臺灣博碩士論文加值系統

隨著數位訊號處理的發展，近年來許多用於音樂創作的電腦音源軟體針對早期產量少、不易取得之類比電子琴進行模擬，將其特有聲響和操作方式以數位形式重現與普及。此類電子琴運用濾波器過濾一擁有豐富頻率成分的聲源作為聲音設計的方法，稱之減法合成。減法合成聲源部分以鋸齒波、方波、三角波和正弦波四種基礎波型最常被使用。虛擬類比電子琴其一重要的議題為找出一有效率的演算法產生週期性的基礎波型聲源，並在音質方面減少失真現象造成聽覺上的干擾。
眾多以數位產生基礎波型運用於聲音合成的研究中，鋸齒波及方波之生成方法最常被討論與研究。本論文欲對另一種常用之基礎波型三角波做一探討與模擬。從正弦波出發，利用一波型成形器塑型後運用濾波器修改諧波大小生成三角波。並使用聽覺閥和聽覺遮蔽效應兩種聽覺感知模型作為音質評斷方法，判定音質是否失真。由模擬所得之三角波在此評斷方法下無失真音最高可達G7 (MIDI number 103)，涵蓋了常使用的樂音範圍。在減法合成聲音設計的架構下，許多只運用三角波為初始聲源的合成聲響可以運用此方法作為聲源產生部分。

This thesis discuss the source geometric waveforms in early analog synthesizer which use subtractive synthesis as sound designing principle. Implement the classical synthesizer triangle waveforms with reduced aliasing. This method are base on the concept of waveshaping a sine wave and modify the harmonic contents with a filter. Sound quality evaluation using masking effect and hearing threshold models shows that waveshape triangle wave method is perceptually alias-free over almost whole register of the grand piano to note G7 (MIDI number 103). It is applicable in digital implementations of subtractive sound synthesizer.

Abstract...............................................i
Acknowledgement......................................iii
Contents..............................................iv
List of Figures.......................................vi
List of Tables........................................vi
Chapter 1 Introduction.................................1
1.1 Background.........................................1
1.2 Research of Virtual Analog Synthesis...............2
1.3 Goals and Outline of the Thesis....................3
Chapter 2 Subtrctive Synthesis and Virtual Analog......4
2.1 Subtractive Synthesis..............................4
2.2 Subtractive Synthesizer............................4
2.2.1 Sound Processing Modules.........................5
2.2.2 Modulation Modules...............................5
2.3 Classic Waveform...................................6
2.3.1 Sawtooth Wave....................................8
2.3.2 Square and Triangle Wave.........................9
2.4 Digital Implement of Classic Waveform..............9
Chapter 3 Algorithms Review...........................13
3.1 Lane’s method....................................13
3.2 Differentiate Parabolic Wave......................16
3.3 Differentiate polynomial wave.....................18
3.4 Bandlimited Impulse Train (BLIT)..................19
3.4.1 Discrete Summation Formula......................20
3.4.2 Sum of Windowed Sincs (BLIT-SWS)................21
Chapter 4 Implement an Alias Suppressed Triangle wave.22
4.1 Nonlinear Waveshaping.............................22
4.2 Hyperbolic Tangent Waveshaper.....................23
4.3 Waveshaper used in Triangle Wave Algorithm........24
4.4 Triangle wave algorithm...........................26
4.5 Comparison........................................28
4.6 Perceptual Evaluation.............................31
Chapter 5 Conclusions and Future Works................34
Bibliography..........................................35

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