EEG Engagement-Index Control Loop (2D)

Neuroadaptive interfaces close the loop between an operator's brain state and the automation itself, shifting task control as cognitive engagement drifts between boredom and overload. The 3D version of this simulator reads theta/alpha/beta band power off a tuned formula of task load. This 2D cross-section measures it for real instead: three digital resonant filters — discretized damped harmonic oscillators, one tuned to each classic EEG band — are driven by load-scaled noise to synthesize an actual raw waveform, and a Goertzel spectral estimator recovers each band's power from a sliding window of that signal every ~125 ms. The resulting engagement index EI = β/(α+θ) feeds the same exponential-moving-average smoothing and 3-level hysteresis controller as the 3D model, so you can watch the synthesized waveform, the measured band powers, the inverted-U performance curve and the automation state all respond to a genuinely closed feedback loop.