本論文將其Roesser模型最小實現理論運用到從Roeeser模型中所衍生出來的Roundoff雜訊之演算法則，以達到將雜訊極小化。

首先介紹二維線性離散系統各模型，然後挑選其最常用之Roesser模型之理論來做其濾波器之設計。其中對於Roesser模型之轉移函數矩陣、可控與可觀性以及最常使用的各模型之最小實現都予以深入探討。最後，藉由二維Roesser模型最小實現之理論與其所衍生出之Roundoff雜訊理論，成功地設計一成本較低、效果較佳之濾波器，以達到去除雜訊之效果。

The purpose of this paper is to minimize the noise by applying the theory of the minimal realization of the Roesser model to the algorithm of the Roundoff noise derived from the Roesse model.

First, each model of two dimensional linear systems was introduced. The Roesser model theory in common use is picked out to design the digital filter. Afterwards, transference function matrix, steerability, observability of Roesser model and the minimal realization in common use were discussed in depth. Finally, the theory of minimal realization of two dimensional Roesser model and the Roundoff noise theory derived from it are used to design a better filter at lower cost successfully to achieve the goal of removing the noise or percolating the noise.

文目錄..………………………………………………………………..i
圖表索引……………………………………………………………….iii
論文摘要(中文)……………………………………………………….vi
論文摘要(英文)……………………………………………………….vii
第一章 緒論
1.1 前言……………………………………………………….1
1.2 研究動機………………………………………………….2
1.3 文獻回顧………………………………………………….3
1.4 內容架構………………………………………………….5
第二章 影像處理應用與簡介
2.1 數位影像資料格式……………………………………….8
2.1.1 空間域數位影像資料格式……………………….....8
2.1.2 空間域數位影像資料格式…………………………..9
2.2 影像數學表示和處理方式.……………………………..10
2.3 範圍影像處理.............................................................11
2.4 影像濾波的定義….…………......................................14
第三章 2-D線性離散系統
3.1 2-D Roesser模型的數學描述…………………………23
3.2 2-D Attas’s和Fornasini-Marchesini’s模型的數學描述
……………………………………………………….......24
3.3 各種典型模型之間之間的相互關係…………...............26
3.4 2-D系統的轉移函數矩陣………………………………..29
3.4.1 2-D Roesser模型的轉移函數矩陣……………......30
3.4.2 2-D Fornasini-Marchesini’s模型的轉移函數
矩陣……………………………………………….....31
3.5 Roesser模型之狀態轉移函數及響應公式………….....33
3.6 2-D系統Roesser模型之可控(可達)與可觀性之
探討………………………………………………..........37
3.6.1 局部可控性和局部可觀性…………………………38
3.6.2 局部可控性……………………………………........38
3.6.3 局部可觀性………………………………………….41
第四章 2-D 系統Roesser模型之狀態空間實現
4.1 2-D Roesser模型全極點與全零點系統狀態空間轉移
函數實現之描述………………………………………....43
4.2 2-D Roesser模型的實現……………………………….53
4.3 單輸入單輸出2-D Roesser模型的最小實現………....60
4.4 單輸入單輸出2-D Roesser模型的典範形實現……....66
第五章 極小化Roundoff雜訊之二維狀態空間數位濾
波器的分析
5.1 雜訊模型的衍生…………………………………………75
5.2 輸出雜訊能量與動態範圍限制…………………………78
5.3 Roundoff雜訊演算法則……………………………......81
第六章 總結與未來展望
6.1 本文總結………………………………………………..100
6.2 未來展望………………………………………………..101

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