Fibonacci signals with timing jitter

D. S. Citrin; D. S. Citrin

doi:10.3934/mine.2023076

Mathematics in Engineering

2023, Volume 5, Issue 4: 1-13. doi: 10.3934/mine.2023076

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Research article

Fibonacci signals with timing jitter

D. S. Citrin ^{1,2
,
,}

1.
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0250, USA
2.
Georgia Tech-CNRS IRL 2958, Georgia Tech Europe, 2 Rue Marconi, 57070 Metz, France

Received: 18 November 2022 Revised: 05 February 2023 Accepted: 05 February 2023 Published: 17 February 2023

The power spectral density of a signal comprised of a sequence of Dirac $ \delta $-functions at successive times determined by a Fibonacci sequence is the temporal analog of the well known structure factor for a Fibonacci chain. Such a signal is quasi-periodic and, under suitable choice of parameters, is the temporal analog of a one-dimensional quasicrystal. While the effects of disorder in the spatial case of Fibonacci chains has been studied numerically, having an analytically tractable stochastic model is needed both for the spatial and temporal cases to be able to study these effects as model parameters are varied. Here, we consider the effects of errors in where the $ \delta $-functions defining the signal in the temporal case occur, i.e., timing jitter. In this work, we present an analytically tractable theory of how timing jitter affects the power spectral density of Fibonacci signals.
- Fibonacci sequences,
- nonperiodic sampling,
- timing jitter
Citation: D. S. Citrin. Fibonacci signals with timing jitter[J]. Mathematics in Engineering, 2023, 5(4): 1-13. doi: 10.3934/mine.2023076

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Abstract

The power spectral density of a signal comprised of a sequence of Dirac $ \delta $-functions at successive times determined by a Fibonacci sequence is the temporal analog of the well known structure factor for a Fibonacci chain. Such a signal is quasi-periodic and, under suitable choice of parameters, is the temporal analog of a one-dimensional quasicrystal. While the effects of disorder in the spatial case of Fibonacci chains has been studied numerically, having an analytically tractable stochastic model is needed both for the spatial and temporal cases to be able to study these effects as model parameters are varied. Here, we consider the effects of errors in where the $ \delta $-functions defining the signal in the temporal case occur, i.e., timing jitter. In this work, we present an analytically tractable theory of how timing jitter affects the power spectral density of Fibonacci signals.

References

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