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

Tohru Kohda; Yoshihiko Horio; Kazuyuki Aihara

doi:10.1016/j.piutam.2012.06.024

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

Tohru Kohda, Yoshihiko Horio, Kazuyuki Aihara

Research output: Contribution to journal › Conference article › peer-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 language	English
Pages (from-to)	187-189
Number of pages	3
Journal	Procedia IUTAM
Volume	5
DOIs	https://doi.org/10.1016/j.piutam.2012.06.024
Publication status	Published - 2012
Externally published	Yes
Event	IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical - Kyoto, Japan Duration: 2011 Nov 28 → 2011 Dec 2

Keywords

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

ASJC Scopus subject areas

Mechanical Engineering

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10.1016/j.piutam.2012.06.024

Cite this

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title = "β- Expansion's attractors observed in A/D converters",

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 R{\'e}nyi-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.",

keywords = "A/D-converter, Attractors, Switched-capacitor circuit, β-encoders, β-expansion",

author = "Tohru Kohda and Yoshihiko Horio and Kazuyuki Aihara",

note = "Funding Information: This research is supported by the Aihara Innovative Mathematical Modelling Project, the Japan Society for the Promotion of Science (JSPS) through the {"}Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program),{"} initiated by the Council for Science and Technology Policy (CSTP).; IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical ; Conference date: 28-11-2011 Through 02-12-2011",

year = "2012",

doi = "10.1016/j.piutam.2012.06.024",

language = "English",

volume = "5",

pages = "187--189",

journal = "Procedia IUTAM",

issn = "2210-9838",

}

TY - JOUR

T1 - β- Expansion's attractors observed in A/D converters

AU - Kohda, Tohru

AU - Horio, Yoshihiko

AU - Aihara, Kazuyuki

N1 - Funding Information: This research is supported by the Aihara Innovative Mathematical Modelling Project, the Japan Society for the Promotion of Science (JSPS) through the "Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)," initiated by the Council for Science and Technology Policy (CSTP).

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - A/D-converter

KW - Attractors

KW - Switched-capacitor circuit

KW - β-encoders

KW - β-expansion

UR - http://www.scopus.com/inward/record.url?scp=84867443982&partnerID=8YFLogxK

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U2 - 10.1016/j.piutam.2012.06.024

DO - 10.1016/j.piutam.2012.06.024

M3 - Conference article

AN - SCOPUS:84867443982

VL - 5

SP - 187

EP - 189

JO - Procedia IUTAM

JF - Procedia IUTAM

SN - 2210-9838

T2 - IUTAM Symposium on 50 Years of Chaos: Applied and Theoretical

Y2 - 28 November 2011 through 2 December 2011

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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