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Multi-Resolution Fourier Analysis Part I: Fundamentals
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International Journal of Communications, Network and System Sciences·Volume 04 (2011)·Pages 364–371·Published 17 June 2011·DOI10.4236/ijcns.2011.46042
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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.
KeywordsMulti-ResolutionSpectral AnalysisFourier AnalysisResolutionFrequency Resolution
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