A tensor approach to higher order expectations of quantized chaotic trajectories - part i: general theory and specialization to piecewise affine markov systems

Riccardo Rovatti; Gianluca Mazzini; Gianluca Setti

doi:10.1109/81.895325

A tensor approach to higher order expectations of quantized chaotic trajectories - part i: general theory and specialization to piecewise affine markov systems

Riccardo Rovatti, Gianluca Mazzini, Gianluca Setti

Research output: Contribution to journal › Article › peer-review

44 Scopus citations

Abstract

The problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron-Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features. As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment. © 2000 IEEE.

Original language	English (US)
Pages (from-to)	1571-1583
Number of pages	13
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	47
Issue number	11
DOIs	https://doi.org/10.1109/81.895325
State	Published - Nov 1 2000
Externally published	Yes

Bibliographical note

Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/81.895325

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abstract = "The problem of computing any-order expectations of trajectories generated by discrete-time one-dimensional chaotic systems is addressed by means of a suitable generalization of the Perron-Frobenius operator and its quantization. Tools from tensor algebra are introduced and analytical expressions for the special case of piecewise-affine Markov maps are obtained. Results are further specialized for a family of maps with quite general features. As an example application, some cross- and self-interference terms are computed, which are involved in the evaluation of the performance of chaos-based DS-CDMA systems in an asynchronous multipath environment. {\textcopyright} 2000 IEEE.",

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A tensor approach to higher order expectations of quantized chaotic trajectories - part i: general theory and specialization to piecewise affine markov systems. / Rovatti, Riccardo; Mazzini, Gianluca; Setti, Gianluca.
In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 47, No. 11, 01.11.2000, p. 1571-1583.

Research output: Contribution to journal › Article › peer-review

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T1 - A tensor approach to higher order expectations of quantized chaotic trajectories - part i: general theory and specialization to piecewise affine markov systems

AU - Rovatti, Riccardo

AU - Mazzini, Gianluca

AU - Setti, Gianluca

N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15

PY - 2000/11/1

Y1 - 2000/11/1

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A tensor approach to higher order expectations of quantized chaotic trajectories - part i: general theory and specialization to piecewise affine markov systems

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