本文提出了一種套用在二維多階基於整數代數的Daub-4小波濾波器架構，它改善了原先的設計，除了能有的效降低濾波器對加法器的需求之外，甚至在二維運算中，節省了一個垂直方向的Daub-4濾波器架構。在這種基於整數代數的多階編碼架構中，有著無乘法器以及精準運算的優點。而為了更加改善濾波器對於硬體的需求，所以改變了資料讀取的順序，以降低轉至記憶體的大小，本文在Daub-4濾波器中，使用隔行運算的方式，能使轉至記憶體的大小從N×N縮小到10，其中N是處理中影像的長跟寬度。最後使用Xilinx Zedboard測試開發版，實現經過改良的一階跟多階二維Daub-4超大積體電路架構，並使用各種不同的圖像進行測試。

This paper proposes a novel architecture for algebraic integer (AI) based multi encoding of 2-D Daubechies-4 wavelet filters. This architecture improves on previous designs, which can significantly reduce the requirement of the adders. Moreover, it also reduces one of 1-D Daubechies-4 wavelet filters in algebraic integer (AI) block. The multi encoded AI framework allows a multiplication-free and computationally accurate architecture. In order to reduce the transpose memory (TM), the 2-D Daubechies-4 wavelet filters will operates follow by Interlaced Read Scan Algorithm (IRSA). The size of the transpose memory (TM) block can be reduced from N×N to 2N as well as increase speed to calculate final value output. The 2-D Daubechies-4 single and multi-level VLSI architectures are implemented on a Xilinx Virtex-6 xc7z020-1clg484 field programmable gate array (FPGA) device. The designs were tested with different gray image size of 512×512 .

目錄
中文摘要....................................................Ⅰ
英文摘要....................................................Ⅱ
目錄........................................................Ⅲ
圖目錄......................................................Ⅴ
表目錄......................................................Ⅶ
第一章	簡介..................................................1
第二章	離散小波轉換原理......................................4
第三章	離散小波轉換應用......................................9
第四章	基於整數代數的Daub-4跟-6濾波器.......................13
4.1數學背景..............................................13
4.2二維濾波器............................................15
4.3基於整數代數的Daub-4跟-6離散小波轉換架構...............17
	4.3.1  Daub-4跟-6整數代數濾波器架構.....................20
	4.3.2組合塊A、B、C跟D架構..........................22
	4.3.3最後重組階段.....................................27
第五章	提出的改良Daub-4跟-6濾波器...........................29
	5.1基於整數代數的濾波器架構..............................29
	5.2二維濾波器架構........................................30
第六章	隔行讀取算法.........................................35
	6.1常規讀取算法..........................................35
	6.2隔行讀取算法..........................................37
	6.3轉至記憶體............................................41
第七章	二維設計與測試結果...................................46
	7.1加法器數量............................................46
	7.2記憶體需求............................................48
7.3硬體資源比較.........................................49
	7.4影像測試..............................................50
	7.5	Daub-6濾波器..........................................51
第八章	結論.................................................55
參考文獻....................................................56





圖目錄
圖2.1、小波展開函數之頻率響應圖..............................5
圖2.2、一階二階離散小波轉換架構..............................7
圖3.1、傳統信號分析時的時間與頻率關係.......................10
圖3.2、Mallat(Dyadic)分析時的時間與頻率關係.....................10
圖3.3、一階二維的分析示意圖.................................12
圖3.4、三階二維的分析示意圖.................................12
圖4.1、四階二維的Daub-4濾波器架構...........................19
圖4.2、四階二維的Daub-6濾波器架構...........................20
圖4.3、Daub-4整數代數濾波器架構..............................21
圖4.4、Daub-6整數代數濾波器架構..............................22
圖4.5、濾波器架構以及組合塊A...............................23
圖4.6、組合塊B.............................................24
圖4.7、濾波器架構以及組合塊C...............................25
圖4.8、組合塊D.............................................26
圖5.1、改良的Daub-4整數代數濾波器架構.......................29
圖5.2、改良的Daub-6整數代數濾波器架構.......................30
圖5.3、二維濾波器運算架構...................................31
圖5.4、改良的二維濾波器運算架構.............................32
圖5.5、二維濾波器運算架構...................................33
圖5.6、改良的二維濾波器運算架構.............................34
圖6.1、傳統的二維離散小波轉換架構...........................36
圖6.2、通常讀取算法的Daub-4濾波器..........................37
圖6.3、隔行讀取算法的Daub-4濾波器..........................40
圖6.4、轉至記憶體的儲存方式.................................42
圖7.1、經由改良過架構的Daub-4濾波器所測試的影像結果，(a)原始影像，(b)一階、(c)二階、(d)三階影像圖...............................50









表目錄
表4.1、DAUB-4濾波器分析......................................17
表7.1、改良以及原先架構的DAUB-4加法器比較...................47
表7.2、隔行跟通常讀取算法的轉至記憶體比較結果...............49
表7.3、一階二維的濾波器架構硬體資源比較.....................50
表7.4、改良以及原先架構的DAUB-6加法器比較..................52
表7.5、隔行跟通常讀取算法的轉至記憶體比較結果...............53
表7.6、一階二維的濾波器架構硬體資源比較.....................54

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