β-expansion attractors observed in A/D converters

Tohru Kohda, Yoshihiko Horio, Kazuyuki Aihara

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The recently proposed β-encoders, analog-to-digital converters using an amplifier with a factor β a flaky quantizer with threshold ν, have proven to be explained by the deterministic dynamics of multi-valued Rényi-Parry maps. Such a map is locally eventually onto [ν-1, ν), which is topologically conjugate to Parry's (β,α)-map with α=(β-1)(ν-1). This implies that β-encoders have a closed subinterval [ν-1,ν), which includes an attractor. Thus, the iteration of the multi-valued Rényi-Parry map performs the β-expansion of x while quantization errors in β-encoders behave chaotically do not converge to a fixed point. This β-expansion attractor is relatively simpler than previously reported attractors. The object of this paper is twofold: to observe the embedded attractors in the β-encoder to identify attractors that are useful for spread-spectrum codes optimization techniques using pseudo-random numbers.

Original languageEnglish
Article number047512
JournalChaos
Volume22
Issue number4
DOIs
Publication statusPublished - 2012 Oct 4
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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