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Time-Frequency High Resolution Using Chaos In Detection
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  • Pedro Pancoatl-Bortolotti ,
  • Rogerio R. Enríquez-Caldera ,
  • Antonio H. Costa ,
  • Maribel Tello-Bello ,
  • Jose F. Guerrero-Castellanos
Pedro Pancoatl-Bortolotti
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Rogerio R. Enríquez-Caldera
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Antonio H. Costa
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Maribel Tello-Bello
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Jose F. Guerrero-Castellanos
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Abstract

A non-linear Liènard-type system based on trigono-metric functions is designed and used as a highly sensitive signal detector. Based on the intermittence mechanism presented in some chaotic systems, an adaptive detection array formed by five chaotic oscillators is designed, tuned, and tested. In the array, each individual oscillator identifies changes in frequency for non-stationary weak signals and, with the array working in an adaptative mode, gives an estimate of the timing at which intermittence occurred allowing the representation of a time-frequency spectrogram even when high-level noise is present. This work also shows that the trigonometric based system has an asymptotically stable limit cycle centered at the origin through two methods: first under the fixed-point analysis and later by the Melnikov method that uses a family of periodic orbits. Once the self-sustained oscillations are produced, the system is configured to drive itself into a saddle-node bifurcation through an iterative method for searching and tuning parameters which, in turn, assures the route to chaotic intermittence. Through this mechanism, the new system can be used as a non-stationary signal detector that also provides a high resolution time-frequency representation. The computer experiments showed that the adaptive array is perfectly compatible with other second-order non-linear oscillators configured in the chaotic intermittence regime such as Duffing, Van der Pol, and Van der Pol - Duffing, achieving high detection rates under noisy conditions. Moreover, when the new Liènard-type oscillators are incorporated into the adaptive array, the detection sensitivity overcomes the SNR threshold present in all oscillators mentioned above and allows for reaching and maintaining a relative error around 1% under severe noise conditions down to about -60 dB SNR.