Adaptive Doppler bio-signal detector and time-frequency representation based on non-Liènard oscillator

The work presented here provides the guidelines and results for designing and implementing a highly sensitive modified Van der Pol - Duffing oscillator with a trigonometric damping function (VTD). This VTD can exhibit periodic and quasi-chaotic behavior necessary for application in weak signal detection. Here, we present two proposals: (1) A method based on a quasi-chaotic intermittent array (ANLIOA), whose all VTD parameters are calculated and fine-tuned toward a critical state between chaotic and periodic state through a Lyapunov exponent procedure, and (2) A method based on a single oscillator in an adaptive stopping oscillation system (ANLSOS), where VTD is established within an oscillatory regime. Both systems can detect non-stationary signals while reconstructing the time-frequency spectrogram in high resolution within severe noise conditions. The systems were adapted for the detection of a synthesized Doppler signal corresponding to the blood flow velocity profile from an artery. Comparative results using typical oscillators such as Duffing or Van der Pol demonstrate the superiority of the VTD oscillator in detection when used for both methods, whose mean absolute percentage error reached around 6% for a signal-to-noise ratio (SNR) of -10 dB. Furthermore, compared to other time-frequency methods, ANLIOA and ANLSOS promise high precision in detecting Doppler signals with low rates of frequency changes while minimizing energy emission and avoiding possible bio-thermal effects.