臺灣博碩士論文加值系統

小波轉換在理論上為利用一原始函數所產生之多階基底函數對訊號進行多重解析度之時頻域分析技術，其在訊號處理相關應用上提供了一新穎又有效的方法；利用小波轉換，可有效分離出訊號各頻段的資訊，而由於多重解析度的特性，抵補了傳統傅立葉轉換的不足之處，故其目前被廣泛應用於各式訊號處理、影像處理等研究課題上。在本論文中，提出並實現一個以離散小波轉換為基礎之去雜訊電路架構，此一電路可應用於生理訊號之去雜訊處理。在此，我們針對Daubechies 4的三階離散小波轉換之去雜訊電路進行設計，此電路架構可分為三部份：離散小波正轉換、thresholding以及離散小波反轉換。針對所設計出之電路各個部份，我們先分別進行軟、硬體模擬，隨後並利用一FPGA做硬體的實現，觀察其實際處理結果與效能。而根據分析結果顯示，將一實際測得帶有嚴重雜訊干擾之心電圖訊號經由此一去雜訊電路處理後，吾人發現此一電路可以充分符合即時性處理的需求，且其在雜訊濾除的效果上亦有不錯的表現。

Wavelet Transform is a multiresolution analysis that decomposes an original signal to multi-octave based functions, and we can analysis the original signal using these functions. It provides a novel and effective tool for many applications in signal processing area. Also, it has the advantage over the traditional Fourier Transform with respect to time-frequency analysis because of its characteristic of multiresolution. Therefore, it has been widely applied into many aspects of signal/image processing-related researches. In this thesis, we proposed and realized a Discrete Wavelet Transform (DWT) based de-noising circuit architecture with the applications into the noise reduction for medical signals. Here, our design was based on a three octave-level with Daubechies 4 filters. The circuit consists of three parts: DWT, thresholding, and IDWT. Software and hardware simulations were performed first. Furthermore, we implemented the de-noising circuit by downloading the Verilog codes to an FPGA to observe its practical processing ability. As a result, by inputting a noisy Electrocardiogram (ECG) into the de-noising circuit we found that the circuit satisfied the requirement of real-time processing, and also achieved pretty good performance for noise reduction.

目錄
致謝..................................................... iii
中文摘要.................................................. iv
英文摘要.................................................. v
目錄..................................................... vi
圖目錄................................................... viii
表目錄................................................... xi
第一章 序論............................................... 1
1.1研究背景與動機.......................................... 1
1.2小波轉換去雜訊之原理與應用................................ 2
1.3離散小波轉換相關研究介紹.................................. 3
1.4章節概要................................................ 5
第二章 離散小波轉換電路設計................................ 6
2.1離散小波轉換原理......................................... 6
2.2遞迴金字塔演算法......................................... 8
2.3電路設計................................................ 15
2.3.1一階電路架構.......................................... 15
2.3.2二階與二階以上電路架構.................................. 18
2.3.3電路架構軟體模擬....................................... 22
第三章 反離散小波轉換電路設計................................ 26
3.1反離散小波轉換原理....................................... 26
3.2反遞迴金字塔演算法....................................... 27
3.3電路設計................................................ 29
3.3.1一階電路架構........................................... 29
3.3.2二階與二階以上電路架構.................................. 31
3.3.3電路架構軟體模擬....................................... 35
第四章 Thresholding去雜訊電路設計........................ 42
4.1離散小波轉換去雜訊電路之重要性簡介........................ 42
4.2 Thresholding演算法.................................... 44
4.3電路設計與模擬.......................................... 45
第五章 設計流程與模擬結果.................................. 51
5.1軟體模擬結果........................................... 51
5.2乘法器與加法器硬設計.................................... 54
5.3硬體驗證結果........................................... 61
第六章 結論與未來研究方向................................ 64
參考文獻................................................. 66
附錄一................................................... 69

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