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Multi-Resolution Fourier Analysis Part I: Fundamentals

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Author(s): Nourédine Yahya Bey

Journal: International Journal of Communications, Network and System Sciences
ISSN 1913-3715

Volume: 04;
Issue: 06;
Start page: 364;
Date: 2011;
Original page

Keywords: Multi-Resolution | Spectral Analysis | Fourier Analysis | Resolution | Frequency Resolution

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.

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