. Diffraction is expected to be a detriment to autoproduct techniques due to its sensitivity to frequency. Two ideal shadow-zone environments with exact analytic Helmholtz-equation solutions are considered: Sommerfeld's half-plane problem, also known as knife-edge diffraction, and Mie scattering from a sphere with ka = 40, where k is the wavenumber and a is the sphere's radius. With the exception of the shadow regions, autoproducts experience only mild degradation in field-mimicry performance when compared to what the ray-based theory would predict.
自积量是由具有非零带宽的声场发展而来的非线性数学结构。当通过场的带宽进行平均时，自积量可能会在低于或高于原始场带宽的频率上模拟真实的声场。对于许多信号处理算法而言，由此产生的将信号处理扩展到用户可选择的带外频率的机会很有吸引力。基于先前的工作，当带内声场由射线声学很好地表示时，自积量对带外场的模拟的局限性是已知的。因此，本研究的重点是仅包含衍射声场的障碍物后面的声影区内的自积量，在这些区域中，射线路径贡献的总和不足以描述声场。由于衍射对频率敏感，预计它会对自积量技术产生不利影响。考虑了两种具有精确解析亥姆霍兹方程解的理想声影区环境：索末菲半平面问题，也称为刃形衍射，以及来自ka = 40的球体的米氏散射，其中k是波数，a是球体半径。除了声影区域外，与基于射线的理论预测相比，自积量在场模拟性能方面仅经历轻微的退化。
