Mathematical Reasoning in application of wavelet analysis and related problems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540197
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Osaka Electro-Communication University
• Principal Investigator: Mandai Takeshi 大阪電気通信大学, 工学部, 教授 (10181843)
• Co-Investigator(Kenkyū-buntansha): ASHINO Ryuichi 大阪教育大学, 教育学部, 教授 (80249490)
• Co-Investigator(Renkei-kenkyūsha): MORIMOTO Akira 大阪教育大学, 教育学部, 准教授 (50239688)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: ウェーブレット / スケーリング関数 / ヒルベルト変換 / 信号源分離 / 解析信号 / 瞬間振幅

Outline of Final Research Achievements

We considered several mathematical problems, which occur when we apply wavelet analysis, especially (continuous or discrete) wavelet transforms, and we make clear the basic properties of the transforms which would be useful in applications. Especially, we found the transform of scaling functions corresponding to the (fractional) Hilbert transforms of wavelet functions. By this, an important property of Meyer wavelets is made mathematically clear. This result could also be applied to blind source separation (the problem to extract information about original signals from observed signals which are unknown mixtures of the original signals).

Free Research Field

ウェーブレット解析