1999 Fiscal Year Final Research Report Summary
Application of Wavelets to Observational Data Analysis
| Project/Area Number |
09554002
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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 | University of Tokyo |
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Principal Investigator |
YAMADA Michio Dept. of Math. Sci., Univ. of Tokyo, Prof., 大学院・数理科学研究科, 教授 (90166736)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAKIBARA Susumu Dept. of Sci. and Eng., Iwaki Meisei Univ. Prof., 理工学部, 教授 (70196062)
ISHIOKA Keiichi Dept. of Math. Sci., Univ. of Tokyo, Prof., 大学院・数理科学研究科, 助教授 (90292804)
SATSUMA Junkichi Dept. of Math. Sci., Univ. of Tokyo, Prof., 大学院・数理科学研究科, 教授 (70093242)
KOBAYASHI Mei Tokyo Research Lab., IBM, Researcher, 東京基礎研究所, 副主任研究員
SASAKI Fumio Intelligent Systems Dept., Kajima Co., Researcher, 情報システム部, 主査(研究職)
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| Project Period (FY) |
1997 – 1999
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| Keywords | wavelet / biorthogonal wavelet / time-frequency analysis / block-diagonalization / base-line correction / Riesz potential / seismic data / time-series analysis |
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| Research Abstract |
Application of wavelet analysis to observational data is studied. Taking an acceleration data of earthquake as an example, we propose a data correction method consisting of biorthogonal wavelet expansion and Lagrange multiplier method. This method is based on wavelet expansion and enables us to correct the data locally in time-frequency domain. Moreover we devised an algorithm to generate biorthogonal wavelets which diagonalize/semi-diagonalize a class of linear operators in-variant to scale transformation, in order to reduce numerical task in the data correction including, integration, for example. We applied this algorithm to Riesz potential, derivative Hilbert transformation and Abel transformation. Numerical inspection shows that elements of the representation matrices decay rapidly in the off-diagonal region. This means that the matrices can accually be treated as band-diagonal ones, and permits us fast calculation. We also studied engineering application of wavelets to problems including friction and oscillation absorption.
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