{
  "title": "Illustrative received SNR and narrowband coherent wave interference",
  "evidence_status": "New deterministic analytical teaching study; no physical measurements, listening tests or clinical outcomes.",
  "snr_parameters": {
    "voice_level_db": 60,
    "background_level_db": 50,
    "competing_talker_level_db": 50,
    "level_convention": "Illustrative unweighted band-matched received sound pressure levels with common reference. Noise components assumed mutually uncorrelated. No absolute calibration or safety implication."
  },
  "anc_parameters": {
    "sound_speed_m_s": 343.0,
    "frequencies_hz": [
      125,
      250,
      500,
      1000
    ],
    "geometry": "Two oppositely travelling 1D plane waves in a lossless medium; equal pressure amplitudes for spatial plot; secondary antiphase at x=0.",
    "plot_floor_db": -60,
    "null_representation": "JSON null / empty CSV level_change_db with exact_null=true means negative infinity, not missing measurement."
  },
  "equations": {
    "noise": "10 log10(10^(Lb/10)+10^(Lt/10))",
    "snr": "Lvoice-Lnoise",
    "waves": "p1=A cos(omega*t-k*x); p2=-r*A cos(omega*t+k*x+epsilon)",
    "rms_ratio": "sqrt((1-r)^2+4*r*sin((2*k*x+epsilon)/2)^2)",
    "level_change": "20 log10(rms_ratio)",
    "mean_square_sum": "1+r^2-2*r*cos(2*k*x+epsilon); spatial mean over full wavelength = 1+r^2"
  },
  "limitations": [
    "SNR is not a speech recognition or intelligibility score.",
    "Common gain invariance assumes no clipping, quantization or added noise.",
    "Two coherent waves cannot be added as independent powers locally.",
    "The cancellation plot is single-frequency and one-dimensional, with prescribed waves, not a room, active controller, broadband field, energy-flux model or clinical device.",
    "Plane waves have no geometric spreading; reflecting walls, adaptation, latency and transducer limits are absent.",
    "The -60 dB display floor is graphical only, not measured attenuation."
  ],
  "row_counts": {
    "snr_gain": 61,
    "noise_sum": 161,
    "anc_position": 8004,
    "anc_errors": 905
  },
  "checks": {
    "equal_noise_addition_db": 3.0102999566398125,
    "equal_noise_expected_db": 3.010299956639812,
    "postmix_snr_max_change_db": 0.0,
    "null_pressure_ratio": 0.0,
    "quarter_wavelength_level_db": 6.020599913279624,
    "quarter_wavelength_expected_db": 6.020599913279624,
    "no_secondary_ratio": 1.0,
    "phase_180_level_db": 6.020599913279624,
    "spatial_mean_pressure_ratio_squared": 1.64,
    "spatial_mean_expected": 1.6400000000000001,
    "frequency_position_scaling_error": 0.0
  },
  "sources": [
    "https://www.nist.gov/itl/iad/mltg/nist-speech-signal-noise-ratio-measurements",
    "https://resource.isvr.soton.ac.uk/spcg/tutorial/tutorial/Tutorial_files/Web-inter-applications.htm",
    "https://www.osha.gov/otm/section-3-health-hazards/chapter-5"
  ]
}