聲學頭部關係轉移函數(Head related transfer function, HRTF)係指在自由聲場下，聲音傳遞至人耳的轉移函數。由於人頭與耳廓等幾何形狀影響聲場的散射與繞射等效應，HRTF之分佈與音源-人頭的相對方向有莫大關係。因此HRTF對於研究音源對於人耳感受之研究頗為重要，對應於心理聲學與雙耳量測技術中，扮演相當重要的腳色。本文以理論解與邊界元素法分析剛性圓球模型周圍聲場，確認聲場與HRTF模擬之正確性。再探討以橢圓球與加上耳廓的類人頭模型作為簡化人頭的頭部關係轉移函數特性，並利用聲學互易原理縮減HRTF的計算量。另外，整理MIT依KEMAR的人體模型建立的HRTF資料庫之基本特性，與橢圓球與加上耳廓的類人頭模型之分析結果進行比較；分析結果顯示加上耳廓的類人頭模型，已能表現大部分KEMAR人體模型具備的HRTF特性。橢圓球與加上耳廓的類人頭模型之分析結果與實驗結果一致性很高。將實驗結果加上心理聲學參數，探討不同方位的聲音對響度與銳度計算結果之影響。

The Head Related Transfer Functions (HRTFs) describe the effects of human head and ears on sound wave propagation from sound source to ears in free field, which are defined to indicate the characteristics of human hearing acoustic. Owing to the geometric parameters of human head and ears, the distribution of HRTF has close relationship of relative positions between sound source and human ears. HRTFs are important on the hearing perception and binaural technique in psychoacoustic research. In this reasearch, the basic characters of a rigid sphere HRTFs were investigated by using analytical solution and boundary element method (BEM). Then, the HRTFs for a simplified ellipsoid head with and without ears models were examined. To reduce the computation resource, the acoustic reciprocal principle was used for numerical analysis. The HRTFs of these two models were compared with the characters of MIT KEMAR HRTF database, and the results show that the characters of the with ears model match well with MIT KEMAR HRTF database. T he simulated results match well with the experimental data. Finally, the experimental data are examined with several psychoacoustic parameters, and the effects sound directions on the loudness and sharpness were investigated.

誌謝........................................................... i
中文摘要...................................................... iii
Abstract ...................................................... v
目 錄......................................................... vii
圖目錄......................................................... xi
表目錄........................................................ xix
第一章 緒論..................................................... 1
1.1 研究動機.................................................... 1
1.2 文獻探討.................................................... 2
1.3 研究方法與目的.............................................. 4
第二章 基本理論介紹.............................................. 7
2.1 聲學基本理論................................................. 7
2.1.1 聲波的散射(scattering)與繞射(diffraction) ................. 7
2.1.2 聲學互易性(acoustic reciprocity) .......................... 8
2.1.3 頭部關係轉移函數........................................... 9
2.1.4 MIT HRTF 資料庫 ........................................... 11
2.2 聲學邊界元素法............................................... 15
2.3 心理聲學基本理論............................................. 18
2.3.1 遮蔽效應(Masking) ......................................... 18
2.3.2 三分之一倍頻程(Third Octave) .............................. 18
2.3.3 臨界頻帶(Critical Bands) .................................. 20
2.3.4 心理聲學參數............................................... 21
第三章 剛性球模型的HRTF 之解析解與數值解......................... 25
3.1 入射平面波在剛性圓球上散射的解析解的推導..................... 25
3.2 剛性圓球模型HRTF 的解析解.................................... 30
3.3 邊界元素法計算剛性圓球模型HRTF............................... 32
3.3.1 直接改變音源位置與利用聲學互易原理計算HRTF................. 32
3.3.2 以直接改變音源位置分析剛性圓球模型HRTF..................... 33
3.3.3 以聲學互易原理分析剛性圓球模型HRTF......................... 38
3.4 討論......................................................... 41
第四章 簡化仿真人偶的HRTF 特性分析............................... 43
4.1 幾何模型說明................................................. 44
4.2 邊界元素模型................................................. 47
4.3 簡化仿真人偶聲場分析......................................... 48
4.3.1 直接法與互易原理比較....................................... 48
4.3.2 分析結果討論............................................... 49
4.4 單耳聲場分析................................................. 71
ix
第五章 HRTF 量測實驗............................................. 73
5.1 實驗場地介紹................................................. 73
5.2 簡化型聲學仿真人偶模型....................................... 73
5.3 實驗儀器與實驗佈置........................................... 75
5.3.1 實驗儀器介紹............................................... 75
5.3.2 實驗佈置................................................... 79
5.4 實驗流程..................................................... 82
5.5 實驗結果與討論............................................... 83
5.5.1 實驗與分析結果比較......................................... 83
5.5.2 心理聲學參數計算結果....................................... 87
5.5.3 心理聲學參數計算結果討論................................... 92
第六章 結論...................................................... 95
參考文獻......................................................... 97
附 錄............................................................ 101
A. MIT HRTF 資料庫(Gardner & Martin, 1994b) ..................... 101
B. 單體喇叭規格 ................................................. 108
C. 麥克風規格 ................................................... 109

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