抄録
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.
本文言語 | English |
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論文番号 | 047512 |
ジャーナル | Chaos |
巻 | 22 |
号 | 4 |
DOI | |
出版ステータス | Published - 2012 10 4 |
外部発表 | はい |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics