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has been cited by the following article:

• 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.