{
  "title": "Synthetic harmonic source through a first-order low-pass filter",
  "status": "Analytical illustrative study, not recorded speech, intelligibility or clinical evidence",
  "parameters": {
    "fundamentals_hz": [
      100,
      200
    ],
    "harmonics": [
      1,
      2,
      3,
      4,
      5,
      6,
      7,
      8,
      9,
      10,
      11,
      12,
      13,
      14,
      15,
      16,
      17,
      18,
      19,
      20
    ],
    "source_amplitude": "1/n arbitrary units",
    "cutoffs_hz": [
      500,
      1500
    ],
    "gains_db": [
      0,
      6
    ]
  },
  "equations": {
    "source": "s(t)=sum(n=1..20) sin(2*pi*n*f0*t)/n",
    "filter": "H(f)=1/(1+j*f/fc)",
    "magnitude": "1/sqrt(1+(f/fc)^2)",
    "phase_rad": "-atan(f/fc)",
    "output_amplitude": "(1/n)*abs(H(n*f0))*10^(gain_db/20)"
  },
  "rows": {
    "harmonics": 160,
    "single_tone": 40
  },
  "checks": {
    "gain_6db_amplitude_ratio": 1.9952623149688795,
    "gain_ratio_max_error": 2.220446049250313e-16,
    "cutoff_attenuation_db": -3.0102999566398125,
    "cutoff_expected_db": -3.010299956639812,
    "absent_components_remain_zero": true,
    "frequency_retention": true
  },
  "limitations": [
    "Arbitrary synthetic coefficients; no measured voice or vocal-tract response.",
    "First-order electrical low-pass example is not a vocal-tract or electrolarynx model.",
    "Periodic harmonics omit unvoiced speech and time-varying articulation.",
    "A linear time-invariant filter and gain scale existing components; no missing frequency components are recovered.",
    "No word-recognition, naturalness or clinical outcome is inferred."
  ],
  "source": {
    "url": "https://www.nidcd.nih.gov/news/multimedia/how-does-human-body-produce-voice-and-speech-text-version",
    "verified": "2026-09-27",
    "scope": "Official explanation of airflow, vocal-fold vibration and articulation; it does not specify or validate these model coefficients."
  }
}