Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 2221-2231 |
| Number of pages | 11 |
| Journal | IEEE Transactions on Circuits and Systems I: Regular Papers |
| Volume | 65 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - 7 Dec 2017 |
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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. 65, No. 7, 07.12.2017, p. 2221-2231.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 - 65
SP - 2221
EP - 2231
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
SN - 1549-8328
IS - 7
ER -