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Ramanujan sums for signal processing of low-frequency noise

dc.contributor.authorMichel Planat
dc.contributor.authorRosu Barbus, Haret-Codratian
dc.contributor.authorSerge Perrine
dc.contributor.editorAmerican Physical Society
dc.identifier.citationMichel Planat, Haret Rosu, and Serge Perrine Phys. Rev. E 66, 056128 (November 2002)
dc.description.abstract"An aperiodic (low-frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Mobius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier transform the analyzing wave is periodic and not well suited to represent the low-frequency regime. In place we introduce a different signal processing tool based on the Ramanujan sums cq(n) well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasiperiodic versus the time n and aperiodic versus the order q of the resonance. Different results arise from the use of this Ramanujan-Fourier transform in the context of arithmetical and experimental signals."
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.titleRamanujan sums for signal processing of low-frequency noise
dc.rights.accessAcceso Abierto

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