Ramanujan sums for signal processing of low frequency noise

Abstract

An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as Möbius 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 new signal processing tool based on the Ramanujan sums c_q(n), well adapted to the analysis of arithmetical sequences with many resonances p/q. The sums are quasi-periodic versus the time n of the resonance and aperiodic versus the order q of the resonance. New results arise from the use of this Ramanujan-Fourier transform (RFT) in the context of arithmetical and experimental signals

11 pages in IOP style, 14 figures, 2 tables, 16 references

References in corpus (1)

• On arithmetic detection of grey pulses with application to Hawking radiation

Cited by in corpus (14)

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• Modular functions and Ramanujan sums for the analysis of 1/f noise in electronic circuits
• Huyghens, Bohr, Riemann and Galois: Phase-Locking
• Detection of large-scale noisy multi-periodic patterns with discrete double Fourier transform
• On arithmetic detection of grey pulses with application to Hawking radiation
• Ramanujan sums as supercharacters
• Invitation to the "Spooky" Quantum Phase-Locking Effect and its Link to 1/F Fluctuations
• Class numbers in the imaginary quadratic field and the 1/f noise of an electron gas
• Doppler Spectrum Estimation by Ramanujan Fourier Transforms
• On the Polynomial Ramanujan Sums over Finite Fields
• Ramanujan in Computing Technology