Study of the approximate restoration of signals based on stochastic sample values 確率的な標本値に基づく信号の近似的な復元に関する研究
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著者
書誌事項
- タイトル
-
Study of the approximate restoration of signals based on stochastic sample values
- タイトル別名
-
確率的な標本値に基づく信号の近似的な復元に関する研究
- 著者名
-
Sa-Nguankotchakorn, Somsak
- 著者別名
-
サ グアンコットチャコン, ソムサック
- 学位授与大学
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東京工業大学
- 取得学位
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博士 (工学)
- 学位授与番号
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甲第2628号
- 学位授与年月日
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1993-03-26
注記・抄録
博士論文
目次
- Contents / p1 (0004.jp2)
- 1 Introduction / p5 (0006.jp2)
- 1.1 Problem Formulation and Objective / p5 (0006.jp2)
- 1.2 Research Background / p7 (0007.jp2)
- 1.3 Research Outline / p9 (0008.jp2)
- 2 Preliminaries / p11 (0009.jp2)
- 2.1 Notations and Definitions / p11 (0009.jp2)
- 2.2 Shannon and Someya's Sampling Theorem / p17 (0012.jp2)
- 3 Generating Function for Sampling Theorem / p19 (0013.jp2)
- 3.1 Introduction / p19 (0013.jp2)
- 3.2 Some Notations and Definitions / p19 (0013.jp2)
- 3.3 Generating Function and Interpolation Functions / p20 (0014.jp2)
- 3.4 Proof of Sufficiency and Necessity / p23 (0015.jp2)
- 3.5 Summary / p28 (0018.jp2)
- 4 Generating Functions Minimizing Some Measures / p29 (0018.jp2)
- 4.1 Introduction / p29 (0018.jp2)
- 4.2 Measure of Weight Factor [数式] / p30 (0019.jp2)
- 4.3 Measure of Weight Factor [数式] / p34 (0021.jp2)
- 4.4 Measure of Generalized Weight Factor / p36 (0022.jp2)
- 4.5 Measure of Weight Factor 1+[数式] / p38 (0023.jp2)
- 4.6 Re-composition of Interpolation Functions / p44 (0026.jp2)
- 4.7 Summary / p46 (0027.jp2)
- 5 Some Considerations on Generalized Sampling Theorem of Low-Pass Stochastic Signals / p47 (0027.jp2)
- 5.1 Introduction / p47 (0027.jp2)
- 5.2 Some Notations and Definitions / p48 (0028.jp2)
- 5.3 Interpolation of Band-limited Stochastic Signals / p49 (0028.jp2)
- 5.4 Calculation of Interpolation Functions / p53 (0030.jp2)
- 5.5 Covariance and Variance of Output Signals / p55 (0031.jp2)
- 5.6 Summary / p57 (0032.jp2)
- 6 Interpolatory Estimation of Multi-Dimensional Orthogo-nal Expansion with Stochastic Coefficients / p59 (0033.jp2)
- 6.1 Introduction / p59 (0033.jp2)
- 6.2 Some Notations and Definitions / p61 (0034.jp2)
- 6.3 Set of Signals under Consideration / p63 (0035.jp2)
- 6.4 Definition of Measure of Error / p67 (0037.jp2)
- 6.5 Concrete Expression of Measure of Error / p69 (0038.jp2)
- 6.6 Summary / p71 (0039.jp2)
- 7 Derivation of Generalized Optimum Interpolation Functions / p73 (0040.jp2)
- 7.1 Introduction / p73 (0040.jp2)
- 7.2 Derivation of Generalized Optimum Interpolation Functions / p74 (0041.jp2)
- 7.3 Generalized Discrete Orthogonality / p77 (0042.jp2)
- 7.4 Simultaneous Minimization of Various Measures of Errors / p80 (0044.jp2)
- 7.5 Additional Considerations / p82 (0045.jp2)
- 7.6 Summary / p84 (0046.jp2)
- 8 Entire Summary / p85 (0046.jp2)
- Acknowledgments / p87 (0047.jp2)
- Bibliography / p89 (0048.jp2)
- Reference of Author's Researches and Presentations / p93 (0050.jp2)
- A General Form of Generating Function / p95 (0051.jp2)
- B General Form of Interpolation Functions / p101 (0054.jp2)
- B.1 Interpolation Functions of General form of Generating Function / p101 (0054.jp2)
- B.2 Interpolation Functions of Theorem 4.5 / p104 (0056.jp2)
- C Proof of Sufficiency and Necessity of Generalized Sampling Theorem / p107 (0057.jp2)
- C.1 Proof of Sufficiency / p107 (0057.jp2)
- C.2 Proof of Necessity / p110 (0059.jp2)
- D Derivation of Power Spectrum Density Functions / p113 (0060.jp2)
- E Some Proofs of Formulas / p115 (0061.jp2)
- F Schwarz Inequality in Statistical Case / p117 (0062.jp2)