### Abstract

Language | English |
---|---|

Pages | 1-10 |

Number of pages | 10 |

Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |

Volume | PP |

Issue number | 99 |

DOIs | |

State | Published - 7 Dec 2017 |

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*IEEE Transactions on Circuits and Systems I: Regular Papers*,

*PP*(99), 1-10. DOI: 10.1109/TCSI.2017.2773202

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*IEEE Transactions on Circuits and Systems I: Regular Papers*, vol PP, no. 99, pp. 1-10. DOI: 10.1109/TCSI.2017.2773202

**An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map.** / Basu, Rajlaxmi; Dutta, Dhrubajyoti; Banerjee, Soumitro; Holmes, Violeta; Mather, Peter.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map

AU - Basu,Rajlaxmi

AU - Dutta,Dhrubajyoti

AU - Banerjee,Soumitro

AU - Holmes,Violeta

AU - Mather,Peter

PY - 2017/12/7

Y1 - 2017/12/7

N2 - 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.

AB - 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.

KW - Initial condition estimation

KW - reduced height map

KW - symbolic dynamics

KW - signal measurement.

U2 - 10.1109/TCSI.2017.2773202

DO - 10.1109/TCSI.2017.2773202

M3 - Article

VL - PP

SP - 1

EP - 10

JO - IEEE Transactions on Circuits and Systems II: Express Briefs

T2 - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

SN - 1549-8328

IS - 99

ER -