An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map

Rajlaxmi Basu, Dhrubajyoti Dutta, Soumitro Banerjee, Violeta Holmes, Peter Mather

Research output: Contribution to journalArticle

Abstract

The symbolic time series generated by a unimodal chaotic map starting from any initial condition creates a binary sequence that contains information about the initial condition. A binary sequence of a given length generated this way has a one-to-one correspondence with a given range of the input signal. This can be used to construct analogue to digital converters (ADC). However, in actual circuit realizations, component imperfections and ambient noise result in deviations in the map function from the ideal, which, in turn, can cause significant error in signal measurement. In this paper, we propose the ways of circumventing these problems through an algorithmic procedure that takes into account the non-idealities. The most common form of non-ideality--reduction in the height of the map function--alters the partitions that correspond to each symbolic sequence. We show that it is possible to define the partitions correctly if the height of the map function is known. We also propose a method to estimate this height from the symbolic sequence obtained. We demonstrate the efficacy of the proposed algorithm with simulation as well as experiment. With this development, practical ADCs utilizing chaotic dynamics may become reality.
LanguageEnglish
Pages1-10
Number of pages10
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
VolumePP
Issue number99
DOIs
StatePublished - 7 Dec 2017

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Binary sequences
Digital to analog conversion
Time series
Defects
Networks (circuits)
Experiments

Cite this

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title = "An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map",
abstract = "The symbolic time series generated by a unimodal chaotic map starting from any initial condition creates a binary sequence that contains information about the initial condition. A binary sequence of a given length generated this way has a one-to-one correspondence with a given range of the input signal. This can be used to construct analogue to digital converters (ADC). However, in actual circuit realizations, component imperfections and ambient noise result in deviations in the map function from the ideal, which, in turn, can cause significant error in signal measurement. In this paper, we propose the ways of circumventing these problems through an algorithmic procedure that takes into account the non-idealities. The most common form of non-ideality--reduction in the height of the map function--alters the partitions that correspond to each symbolic sequence. We show that it is possible to define the partitions correctly if the height of the map function is known. We also propose a method to estimate this height from the symbolic sequence obtained. We demonstrate the efficacy of the proposed algorithm with simulation as well as experiment. With this development, practical ADCs utilizing chaotic dynamics may become reality.",
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An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map. / Basu, Rajlaxmi; Dutta, Dhrubajyoti; Banerjee, Soumitro; Holmes, Violeta; Mather, Peter.

In: IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. PP, No. 99, 07.12.2017, p. 1-10.

Research output: Contribution to journalArticle

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