Multi-Resolution Fourier Analysis Part I: Fundamentals

• 作者: Nourédine Yahya Bey
• 来源期刊: 通讯、网络与系统学国际期刊(英文)
• 学科: 数学
• 关键词: MULTI-RESOLUTION SPECTRAL ANALYSIS FOURIER ANALYSIS RESOLUTION Frequency RESOLUTION
• 年，卷（期）: 2011,（6）
• 页码范围: 364-371
• 页数: 8页
• 分类号: O1

摘要

In the first paper of this series, we propose a multi-resolution theory of Fourier spectral estimates of finite duration signals. It is shown that multi-resolution capability, achieved without further observation, is obtained by constructing multi-resolution signals from the only observed finite duration signal. Achieved resolutions meet bounds of the uncertainty principle (Heisenberg inequality). In the forthcoming parts of this series, multi-resolution Fourier performances are observed, applied to short signals and extended to time-frequency analysis.