# 臺灣博碩士論文加值系統

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 本論文探討之主題在於運用更進一步改善的帕波式演算法(Papoulis-Gerchberg algorithm，PGA)對於重建被可加性高斯白雜訊(Additive white Gaussian noise，AWGN)汙染的訊號之收斂分析。本研究中提出的延伸型帕波式演算法(Extended Papoulis-Gerchberg algorithm，ePGA)在使用條件及已知資訊更加詳細的情況下，分析訊號重建之效果。由於傳統的帕波式演算法多用於理想的狀況下進行訊號還原，本研究將可加性高斯白雜訊加入訊號中，透過改變遺失訊號的初值，探討初值對訊號重建效能之影響，並運用延伸型帕波式演算法找出與原訊號不同之新收斂點，經由模擬實驗結果得知，新收斂點對原訊號亦呈現高斯分佈(Gaussian distribution)，證明雜訊與新收斂點有關連性。
 This is dedicated to analyzes the reconstruction efficiency of extented Papoulis-Gerchberg algorithm (ePGA) with more information and prior knowledge in signals. The traditional ePGA usually performs signal recovery under ideal situations. In this research, AWGN is added into signal for test. By changing the initial value of the missing signal, the effective of the initial value on the signal reconstruction efficiency is also discussed, meanwhile new convergence points through ePGA is explored. After the simulation, the distribution of new convergence points; in comparison to the original signal, found to be Gaussian. Besides, we also confirm the strong correlation between noise and new convergence point.
 誌謝 II摘要 IVABSTRACT VI圖目錄 VIII第壹章 緒論 11.1 研究背景與動機 11.2 研究目標 21.3 本文架構 2第貳章 文獻探討與背景知識 32.1 帕波氏疊代演算法 32.2 帕波氏疊代演算法重建效能分析 5第参章 雜訊訊號重建分析 73.1 延伸型帕波氏疊代演算法 73.1.1延伸型帕波氏演算法重建步驟 73.1.2 驗證ePGA收斂性 93.2 模擬訊號與參數設定 103.3 ePGA訊號重建效能 103.4 ePGA訊號重建分析 123.5 ePGA重建AWGN訊號分析 143.6 不同初值對訊號重建效能之分析 20第肆章 新收斂點分析 244.1 新收斂點位置 244.2 新收斂點對原訊號之分布 28第伍章 結論 32參考文獻 34
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