Complexity and disorder of 1/ fα noises

Chang Francis Hsu, Long Hsu, Sien Chi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The complexity and the disorder of a 1/ fα noise time series are quantified by entropy of entropy (EoE) and average entropy (AE), respectively. The resulting EoE vs. AE plot of a series of 1/ fα noises of various values of α exhibits a distinct inverted U curve. For the 1/ fα noises, we have shown that α decreases monotonically as AE increases, which indicates that α is also a measure of disorder. Furthermore, a 1/ fα noise and a cardiac interbeat (RR) interval series are considered equivalent as they have the same AE. Accordingly, we have found that the 1/ fα noises for α around 1.5 are equivalent to the RR interval series of healthy subjects. The pink noise at α = 1 is equivalent to atrial fibrillation (AF) RR interval series while the white noise at α = 0 is more disordered than AF RR interval series. These results, based on AE, are different from the previous ones based on spectral analysis. The testing macro-average F-score is 0.93 when classifying the RR interval series of three groups using AE-based α, while it is 0.73 when using spectral-analysis-based α.

Original languageEnglish
Article number1127
Pages (from-to)1-10
Number of pages10
Issue number10
StatePublished - Oct 2020


  • 1/ f noises
  • Complexity
  • Disorder
  • Heart rate variability
  • Inverted U curve
  • Power law
  • RR interval

Fingerprint Dive into the research topics of 'Complexity and disorder of 1/ f<sup>α</sup> noises'. Together they form a unique fingerprint.

Cite this