頭部轉移函數之數值計算與量測

Abstract

本文在頭部轉移函數(HRTF)數值計算方面提出一以階層勢能定理為基礎的簡單虛擬聲源重現法。在此方法下，由任意形狀輻射聲源所造成的聲場可以聲波疊加之原理描述。在使用聲源互易性和適當的矩陣規則化之下，每一個方位上的頭部轉移函數可藉由設定外在頭部網格之邊界條件進行數值計算而得到。任意方位上的頭部轉移函數可被描述成是擁有不同體積速度之自由空間格林函數的總和。另外在本文中利用間接邊界元素法和量測所得之頭部轉移函數也用來和經由虛擬聲源重現法所計算出的頭部轉移函數進行比較。在頻率響應分析方面，足夠的網格數目和適當的矩陣規則化可以使得計算出之頭部轉移函數近乎所量測之頭部轉移函數的包絡線。合理的指向性更是驗證了頭部轉移函數數值計算的可行性。在運算量分析上，虛擬聲源重現法在合理的網點數目下展現了在運算時間與記憶體使用上較為少量的需求。在結果的分析上，數值誤差可以藉由增加網點數目來加以改善。數值計算和量測所得的頭部轉移函數也分別實現在數次主觀聆聽實驗中。實驗結果顯示，合成頭部轉移函數的重要定位特徵可以在這些聆聽實驗中成功的產生作用。

A simple virtual source representation motivated by layer potential theory is presented for head related transfer function (HRTF) computations. The acoustic field of arbitrarily shaped radiators is described by using the principle of wave superposition in virtual source representation. With the acoustic reciprocity and appropriate matrix regularization, the HRTFs at each direction are calculated by setting the additional boundary condition of external mesh. The HRTF at an arbitrary direction finally is presented as the sum of free space Green’s functions with different volume velocities. Another numerical method – indirect boundary element method and a HRTF measurement are also implemented to compare with the calculated HRTFs by using virtual source representation. In the frequency response analysis, the calculated HRTFs closely approximate the envelopes of the measured HRTFs with enough mesh nodes and suitable matrix regularization. Reasonable directional responses in both numerical methods also prove the feasibility of HRTF numerical computation. From the comparison of computation loadings, the virtual source representation shows the fewer requirements in computation time and memory use under the reasonable number of mesh nodes. Performance analysis reveals the numerical errors can be improved by increasing the number of nodes. Numerous subjective experiments are also conducted by using calculated HRTFs and measured HRTFs. The results reveal the important characteristics of sound localization are successfully reproduced by the synthesized HRTFs.