EEGProtocol

formal source

  33/-! ## EEG Frequency Predictions -/
  34
  35/-- A complete EEG experimental protocol -/
  36structure EEGProtocol where
  37  /-- Sample size for each group -/
  38  n_subjects : ℕ := 30
  39  /-- Recording duration in seconds -/
  40  duration_sec : ℕ := 600  -- 10 minutes
  41  /-- Sampling rate in Hz -/
  42  sampling_rate : ℕ := 256
  43  /-- Frequency resolution in Hz -/
  44  freq_resolution : ℝ := 0.1
  45  /-- Electrode positions (10-20 system) -/
  46  electrodes : List String := ["Fz", "Cz", "Pz", "O1", "O2"]
  47
  48/-- Predicted EEG peaks with confidence intervals -/
  49structure EEGPrediction where
  50  /-- The mode index n in φ^n -/
  51  mode_index : ℤ
  52  /-- Central frequency (φ^n Hz) -/
  53  center_freq : ℝ
  54  /-- Expected peak width (Hz) -/
  55  bandwidth : ℝ := 0.2
  56  /-- Minimum peak amplitude (μV²/Hz) -/
  57  min_amplitude : ℝ
  58  /-- Confidence level for detection -/
  59  confidence : ℝ := 0.95
  60
  61/-- The set of predicted EEG frequencies -/
  62noncomputable def eegPredictions : List EEGPrediction :=
  63  [⟨-2, φ^(-2 : ℤ), 0.2, 0.5, 0.95⟩,   -- ~0.38 Hz (infra-slow)
  64   ⟨-1, φ^(-1 : ℤ), 0.2, 0.5, 0.95⟩,   -- ~0.62 Hz (delta-low)
  65   ⟨0, 1, 0.2, 1.0, 0.95⟩,              -- 1.00 Hz (delta-high)
  66   ⟨1, φ, 0.2, 1.0, 0.95⟩,              -- ~1.62 Hz (delta-theta)