| Project/Area Number |
12554003
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 展開研究 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | KYOTO UNIVERSITY (2003)
The University of Tokyo (2000-2002) |
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Principal Investigator |
YAMADA Michio YAMADA,Michio, 数理解析研究所, 教授 (90166736)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAKIBARA Susumu Tokyo Denki University, School of Information Environment, Professor, 情報環境学部, 教授 (70196062)
OHKITANI Koji Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (70211787)
OKAMOTO Hisashi Research Institute for Mathematical Sciences, Professor, 数理解析研究所, 教授 (40143359)
KOBAYASHI Mei IBM, Tokyo Research Laboratory, Advisory Researcher, 東京基礎研究所, 副主任研究員
SASAKI Fumio Kajima Co., IT solution devision, Senior Researcher, ITソリューション部, 主査
薩摩 順吉 東京大学, 大学院・数理科学研究科, 教授 (70093242)
石岡 圭一 東京大学, 大学院・数理科学研究科, 助教授 (90292804)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥13,300,000 (Direct Cost: ¥13,300,000)
Fiscal Year 2003: ¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2002: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 2000: ¥4,800,000 (Direct Cost: ¥4,800,000)
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| Keywords | wavelet transformation / orthogonal wavelets / biorthogonal wavelets / symbol functions / variational problem / constraints / seismic wave / entropy / 双直交ウェーブレット / 地震波形 / 離散ウェーブレット / メイヤーウェーブレット / ドブシーウェーブレット / 直交ウェーブレット / 応答スペクトル / 模擬地震波 / ウェーブレット解析 / 離散ウェーブレット変換 / データ解析 / 時系列解析 / 時間周波数解析 / 応用スペクトル解析 / データ処理 / 数値計算 |
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| Research Abstract |
A construction method is proposed for a biorthogonal wavelet which approximates an arbitrary given target function. This method is expected to be useful in the cases where the given data is a superposition of the target functions dilated, and translated. The biorthogonal wavelet then provides an efficient decomposition of the given data into the elements of events. The biorthogonal wavelet is obtained by Lagrange's multiplier method minimizing the L2 norm of the difference between the target function and the primary wavelet. As an example, this method is applied to some target functions to produce biorthogonal wavelets close to these functions. Some seismic signals are decomposed by wavelet expansion with some of these adapted-biorthogonal wavelets, which are found to have less entropy than the expansions with Meyer and Daubechies wavelets. In this research project, engineearing applications of' wavelets were also studied in several fields, including construction of artificial seismic signals, oscillation analysis, fractional derivative viscoelasticity models.
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