Application of Wavelets to Observational Data Analysis

小波在观测数据分析中的应用

• 批准号: 09554002
• 负责人: YAMADA Michio
• 金额: $ 7.81万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09554002/
• 关键词: 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

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.

研究了小波分析到观察数据的应用。以地震的加速数据为例，我们提出了一种数据校正方法，该方法包括由生物表定小波扩展和Lagrange乘数法组成。此方法基于小波的扩展，使我们能够在时频域中校正本地数据。此外，我们设计了一种算法来生成生物三相的小波，该小波将一类线性运算符对准/半分子对扩展转换的变化，以减少数据校正中的数值任务，例如集成。我们将此算法应用于Riesz电位，衍生性希尔伯特转化和亚伯转化。数值检查表明，在非对角线区域中，表示矩阵的元素衰减迅速。这意味着可以将矩阵视为带对角的矩阵，并允许我们快速计算。我们还研究了小波在包括摩擦和振荡吸收在内的问题上的工程应用。

项目成果

M.Yamada: Wavelets and Their Applications. (1998)

M.Yamada：小波及其应用。

M.Sakamoto: "Wavelet Akalysis of Acoustical Signals" Journal of Japan Society for Simulation Technology. 27-34 (1997)

M.Sakamoto：“声学信号的小波分析”日本模拟技术学会杂志。

S.Sakakibara: "A Technique for Reducing Noise in Laboratory Data" Wavelets and Their Applications. (1998)

S.Sakakibara：“一种减少实验室数据噪声的技术”小波及其应用。

S.Sakakibara: "Design of a Wavelet Package on Mathematica Version 3" Innovation in Mathematics(Proc.2nd Mathematics Sym.). 2. 427-434 (1997)

S.Sakakibara：“Mathematica 第 3 版上小波包的设计”数学创新（Proc.2nd Mathematica Sym.）。

M. Kobayashi, M. Sakamoto, T. Saito, Y. Hashimoto, M. Nishimura, and K. Suzuki: "Wavelet Analysis for Text-to-Speech systems in M. Kobayashi, (ed.)"Wavelets and Their Applications : Case Studies. SIAM. 75-100 (1998)

M. Kobayashi、M. Sakamoto、T. Saito、Y. Hashimoto、M. Nishimura 和 K. Suzuki：“M. Kobayashi（编辑）中的文本到语音系统的小波分析”小波及其应用：