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Title: Digital noise generators using one-dimensional chaotic maps

Abstract

This work shows how to improve the statistical distribution of signals produced by digital noise generators designed with one-dimensional (1-D) chaotic maps. It also shows that in a digital electronic design the piecewise linear chaotic maps (PWLCM) should be considered because they do not have stability islands in its chaotic behavior region, as it occurs in the case of the logistic map, which is commonly used to build noise generators. The design and implementation problems of the digital noise generators are analyzed and a solution is proposed. This solution relates the output of PWLCM, usually defined in the real numbers' domain, with a codebook of S elements, previously defined. The proposed solution scheme produces digital noise signals with a statistical distribution close to a uniform distribution. Finally, this work shows that it is possible to have control over the statistical distribution of the noise signal by selecting the control parameter of the PWLCM and using, as a design criterion, the bifurcation diagram.

Authors:
; ; ;  [1];  [2]
  1. Instituto Politécnico Nacional, ESIME-Culhuacan, Santa Ana 1000, 04430, D.F. (Mexico)
  2. Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla (Mexico)
Publication Date:
OSTI Identifier:
22280305
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1598; Journal Issue: 1; Conference: LDSD 2011: 7. international conference on low dimensional structures and devices, Telchac (Mexico), 22-27 May 2011; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; CONTROL; MATHEMATICAL SOLUTIONS; NOISE; ONE-DIMENSIONAL CALCULATIONS; SIGNALS

Citation Formats

Martínez-Ñonthe, J. A, Palacios-Luengas, L., Cruz-Irisson, M., Vazquez Medina, R., and Díaz Méndez, J. A. Digital noise generators using one-dimensional chaotic maps. United States: N. p., 2014. Web. doi:10.1063/1.4878310.
Martínez-Ñonthe, J. A, Palacios-Luengas, L., Cruz-Irisson, M., Vazquez Medina, R., & Díaz Méndez, J. A. Digital noise generators using one-dimensional chaotic maps. United States. doi:10.1063/1.4878310.
Martínez-Ñonthe, J. A, Palacios-Luengas, L., Cruz-Irisson, M., Vazquez Medina, R., and Díaz Méndez, J. A. 2014. "Digital noise generators using one-dimensional chaotic maps". United States. doi:10.1063/1.4878310.
@article{osti_22280305,
title = {Digital noise generators using one-dimensional chaotic maps},
author = {Martínez-Ñonthe, J. A and Palacios-Luengas, L. and Cruz-Irisson, M. and Vazquez Medina, R. and Díaz Méndez, J. A.},
abstractNote = {This work shows how to improve the statistical distribution of signals produced by digital noise generators designed with one-dimensional (1-D) chaotic maps. It also shows that in a digital electronic design the piecewise linear chaotic maps (PWLCM) should be considered because they do not have stability islands in its chaotic behavior region, as it occurs in the case of the logistic map, which is commonly used to build noise generators. The design and implementation problems of the digital noise generators are analyzed and a solution is proposed. This solution relates the output of PWLCM, usually defined in the real numbers' domain, with a codebook of S elements, previously defined. The proposed solution scheme produces digital noise signals with a statistical distribution close to a uniform distribution. Finally, this work shows that it is possible to have control over the statistical distribution of the noise signal by selecting the control parameter of the PWLCM and using, as a design criterion, the bifurcation diagram.},
doi = {10.1063/1.4878310},
journal = {AIP Conference Proceedings},
number = 1,
volume = 1598,
place = {United States},
year = 2014,
month = 5
}
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