Algorithms in Detail

Mathematical and implementation details for EEG analysis algorithms.

Engagement Index

EI = β / (α + θ). Higher EI → more engaged. Reference: Pope et al. (1995).

EMA Smoothing

smoothEI[t] = α × rawEI[t] + (1−α) × smoothEI[t−1]

Default α = 0.1. Applied only in Zustand store layer.

Alert Threshold

Default 0.3. Also feeds AI focus inference: FOCUS_SUPPORT_RATIO_THRESHOLD and FOCUS_MIXED_RATIO_THRESHOLD.

Focus Classification

4-state FSM. Baseline = median EI during collection window. Classification: compare current window median vs baseline reference.

Parameter	Default	Range
Warmup	30s	20–60
Baseline	15s	15–60
Decision	15s	5–300

FFT Spectral Analysis

Hann window → FFT (512 points, 250 Hz) → Δf ≈ 0.488 Hz. Band power = Σ|X[k]|² over band bins, normalized.

Butterworth IIR Filter

4th-order, Direct Form II, RBJ Audio EQ Cookbook coefficients. Q = 1/√2 per stage.

Initial Unreliable Period

First N seconds (default 30s) excluded from CSV, EI trend, and focus classification.