β- Expansion's attractors observed in A/D converters

Tohru Kohda, Yoshihiko Horio, Kazuyuki Aihara

Research output: Contribution to journalConference articlepeer-review

Abstract

The β-encoders, recently proposed analog-to-digital converters using an amplifier with factor βand a flaky quantizer with threshold ν have been proven to be explained as 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). Switched-capacitor electronic circuits realizing the scaled ordinary and negative β-encoders lead us to observe their embedded attractors.

Original languageEnglish
Pages (from-to)187-189
Number of pages3
JournalProcedia IUTAM
Volume5
DOIs
Publication statusPublished - 2012
EventIUTAM Symposium on 50 Years of Chaos: Applied and Theoretical - Kyoto, Japan
Duration: 2011 Nov 282011 Dec 2

Keywords

  • A/D-converter
  • Attractors
  • Switched-capacitor circuit
  • β-encoders
  • β-expansion

ASJC Scopus subject areas

  • Mechanical Engineering

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