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研究生:葉斯雄
研究生(外文):Szu-Hsiung Yeh
論文名稱:信號重建使用P.G.演算法之收斂研究改善
論文名稱(外文):THE STUDY OF CONVERGENCE IMPROVEMENT IN PAPOULIS-GERCHBERG ALGORITHM FOR SIGNAL RECONSTRUCTION
指導教授:許超雲許超雲引用關係
指導教授(外文):Chau-Yun Hsu
學位類別:碩士
校院名稱:大同大學
系所名稱:通訊工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2007
畢業學年度:95
語文別:英文
論文頁數:57
中文關鍵詞:線性內插法P.G. 演算法
外文關鍵詞:Papoulis-Gerchberg AlgorithmLinear Interpolation
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摘 要
本論文探討之主題在於進一步改善帕波氏 (Papoulis-Gerchberg)疊代演算法信號重建的收斂速度。
許超雲和羅聰明應用「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。但是,其演算收斂速度還不夠快,因此,本研究著重加快演算收斂速度並且努力保持信號重建效果。
第一個改善方法:調整式低通頻寬。先降低前面疊代操作的頻寬,然後恢復後續疊代操作的頻寬。此改善方法能夠達成較快的演算收斂速度。
由於帕波氏疊代演算法假設丟失的數據為零值。因此,第二個改善方法:應用線性內插法(類似一階保持法) 取代零值的初始設定。經由合併兩個改善方法,模擬實驗達成比第一改善方法更快的演算收斂速度,其疊代次數< 10次。
ABSTRACT
This thesis is devoted to the study of further improving the speed of convergence of Papoulis-Gerchberg (P.G.) iterative algorithm for signal reconstruction.
Hsu and Lo proposed a boundary-matched algothrim, there will be significant improvement on mean square error and convergence speed of the P.G. iterative algorithm by introducing a ‘pre-process’ to the P.G. iterative algorithm. However, there is still room for improvement in the convergence rate. This study is dedicated to speed up the convergence of iteration but keen the M.S.E. level.
Our first proposed approach is to adjust the low-pass band width with decreasing passed band width during the iteration for the P.G.. Finally, restore the band width. This proposed approach achieved better convergence.
Since the original initialization of P.G. algorithm for the lost sample data is set to be zero. Our second proposed approach is to use the Linear Interpolation technique (approximate to be first order hold) to replace zero assumption of the initial setting. By combining the first & second approaches, a better convergence very early iterations (< 10 times) can be achieved in the simulation.
TABLES OF CONTENTS
ACKNOWLEDGEMENTS I
ENGLISH ABSTRACT II
CHINESE ABSTRACT. III
TABLE OF CONTENTS V
LIST OF TABLES VII
LIST OF FIGURES IX
LIST OF ABBREVIATIONS XII

CHAPTER
I Introduction 1
1.1 Research Motivation 1
1.2 Literature Review 1
II The Basic Theorem of the Iterative Agorithm 13
2.1 Introduction 13
2.2 The Iterative Algorithm of Papoulis-Gerchberg 14
2.3 The Criterion of Mean Square Error 17
2.4 Hsu and Lo’s Proposed Modified-I & II Scheme of the Papoulis-Gerchberg Algorithm 19
2.4.1 Proposed Modified-I Scheme in Time Domain 19
2.4.2 Simulations and Results of Modified-I Scheme in Time Domain. 21
2.4.3 Proposed Modified-II Scheme in Frequency Domain 24
2.4.4 Simulations and Results of Modified-II Scheme in Frequency Domain.. 27
2.4.5 Summary 29


III PROPOSED APPROACH-1 — TO SPEEDUP THE PAPOULIS-GERCHBERG ALGORITHM 33
3.1 Introduction. 33
3.2 The Improved Method with Adjustable Low-pass Bandwidth Technique 34
3.3 The Proposed Approach-1 Scheme of the Iteration Algorithm 36
3.4 Simulations and Results 37
3.5 Summary 42
IV PROPOSED APPROCH-2 — VIA IMPROVED INITIAL VALUE PREDICTION TECHNIQUE OF LINEAR INTERPOLATION 44
4.1 Introduction 44
4.2 The Improved Method with Initial Value Prediction Technique 44
4.3 The Approach-2 Scheme of the Iteration Algorithm 46
4.4 Simulations and Results 47
4.5 Summary 52
V Conclusions 53
5.1 Conclusions 53
REFERENCES 55
VITA 58
REFERENCES
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[11]M. Yuit and N. Matsuo, “A new sample-interpolation method for recovering missing speech samples in packet voice communications”, IEEE International Conference on Acoustic, Speech, Signal Processing, pp.381-384, 1989.
[12]R. J. Marks, II, “Restoring lost samples from an over-sampled band-limited signal”, IEEE Transactions on Acoustic, Speech and Signal Processing, vol. ASSP-31, no. 3 pp.752-755, Mar. 1983.
[13]J. A. Cadzow, “An extrapolation procedure for band-limited signals”, IEEE Transactions on Acoustic, Speech, and Signal Processing, vol. ASSP-27, pp.4-12, Feb. 1979.
[14]C. Y. Hsu and Y. F. Liou, “Fast discrete extrapolation via the fast Hartley transform”, IEEE Transactions on Circuits and Systems–II , vol. 40, no. 8, pp.502-504, Aug. 1993.
[15]R. N. Bracewell, The Fourier Transform and Its Applications, 3rd Edition, McGraw-Hill, Printed in Singapore, International Editions, 2000.
[16]P. S. Naidu and B. Paramasivaih, “Estimation of sinusoids form incomplete time series”, IEEE Transactions on Acoustic, Speech, and Signal Processing, vol. ASSP-32, no. 3, pp.559-562, Mar. 1984.
[17]Paulo Jorge S. G. Ferreira, “Non-iterative and fast iterative methods for interpolation and extrapolation”, IEEE Transaction on Acoustic. Signal Processing, vol. 42, no. 11, pp. 3278-3282, Nov. 1994.
[18]C-Y Hsu and T-M Lo, "Signal Reconstruction with Boundary-matching via Iterative Algorithm," IEICE Transaction on Fundamentals of Electronics, Communications and Computer Science, vol.E89-A,pp.3283-3289, Nov. 2006.
[19]T. M. Lo, “The Studies of Signal Reconstruction Algorithm”, Ph. D Dissertation, Department of Electrical Engineering, Tatung University, Oct. 2006.
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