Author(s)

Nourédine Yahya Bey

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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.

Multi-Resolution, Spectral Analysis, Fourier Analysis, Resolution, Frequency Resolution

N. Bey, "Multi-Resolution Fourier Analysis Part I: Fundamentals," International Journal of Communications, Network and System Sciences, Vol. 4 No. 6, 2011, pp. 364-371. doi: 10.4236/ijcns.2011.46042.