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研究生:鍾威漢
研究生(外文):Wei-Han Chung
論文名稱:連續係數之數位濾波器與數位濾波器組之最佳設計
論文名稱(外文):Optimal Design of Digital Filters and Digital Filter Banks with Continuous Coefficients
指導教授:李枝宏李枝宏引用關係
指導教授(外文):J.-H. Lee
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:電信工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2001
畢業學年度:89
語文別:中文
論文頁數:177
中文關鍵詞:最佳設計濾波器連續係數濾波器組線性規劃
外文關鍵詞:optimal designfiltercontinuous coefficientfilter banklinear programming
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本論文針對具低延遲性質的FIR數位濾波器與FIR和IIR數位濾波器組設計問題進行探討。
設計方法乃基於線性規劃中內部點演算法並結合近似的方法應用至我們的濾波器與濾波器組的設計問題上。
在FIR數位濾波器設計方面,我們針對Minimax準則下進行我們的設計工作。
至於FIR和IIR濾波器組設計方面,我們針對L1準則進行我們的設計工作並提出幾個模擬結果作為例證與比較。相較於[26][27]的L2設計,我們所提出的L1準則設計有令人滿意的設計結果。

In this thesis,we deal with the problem of designing FIR digital filters ,FIR and IIR filter banks with low-delay property.
The design techniques based on modified primal-affine scaling algorithm and modified dual-affine scaling algorithm,in conjunc-tion with approximation schemes,are then developed for solving the resulting nonlinear optimization.
For FIR digital filters,we using minimax criteria to formul-ate our design problem.
With regard to the FIR and IIR digital filter banks,we using criteria to formulate our design problem,and some simulation results are provided for illustration and comparision.
To compare with the L2 design in[26][27],we find the L1 design we proposed have the satisfactory design results.

目 錄
第一章 序論 1
1.1 研究動機………………………………………………… 1
1.2 論文之貢獻……………………………………………… 2
1.3 論文之組織架構………………………………………… 3
第二章 最佳化的問題與演算法 5
2.1 簡介……………………………………………………… 5
2.2 最佳化問題的數學模型………………………………… 6
2.3 內部點搜尋法…………………………………………… 8
2.3.1 內部點搜尋法的原理…………………………….. 8
2.3.2 Primal Affine Scaling(PAS) Karmarkar Algorithm… 9
2.3.3 Dual Affine Scaling(DAS) Karmarkar Algorithm… 13
2.4 基於Minimax準則的WLS演算法…………………… 16
第三章 具有線性相位之一維FIR濾波器設計 21
3.1 近似問題的形成 ……………………………………… 21
3.2 基於Linf norm的PAS和DAS演算法………………….. 23
3.2.1基於Linf norm的 DAS演算法…………………… 23
3.2.2基於Linf norm的 PAS演算法…………………… 25
3.3.3 基於Linf norm設計的線性相位FIR濾波器…………… 27
3.4 基於Linf norm設計的數位微分器……………………… 30
3.5 設計實例與結果討論…………………………………. 32
第四章 具有任意相位及任意振幅之一維FIR濾波器設計 49
4.1 基於Linf norm之低延遲一維FIR濾波器設計………… 49
4.2基於Linf norm之低延遲數位微分器與希爾伯特(Hilbert)轉換器之設
計………………………………………… 59
4.2.1 Hilbert Transformer………………………………... 59
4.2.2 數位微分器………………………………………. 61
4.3基於Linf norm之複係數數位濾波器設計……………….. 62
4.4設計實例與結果討論……………………………………71
第五章 低延遲之FIR正交鏡像濾波器組設計 103
5.1簡介…………………………………………………… 103
5.2正交鏡向濾波器組之架構及理論分析……………… 104
5.3基於L1+Linf norm準則之設計………………………… 107
5.4設計實例與結果討論………………………………… 116
第六章 低延遲之IIR正交鏡像濾波器組設計 123
6.1簡介……………………………………………………..123
6.2架構及理論分析………………………………………..124
6.2.1 濾波器組之架構及理論分析……………………124
6.2.2 分析濾波器架構…………………………………124
6.3基於L1+Linf norm準則之設計…………………………...126
6.4設計實例與結果討論…………………………………..136
第七章 具有低延遲特性之一維IIR非均勻濾波器組設計 143
7.1簡介……………………………………………………..143
7.2 IIR非均勻濾波器組架構及理論分析…………………144
7.2.1 非均勻濾波器組之架構與完美重建條件……… 145
7.2.2 分析濾波器架構………………………………….. 151
7.3基於L1 norm準則之設計………………………………..151
7.4設計實例與結果討論…………………………………..163
第八章 結論 171
參考文獻 173

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