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

Basu, Rajlaxmi, Dutta, Dhrubajyoti, Banerjee, Soumitro, Holmes, Violeta and Mather, Peter (2017) An Algorithmic Approach for Signal Measurement Using Symbolic Dynamics of Tent Map. IEEE Transactions on Circuits and Systems I: Regular Papers, 65 (7). pp. 2221-2231. ISSN 1549-8328

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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.

Item Type: Article
Additional Information: (c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Subjects: T Technology > T Technology (General)
Schools: School of Computing and Engineering
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Depositing User: Sharon Beastall
Date Deposited: 18 Dec 2017 12:37
Last Modified: 28 Aug 2021 14:15


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