| 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)
林 祥介 東京大学, 大学院・数理科学研究科, 助教授 (20180979)
三村 昌泰 東京大学, 大学院・数理科学研究科, 教授 (50068128)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥12,200,000 (Direct Cost: ¥12,200,000)
Fiscal Year 1999: ¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1998: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 1997: ¥9,200,000 (Direct Cost: ¥9,200,000)
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| Keywords | wavelet / biorthogonal wavelet / time-frequency analysis / block-diagonalization / base-line correction / Riesz potential / seismic data / time-series analysis / ウェーブレット解析 / データ解析 / 画像解析 / 話者分離 / ドップラーレーダー / メソサイクロン / 竜巻 / 画像処理 / 時間-周波数解析 / 1 / fスペクトル / 地震加速度 / 音声信号処理 / ドップラーデータ / 地震波解析 / 音声処理 / 雑音除去 |
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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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