| dc.contributor | GUILLERMO ESPINOSA FLORES VERDAD | |
| dc.creator | LUCIO FIDEL REBOLLEDO HERRERA | |
| dc.date | 2017-01 | |
| dc.date.accessioned | 2023-07-25T16:21:20Z | |
| dc.date.available | 2023-07-25T16:21:20Z | |
| dc.identifier | http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/324 | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7805544 | |
| dc.description | In this dissertation the phenomenon of stochastic resonance was investigated, i.e. the
optimal noise-induced increase of a dynamical system's sensitivity and its ability to
amplify small periodic signals. We have considered bistable stochastic systems fed
with a small periodic signal (two-state Markov chains) with discrete and continuous
time and diffusions in double-well potentials. In the Markov chain case, one-step
or infinitesimal probabilities are periodically modulated. In the diffusion case,
depths of the potential wells are periodically changed in time. We introduce several
measures of goodness for tuning, the most important one of which is the coeficient
signal-to-noise ratio and harmonic distortion (SINAD), which describes the spectral
content carried by the averaged random output corresponding to the frequency of a
small deterministic periodic perturbation.
Quartic double well (QDW) modulation was performed by moving the wells separation,
depth and friction, supposing a particle forced by stochastic Brownian
movement described by the modified Duffing system forced by white Gaussian noise.
This approach leads to Langevine equations definition, analyzed by its corresponding
Fokker-Planck equation and sustained by two state theory, to acquire the transition
rate between wells for Stochastic Resonance (SR) induction.
Also, QDW modulation will be shown to recover the input signals by pushing the
Duffing system into pseudo-separatrix states and, thus, forcing a limit cycle by the
stochastic force.
The proposed methodology was algorithmically implemented based on Runge-Kutta
integration and tested with input signals under -10dB. Discrete wavelet transform
DWT and autocorrelation were compared with the modulated QDW methodology
with interesting results. Moreover, Electroencephalogram (EEG) signals where
processed under our methodology, showing enhanced results compared with other
methods. | |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Instituto Nacional de Astrofísica, Óptica y Electrónica | |
| dc.relation | citation:Rebolledo-Herrera L.F. | |
| dc.rights | info:eu-repo/semantics/openAccess | |
| dc.rights | http://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | info:eu-repo/classification/Resonancia estocástica/Stochastic resonance | |
| dc.subject | info:eu-repo/classification/Detección de señal débil/Weak signal detection | |
| dc.subject | info:eu-repo/classification/Sistema de escape/Duffing system | |
| dc.subject | info:eu-repo/classification/No lineal/Nonlinear | |
| dc.subject | info:eu-repo/classification/Dinámica estocástica/Stochastic dynamics | |
| dc.subject | info:eu-repo/classification/cti/1 | |
| dc.subject | info:eu-repo/classification/cti/22 | |
| dc.subject | info:eu-repo/classification/cti/2203 | |
| dc.subject | info:eu-repo/classification/cti/2203 | |
| dc.title | EEG signal processing based on stochastic resonance | |
| dc.type | info:eu-repo/semantics/doctoralThesis | |
| dc.type | info:eu-repo/semantics/acceptedVersion | |
| dc.audience | students | |
| dc.audience | researchers | |
| dc.audience | generalPublic | |
