本論文針對三維完美重建濾波器組、數位全通濾波器及複數係數數位濾波器在最小極大值準則下的設計提出幾個新而有效的設計方法。本篇論文提出的方法是根據Karmarkar演算法的affine scaling及dual affine scaling變型發展而得。
對於三維數位濾波器組，本論文提出兩種新的設計方法可供設計具有線性相角響應之FIR分析濾波器及合成濾波器的完美重建濾波器組。所設計的分析濾波器及合成濾波器均在完美重建的限制下依最小極大值誤差準則設計而得。
在數位全通濾波器方面，本文提藉著同時減少最大的振幅及相位誤差或同時減少最大的振幅及群延遲誤差的設計技術，而濾波器的係數就可以由Karmarkar的affine scaling變型演算法獲得。
而在設計複數數位濾波器方面，原始的複數近似值首先被分解成兩個實數部分，然後Karmarkar的affine scaling變型演算法就可以依最小極大值大準大則來減少實數及虛數部分的誤差以得到複數脈波響應的係數。
由本論文各章中的計算機模擬範例結果顯示,本文針對各設計問題所提出的設計方法，其有效性均得以確認。

This thesis presents several novel and efficient techniques for designing three-dimensional (3-D) perfect reconstruction (PR) filter banks, FIR digital all-pass filters, and complex FIR digital filters in minimax sense. The proposed approaches are developed based on the affine and dual affine scaling variants of Karmarkar's algorithm.
As for the 3-D perfect reconstruction digital filter banks, two novel techniques are proposed for designing PR filter banks with FIR analysis and synthesis filters having linear phase responses. The designed analysis and synthesis filters are in the minimax sense subject to the perfect reconstruction constraints.
With regard to the design of FIR digital all-pass filters, we propose design techniques via minimizing the peak magnitude error and peak phase error simultaneously or minimizing the peak magnitude error and peak group delay error simultaneously. The filter coefficients are obtained by an affine scaling variant of Karmarkar's algorithm.
For designing complex FIR digital filters, the original complex approximation is divided into two real ones first. Then the affine scaling variant of Karmarkar's algorithm is also applied to minimize the real part and imaginary part error in minimax sense to get the complex impulse response coefficients.
From the simulation examples demonstrated in each chapter of this thesis, the effectiveness of the proposed design techniques for each considered problem can be confirmed.

中文摘要…………………………………………………………………………….I
ABSTRACT.….……………………………………………………………………II
誌謝………………………………………………………………………………..III
圖表索引…………………………………………………………………………..VI
CHAPTER 1 INTRODUCTION…………………………………………………...1
CHAPTER 2 TWO CHANNEL FCOFB WITH MINIMAX AND
PERFECT RECONSTRUCTION DESIGN…………………………3
2.1 Introduction………………………………………………………3
2.2 Problem Formulation………………………………………….….4
2.2.1 The Perfect Reconstruction FIR Linear Phase
Filter Banks…………………………………………………5
2.2.2 Desired Response for the Analysis Filters…………………7
2.2.3 Formulation of the Design Problem……………………….9
2.3 The Proposed Approach………………………………………...11
2.3.1 Updating for Minimax Optimization Proble...……….13
2.3.2 Updating for PR by first-order approximation
schem………………………………………………………14
2.4 Design Example………………………………………………...16
2.5 Conclusion………………………………………………………17
CHAPTER 3 MINIMAX DESIGN OF FIR DIGITAL ALL-PASS FILTERS………25
3.1 Introduction………………………………………………………..25
3.2 FIR Digital All-Pass Filter Design………………………………...26
3.3 Algorithm to Design FIR Digital All-pass Filters…………………29
3.4 Computer Simulation Examples…………………………………...33
3.5 Conclusion…………………………………………………………34
CHAPTER 4 MINIMAX DESIGN OF COMPLEX FIR DIGITAL FILTERS
WITH ARBITRARY COMPLEX FREQUENCY RESPONSE……...42
4.1 Introduction………………………………………………………..42
4.2 Problem Formulation for Complex FIR Filter Design…………….43
4.3 Algorithm to Design Complex FIR Digital Filters………………...47
4.4 Design of Complex FIR All-Pass Filters…………………………..48
4.5 Computer simulation examples and comparisons…………………49
4.6 Conclusion..………………………………………………………..51
CHAPTER 5 CONCLUSION AND POSSIBLE FUTURE RESEAECH WOEKS...59
REFERENCES……………………………………………………………………….60
Appendix A SOME MATRICE' CONTENT AND MATHEMATIC
DERIVATION IN CHAPTER 2………………………………………..64
Appendix B "Two Channel FCOFB with Minimax And
Perfect Reconstruction Design" revised letter…………………………66
Appendix C "Minimax Design of FIR Digital All-Pass Filters" revised letter………67
Appendix D "Minimax Design of Complex FIR Digital Filters with Arbitrary
Complex Frequency Responses" revised letter..………………………68
作者簡介……………………………………………………………………………..69
授權書………………………………………………………………………………..70

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