TITLE:
Multi-Resolution Fourier Analysis Part I: Fundamentals
AUTHORS:
Nourédine Yahya Bey
KEYWORDS:
Multi-Resolution, Spectral Analysis, Fourier Analysis, Resolution, Frequency Resolution
JOURNAL NAME:
International Journal of Communications, Network and System Sciences,
Vol.4 No.6,
June
17,
2011
ABSTRACT: 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.