臺灣博碩士論文加值系統

本篇論文的主題在找出一串有限長度的正數列，使其頻譜能夠近似於一個巳給定的非負頻譜。此問題可表示為凸性半無限維最佳化問題(convex semi-infinite optimization problem)。我們使用最小平方誤差指標及Lagrange multiplier為基礎發展一套適用於本系統的演算法，其優點可以將原來半無限維(semi-infinite)最佳化問題轉換成有限維度(finite-dimensional)最佳化問題來解決。文中將會用三種演算法來做比較，並以幾個不同階數的例子來探討此三個演算法的優缺點。

The purpose of this thesis is searching for a finite-length positive sequence so that its spectrum can optimally approximate to a given spectrum. The design problem is formulated as a convex semi-infinite optimization problem. The algorithm uses the least square criterion and Lagrange multipliers on each iteration. The advantage of this approach is that the original semi-infinite programming problem can be solved directly as a finite-dimensional optimization problem. In this thesis we will use three algorithms and discuss their advantages and disadvantages by using some numerical examples.

中文摘要 -------------------------------------I
英文摘要 -------------------------------------II
誌謝 -----------------------------------------III
目錄 -----------------------------------------IV
表目錄 ---------------------------------------VI
圖目錄 ---------------------------------------VII
符號說明--------------------------------------X
第一章 諸論-----------------------------------1
1.1 簡介--------------------------------------1
1.2 FIR濾波器之最佳化設計---------------------2
1.3 研究方法與背景----------------------------3
1.4 章節介紹---------------------------------3
第二章 正數列與凸函數之基本特性---------------4
2.1正數列的特性-------------------------------4
2.2 凸函數(convex function)之描述-------------5
第三章 相關理論背景---------------------------9
3.1 問題型式---------------------------------9
3.2 不等式限制最佳化問題----------------------10
第四章 演算法---------------------------------14
4.1演算法分析---------------------------------14
4.2演算法疊代過程及流程圖----------------------23
4.3數值範例-----------------------------------25
第五章 方法比較-------------------------------32
5.1等值漣波FIR濾波器設計方法之簡介-----------32
5.2 利用Minimax最佳化法設計正數列-------------33
5.2.1等值漣波正數列設計-----------------------33
5.2.1 數值範例--------------------------------37
5.3 利用平移方法在最小平方指標下設計正數列-----42
5.3.1 數值範例---------------------------------44
5.4 三種演算法比較----------------------------50
5.4.1範例比較---------------------------------50
5.4.2誤差比較---------------------------------56
第六章 結論-----------------------------------58
參考文獻--------------------------------------59

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