本論文提出了基於複合型模型之小號聲音合成方法。首先，本論文的基礎為數位導波模型，而為了使其合成結果趨向真實，提出額外得補償系統以增進合成品質。特別的地方在於，此系統並非對某個已知的物理系統求解，而是根據優化學習型模型而建立的。在物理模型的幫助下，預期只需要少量之資料即可成功訓練系統。在實驗中，為了先檢測了物理模型之模擬是否合理，可以透過模擬之聲波阻抗，觀察其是否符合真實小號之聲音特性。對於補償系統之實驗，本論文使用了兩段來自Good-Sounds dataset 的音訊作為訓練資料。其結果顯示：可合成頻率範圍比訓練資料廣泛之小號聲音，所建立之複合型模型可合成頻率範圍比訓練資料根為廣泛之小號聲音，換言之，此系統具有推廣能力。同時，其所產生之音檔也可以直接聆聽比較。

In this thesis, a hybrid model is proposed for synthesizing the sound of trumpet. A simple physical model developed by digital waveguides (DWG) modeling is adopted as a baseline system. To achieve realistic trumpet sound synthesis, a compensating system is introduced for improving the simulation quality. An unique characteristic of the system is that, in contrast to solving a mathematical expressions for a physical system, this compensating system is constructed by optimizing a learning based
model. With the help of the physical model, it is expected that only a small amount of data is needed for training the unknown system. In experiments, to validate the used physical model, the simulated acoustic impedance is compared with the measurement of the trumpet. For the compensating system, two audio segment in
Good-Sounds datatset were used. The results show that a trumpet sound can be successfully synthesized with a frequency range which is wider than that of the training data. For this sense, the system has demonstrated an ability to generalize from limited training data. The synthesis audio can be also compared by direct listening.

摘要 i
Abstract ii
1 Introduction
1.1 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Methods
2.1 Wave Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 TravelingWave
Solution . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Digital waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Bidirectional delay line . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2 Ideal acoustic tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Viscothermal loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 DWG Juction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.5 The Limitation of DWG Model . . . . . . . . . . . . . . . . . . . . . 10
2.3 Lip Buzzing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Lip’s motion mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Airflow Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.3 Procedure of simulation . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Full Bore Simulation with Lip Excitation . . . . . . . . . . . . . . . . . . . . 14
2.5 A Compensating System based on Neural Network . . . . . . . . . . . . . . . 15
2.5.1 An Introduction to Neural Network . . . . . . . . . . . . . . . . . . . 15
2.5.2 Fully Connected Layer . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.3 Convolution Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.4 Loss and Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.5 Proposed Compensating System . . . . . . . . . . . . . . . . . . . . . 18
3 Experiments and Discussions
3.1 Bore Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Estimation of Acoustic Impedance . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Lead Pipe and Main Bore . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2.2 Mouthpiece . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.3 Bell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.4 Full bore simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3 Lip Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3.1 Full Bore Simulation with Lip Excitation . . . . . . . . . . . . . . . . 28
3.4 Analysis and Synthesis from Real Recordings . . . . . . . . . . . . . . . . . . 29
3.5 Training the Compensating System . . . . . . . . . . . . . . . . . . . . . . . . 30
iii
3.5.1 Training Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.2 Training Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.3 A Mismatch between Simulation and Real Data . . . . . . . . . . . . . 31
3.5.4 Training by Different Loss Function . . . . . . . . . . . . . . . . . . . 32
3.5.5 Generated Samples with Other Pitches . . . . . . . . . . . . . . . . . . 34
4 Conclusions and Future Works
4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References 36
Appendix 41

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