微扰法分析躯干散射对近场头相关传输函数的影响

本文提出微扰与多极展开相结合的方法，近似计算雪人模型近场头相关传输函数（HRTF），并利用此方法定量分析躯干散（反）射声波对HRTF的影响。计算结果表明，躯干散射对HRTF的影响与微扰近似的阶数、频率、声源位置（包括方向和距离）等有关。在一级微扰近似下，躯干散射对HRTF的影响整体上随频率的升高、或声源距离的减小、或仰角的降低、或声源相对受声耳方向的偏离角度的增大而增大。随着微扰级数的增加，高阶微扰项对计算结果的贡献迅速减少。在声源距离不小于0.02 m 以及仰角不小于135°的条件下，对 20 kHz 以下的频率范围，采用三阶微扰近似的计算误差在 ± 1.0dB 以内。 由于 n 阶微扰在物理上是和头部和躯干之间的 n 重散射相对应的，因而本文的结果表明，在雪人模型的条件下， 头部和躯干的前三阶多重散射对 HRTF 是重要的，四阶及以上散射可以忽略。

Analyse on the Effects of Torso Scatterings on Near-field Head-related Transfer Functions Using Perturbation Method

The perturbation method combined with multipole expansion method to calculate the head-related transfer functions (HRTFs) of the snowman mode approximately, and the effects of the torso scatterings and reflections on HRTFs are analysed quantitatively. The results indicate that the contribution of the torso scatterings on HRTFs depends on the order of perturbation, frequency and position of sound source. Under the first perturbation approximation, the contribution of the torso scatterings increases with higher frequency, with shorter distance between the source and head center, with lower elevation of the source, and with azimuth departing from the ear. For the source distances not shorter than 0.2m and the elevations not lower than 45° under the horizontal plane, the errors in the third-order perturbation solutions are within ±1.0 dB below 20 kHz. The nth order perturbation corresponds to the nth order scatterings and reflections between the head and torso, therefore, for the conditions of the snowman model, the effects of the earlier three scatterings and reflections on HRTFs are important, and the contributions of the fourth-order and higher-order ones are neglectable.