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  • Letter
  • Open Access

Apparent universality of 1/f spectra as an artifact of finite-size effects

M. A. Korzeniowska1,*, A. Theodorsen1,†, M. Rypdal2,‡, and O. E. Garcia1,§

  • 1Department of Physics and Technology, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
  • 2Department of Mathematics and Statistics, UiT The Arctic University of Norway, N-9037 Tromsø, Norway

  • *magdalena.a.korzeniowska@uit.no
  • †audun.theodorsen@uit.no
  • ‡martin.rypdal@uit.no
  • §odd.erik.garcia@uit.no
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Phys. Rev. Research 5, L022066 – Published 29 June, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022066

Abstract

Power spectral density scaling with frequency f as 1/fβ and β≈1 is widely found in natural and socioeconomic systems. Consequently, it has been suggested that such self-similar spectra reflect the universal dynamics of complex phenomena. Here, we show that for a superposition of uncorrelated pulses with a power-law distribution of duration times the estimated scaling exponents β¯ depend on the system size. We derive a parametrized, closed-form expression for the power spectral density, and demonstrate that for β∈[0,2] the estimated scaling exponents have a bias towards β¯=1. For β=0 and β=2 the explicit logarithmic corrections to frequency scaling are derived. The bias is particularly strong when the scale invariance spans less than four decades in frequency. Since this is the case for the majority of empirical data, the boundedness of systems well described by the superposition of uncorrelated pulses may contribute to overemphasizing the universality of 1/f.

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Phys. Rev. Research 5, L022066– Published 29 June, 2023
  • Received 1 December 2022
  • Accepted 23 May 2023
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