對於輕便型音訊裝置在數位音訊的錄放裝置中，如果沒有特殊的低音擴音器或較為昂貴的播放器或耳機，僅利用一般小型多媒體的播放器或耳機播放較低頻的低音是較為困難的。因而眾多文獻指出了低頻頻寬擴展的方法或者可稱作虛擬音高(虛擬低音)，可以在不提高成本的情況下播放出較低頻的低音部份。虛擬音高是利用”遺失基頻”的心理聲學概念去建立的，不過由於當在產生虛擬音高的同時，也會造成非線性失真，導致音訊失真，進而使人類感知聽覺受到影響。因而我們的研究針對虛擬低音中的非線性失真的部份，提出利用小波轉換信號分析的方法，改善其非線性失真所帶來的音訊失真。最後達到優化虛擬低音的目標。

In digital audio playback systems for portable audio device, there is a strong demand to produce deep bass using small multimedia speakers and earphones, without the need for additional subwoofer or expensive speakers/earphones. Therefore, many documents have pointed out the low frequency bandwidth extension method or can be called the virtual pitch (virtual bass), and it can comparatively broadcast out the bass part of low frequency in case of rising cost. The virtual pitch is utilizing and setting up because of ‘missing fundamental’ of the psychoacoustic concept. But because will cause non-linear distortion while producing virtual pitch, causing the audio signal to be distorted, and making the perceptual hearing of human influences. Therefore our research focuses on the non-linear distortion part of virtual bass, utilizing the wavelet transform and improve its non-linear distortion caused the audio signal of distortion. Finally, reach the goal of optimizing virtual bass.

摘要 i
ABSTRACT ii
誌謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 - 導論 1
1.1. 導論 1
1.2. 心理聲學的效用對於頻帶受限喇叭的低頻增強 1
1.2.1. 音高 (Pitch) 2
1.2.2. 虛擬音高 (Virtual Pitch) 4
1.2.3. 響度影響 (Loudness Effect) 5
1.3. 動機 6
1.4. 章節組織 7
第二章 – 虛擬低音 8
2.1. 概論 8
2.2. 非線性系統 (NLD) 9
2.3. 濾波器 10
2.3.1. 高通濾波器 (HFIL) 10
2.3.2. 第一帶通濾波器 (FIL1) 10
2.3.3. 第二帶通濾波器 (FIL2) 11
2.4. 諧波信號的增益 (Gain) 12
2.4.1. 固定增益 (Fixed Gain) 13
2.4.2. 適應性頻率增益 (Frequency-adaptive Gain) 13
第三章 – 小波轉換 16
3.1. 導論 16
3.2. 小波轉換和信號多階層分析 17
3.3. 分頻編碼 18
3.4. 離散小波轉換 20
3.5. 離散小波封包轉換 21
第四章 –低頻頻寬擴展 22
4.1. 頻寬擴展中的諧波產生器 22
4.2. 全波整流器 23
4.2.1. 頻域特性 (Spectral Characteristics) 23
4.2.2. 時域特性 (Temporal Characteristics) 24
4.3. 積分器 25
4.3.1. 頻域特性 25
4.3.2. 時域特性 27
4.4. 截止器 28
4.4.1. 頻域特性 28
4.4.2. 時域特性 30
4.5. 改良型乘法器 31
4.5.1. 頻域特性 31
4.5.2. 時域特性 34
4.6. 分析各諧波產生器的互調失真 35
4.6.1. 全波整流器的互調失真 36
4.6.2. 積分器的互調失真 37
4.6.3. 截止器的互調失真 39
4.6.4. 改良型乘法器的互調失真 41
4.7. 研究理論—低頻頻寬擴展結合小波轉換 44
第五章 – 實驗結果 55
5.1. 頻率響應分析 (諧波失真) 55
5.2. 頻率響應分析 (頻譜差異度) 69
5.3. 主觀的效果評比 70
第六章 – 結論與未來工作 74
6.1.結論 74
6.2.未來工作 74
參考文獻 75

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