訊號重建演算法之研究

THE STUDIES OF SIGNAL RECONSTRUCTION ALGORITHMS

羅聰明(Tsung-Ming Lo)

指導教授 ： 許超雲

大同大學/電機資訊學院/電機工程學系所/博士(2006年)

摘要

本論文探討之主題在於改善帕波氏 (Papoulis-Gerchberg)疊代演算法信號重建的研究。應用「邊界匹配」的概念，在帕波氏疊代演算結構中插入一組多項式修正程序法則，而同時達到提升其疊代演算之收斂速度及重建效果的顯著改善，經由此「邊界匹配」概念之運用，將所謂「前置處理」程序導入帕波氏疊代演算結構以提升其效能。我們針對帕波氏疊代演算法則本質上存在著疊代收斂速度較慢及重建信號精準度有限之先天缺陷，導入樣本信號前置處理觀念，並提出兩種改善方案，分別在原始域(time domain)及轉換域(frequency domain)以不同觀點推論出新的演算架構。在原始域以信號樣本端點連續觀點推論，針對待處理之信號 必須設定滿足 之邊界條件；在轉換域以信號帶限近似觀點推論，合理地逕予假設其中間點為0(即強制消弭高頻成分顧慮)，針對待處理之信號 必須設定其對映之轉換域函數 滿足中間點為0之邊界匹配條件。
我們所提的新架構擁有高結構化，快速與高精確度等優點。從實驗結果顯示，無論信號型態為何(帶限函數或非帶限函數)？均可獲得良好的重建信號，明顯地改善遺失信號樣本重建效果。以均方誤差(Mean Square Error；簡稱MSE)比值分析，我們所提出的新架構較傳統演算法可達2個order以上(由10-3→10-5)之顯著成效。

關鍵字

訊號重建

並列摘要

This dissertation is devoted to the study of improving Papoulis-Gerchberg (PG) iterative algorithm for signal reconstruction. Applying the boundary-matched concept, a significant improvement in performance, efficiency and speed of the PG iterative algorithm is achieved by inserting a ‘pre-process’, a polynomial, into the PG iterative algorithm.
Two efficient approaches, one in the time domain and the other in the frequency domain, are proposed to restore lost samples. In the time domain, based on boundary-matched concept, signal x(n) to be processed must meet the boundary condition x(0)=x(N). In the frequency domain, based on the concept of the approximate to band-limited signal in which reasonably assume that the component of the highest frequency is forced to zero, the middle point of the boundary-matched condition of the frequency domain function G(k) of the to be processed signal x(n) is set to be 0.
The proposed new model is well-structured with high precision and performance. According to experiment results, based on the mean square error (MSE) analysis, the improvement of the precision of signal reconstruction of the proposed algorithm is O(10+3) , from 10-2 to 10-5, no matter the original signal is band-limited signal or nonband-limited signal.

並列關鍵字

Papoulis-Gerchberg ； boundary-matched ； band-limited ； pre-process

參考文獻

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