鄭士康臺灣大學：電信工程學研究所賴俞佑Lai, Yu-YoYu-YoLai2007-11-272018-07-052007-11-272018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/58699本論文提出一個最佳化FM (Frequency Modulation)合成器參數的系統。此系統使用基因演算法 (Genetic Algorithm)尋找一組適當的FM參數並且產生相近於目標音色的聲音。這些參數被視為基因演算法中的基因，而一組能夠產生聲音的參數被視為一個個體。一開始系統輸入一個wave格式的目標聲音檔，然後GA核心亂數產生一組FM合成器的初始參數。經過計算各組參數的適應値之後，系統使用自然選擇的程序來挑選進入變異階段的個體。在變異階段，不同的運作程序可使個體的基因重新組合，最後進入下一世代的運作。個體經過世代的更迭會更接近實際解，包含適當的參數以產生相似於目標的聲音。在這篇論文中我們也提出一種新的方法，結合頻譜距離和頻譜重心兩種音色特徵為GA運作核心的適應函數。實驗測試了五種目標音色：平台鋼琴、金屬鍵琴、管風琴、單簧管和尼龍弦吉他。實驗結果顯示，我們所提出的方法比傳統只使用頻譜距離的方法更加出色。我們也執行了一些實驗用以決定音色特徵合併的權重和測定其他音色特徵的特性。In this thesis we propose a system to optimize the parameters of an FM (Frequency Modulation) synthesizer. The system can find the parameters of FM synthesizers based on GA (Genetic Algorithm), and generate a sound similar to the target sound. In the GA process, the parameters of the FM synthesizer are viewed as genes, and the set of parameters that can generate a sound is viewed as an individual. Initially, the system inputs a wave format file as the target sound, and then the GA core randomly initializes a set of parameters for FM synthesis. Then, the system calculates the fitness value for each individual and selects individuals for the variation step through natural selection. In the variation step, different operations are applied to modify the genes of the individuals. Finally, the process moves on to the next generation. After several generations, the individuals will be close to the solutions and contain proper parameters to generate similar sounds. In this thesis, we also propose a novel approach that combines two timbral features: spectral norm and spectral centroid distance as the fitness function of GA process. We conducted experiments with five target tones: grand piano, celesta, organ, clarinet and nylon guitar. Results of the experiments show that our approach outperforms the conventional approach that only applied spectral norm. We also conducted experiments for deciding the weighting of the combined features and determining the characteristics of selected timbral features.Abstract i 摘要 ii Contents iii List of Figures v List of tables vii Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Literature Survey 2 1.3 Approach 3 1.4 Organization of Thesis 4 Chapter 2 Background 5 2.1 FM Synthesis Techniques 5 2.2 The Genetic Algorithm 6 2.3 Timbral Features 7 Chapter 3 Parameter Optimization System for FM Synthesis Based on Genetic Algorithm 11 3.1 Introduction 11 3.2 The FM Synthesizer 12 3.2.1 The Operator 12 3.2.2 Waveform Types 13 3.2.3 The Envelope Generator 13 3.2.4 Cascading the Operators 14 3.2.5 Parameters of the FM Synthesizer 16 3.2.6 Synthesis Examples 17 3.3 Feature Extraction and Comparison 21 3.4 The Implementation of the Genetic Algorithm 31 3.4.1 Process for the Genetic Algorithm 31 3.4.2 Operations for the Genetic Algorithm 32 3.4.3 Selection 34 3.4.4 Niche count 35 3.5 Combination of Timbral Features 37 Chapter 4 Experiments and Results 39 4.1 Experiments with a Single Objective Function 39 4.2 Determining the Weightings of the Timbral Features 43 4.3 Experiments with Combined Objective Function 45 4.4 Summary 51 Chapter 5 Further Discussions 52 5.1 Sounds with Low Energy 52 5.1.1 The weakness checker 52 5.2 The Critical Population Size 54 5.3 Reducing the Searching Space 56 Chapter 6 Conclusions 58 References 60569413 bytesapplication/pdfen-USFM合成基因演算法音色特徵參數最佳化FM SynthesisGenetic AlgorithmTimbral FeaturesOptimization for Parametersthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/58699/1/ntu-95-R93942114-1.pdf