臺灣博碩士論文加值系統

　　數位濾波器是數位信號處理中兩大主題之一，而現場可規劃閘陣列（FPGA）已成為ASIC設計的一種新趨勢，因此在本論文中，我們特利用FPGA來實現各種濾波器架構，包含一維濾波器、二維濾波器、全通濾波器及雙通道二維濾波器組。另外，我們亦將以麥克連轉換的技巧，以一維濾波器實現二維濾波器之架構。
　　在濾波器硬體設計的過程中，係數的量化是主要的困難點所在。在本論文中，我們是以反覆拉氏乘數法求得次最佳化之量化係數，甚至我們可將係數表示成帶符號之二冪次方式，如此不需使用乘法器即可設計濾波器，降低了硬體的複雜度，也提高了執行速度。另外，我們以麥克連轉換的技術實現二維濾波器的設計，只需改變少數係數，即可改變濾波器的形狀。在架構雙通道二維濾波器組方面，我們將傳送端的分解系統與接收端的合成系統全植入同一晶片中，可用來達成編碼或解碼的動作。
　　上述濾波器的實現均使用Verilog硬體描述語言與FPGA來完成，實驗驗證得到不錯的執行效率，可用於即時信號處理系統。

　　Digital filters designs are one of the two main topics in digital signal processing, while FPGA has become a new trend of the ASIC design. So in this thesis we will apply FPGA technique to implement several filters including one-dimensional filters, two-dimensional filters, all-pass filters and two-channel two-dimensional filter banks. Moreover, we will realize two-dimensional filters using one-dimensional architecture by McClellan transformation.
　　Coefficient quantization is the main problem while implementing the filters, and in this thesis we will use the iterative Lagrange multiplier approach to achieve sub-optimal quantized coefficients; or the coefficients can be expressed as signed-powers-of-two and the implementation can be achieved without using multipliers, which will reduce the complication of the hardware and increase the speed. In this thesis, we also implement two-dimensional filters using one-dimensional architecture by McClellan transformation techniques, and the shape of the designed filters can be changed with renewing a few coefficients. As to the implementation of two-channel two-dimensional filter banks, we combine the analysis filter banks and synthesis filter banks in a single chip, so the designed chip can be used as a coder or a decoder.
　　All the above filters have been implemented by using Verilog hardware description language and FPGA technique, and the simulation shows that the performances are satisfied and the designed systems can be applied in real-time systems.

中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒 論 1
1.1 研究背景與動機 1
1.2 論文組織 2
第二章 一維濾波器設計與實現 4
2.1一維線性相位有限脈衝響應濾波器設計 4
2.1.1以權重最小均方法設計類型I低通濾波器 6
2.1.2離散係數FIR濾波器設計 8
2.2一維FIR濾波器結構 11
2.2.1濾波器係數分析與乘法器 12
2.2.2分散式算術的運用 14
2.3使用FPGA實現一維FIR濾波器 18
第三章 二維濾波器設計與實現 25
3.1二維線性相位有限脈衝響應濾波器設計 25
3.1.1設計類型I-1二維低通濾波器 25
3.1.2離散係數二維FIR濾波器設計實例 27
3.2二維FIR濾波器結構 30
3.3使用FPGA實現二維FIR濾波器 32
第四章 應用McClellan轉換的二維濾波器設計與實現 40
4.1一維濾波器至二維濾波器的轉換 40
4.2使用麥克連轉換的濾波器結構 43
4.3使用FPGA實現McClellan轉換二維濾波器 45
第五章 雙通道二維濾波器組的設計與實現 54
5.1無乘法器雙通道二維濾波器組設計 54
5.1.1設計二維完美重建濾波器 56
5.1.2設計二維離散係數濾波器 57
5.1.3設計無乘法器雙通道二維濾波器組 59
5.2雙通道二維濾波器組硬體架構 60
5.3使用FPGA實現雙通道二維濾波器組 63
第六章 全通濾波器設計與實現 70
6.1無限脈衝響應數位全通濾波器設計 70
6.2數位全通濾波器結構 72
6.3使用FPGA實現一維IIR全通濾波器 75
第七章 結 論 80
7.1結論 80
7.2未來展望 81
參考文獻 82

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