biquad.hpp

  case Type::LowShelf:
    if(gain >= 0) {
      n = 1 / (1 + k / q + k * k);
      a0 = (1 + sqrt(v) / q * k + v * k * k) * n;
      a1 = 2 * (v * k * k - 1) * n;
      a2 = (1 - sqrt(v) / q * k + v * k * k) * n;
      b1 = 2 * (k * k - 1) * n;
      b2 = (1 - k / q + k * k) * n;
    } else {
      n = 1 / (1 + sqrt(v) / q * k + v * k * k);
      a0 = (1 + k / q + k * k) * n;
      a1 = 2 * (k * k - 1) * n;
      a2 = (1 - k / q + k * k) * n;
      b1 = 2 * (v * k * k - 1) * n;
      b2 = (1 - sqrt(v) / q * k + v * k * k) * n;
    }
    break;

  case Type::HighShelf:
    if(gain >= 0) {
      n = 1 / (1 + k / q + k * k);
      a0 = (v + sqrt(v) / q * k + k * k) * n;
      a1 = 2 * (k * k - v) * n;
      a2 = (v - sqrt(v) / q * k + k * k) * n;
      b1 = 2 * (k * k - 1) * n;
      b2 = (1 - k / q + k * k) * n;
    } else {
      n = 1 / (v + sqrt(v) / q * k + k * k);
      a0 = (1 + k / q + k * k) * n;
      a1 = 2 * (k * k - 1) * n;
      a2 = (1 - k / q + k * k) * n;
      b1 = 2 * (k * k - v) * n;
      b2 = (v - sqrt(v) / q * k + k * k) * n;
    }
    break;

// https://dsp.stackexchange.com/a/30429
auto Biquad::shelfQuality(double gain, double slope) -> double {
  double A = pow(10, gain / 40);
  return 1 / sqrt((A + 1 / A) * (1 / slope - 1) + 2);
}