以弦及音箱之物理模型合成吉他音樂

Abstract

常見的音樂合成方法有頻率調變合成法(Frequency Modulation Synthesis Method)，波形表合成法(Wavetable Synthesis Method)及物 理模型合成法(Physical Modeling)等。頻率調變合成法產生方式簡單， 但是其參數不易控制，而且難以合成高品質的音樂。波形表合成法可以產 生高傳真、高品質的音樂，但需要大量記憶體來儲存取樣的音樂訊號，而 且如果要產生不同長度音樂或分辨兩支同種類樂器的聲音會相當困難。而 使用物理模型合成法就可解決以上的困難。目前在物理模型合成法中，以 數位導波管方法(Digital Waveguide)較為著名，亦有類似物理模型合成 法的K-S(Karplus-Strong)方法，使用數位濾波器的方法來產生音樂。數 位導波管方法及K-S方法只有模擬弦的振動行為，但無法準確模擬弦的振 幅大小會隨頻率而變化的情形。 在本文我們提出一以物理模型方法來合 成吉他音樂訊號。我們以(1)弦振動模型及(2)音箱振動模型來模擬整個吉 他發聲系統。我們使用橫波波動方程式(Transverse Wave Equation)推導 出弦振盪輸出並配合自然指數(Exponential)函數來描述弦振盪幅度，以 形成弦振動模式；音箱振動系統則以一IIR濾波器來描述。弦模式參數以 RLS(Recursive Least-Square Algorithm)來求取，音箱IIR系統之參數則 使用SMM(Steiglitz-McBride Method)系統判別技術來獲取。我們的弦振 動模型能準確模擬出在不同頻率，不同音高的弦振幅變化行為，因此可以 反映出在不同頻率時的振幅衰減情形。以我們所提出的物理模型方法產生 吉他音樂訊號，所需計算量及記憶體均小而且所合成之吉他音樂品質亦達 滿意。 Most modern music synthesis uses one of three major techniques, FM(Frequency Modulation), wavetable and physical modeling approaches.FM is simple to implement; however it is difficult to associate its parameters with the sound quality. Thus, FM is not easy to generate the music with high sound quality. The wavetable approach can reproduce more realistic sound, but it takes a large amount of memory to store the natural music samples. Moveover, it is difficultto play the music notes for different length and distinguish the sounds from two instruments of the same kind. However, the physical modeling can avoid the drawbacks of above approaches. The digital waveguide and K-S(Karplus-Strong) methods are two well-known physicalmodeling approaches. Nevertheless, the digital waveguide and K-S methods are used to imitate only the vibration of the string. Furthermore, they can not describe the decay phenomenon of the vibrating string exactly. In this thesis, we propose a physical modelto synthesize the guitar music; we employ both the string model and the body model to simulate the guitar. The string model is obtainedby representing the vibrating guitar string using the transverse waveequation and applying the exponential function to approximate the amplitude decay of the string. The guitar body model is expressed by an IIR function. We compute the string model parameters using RLS(Recursive Least Square) method and the body model parametersusing SMM(Steiglitz- McBride) method. Our string model can accuratelycharacterize the decay phenomenon of the vibrating string for each music note. The proposed approach requires less computationalcomplexity and memory, and the synthesized guitar music exhibits satisfactory sound quality.