private double Ω_ZR(double m, double k)
{
// Analog Electronic Filters pp.178
// Equation 4.34
double z = (2.0 * m - 1) / 2 / mN + 0.5;
double y = Math.Exp(-Math.PI * Functions.AGM(1, Math.Sqrt(1.0 - k * k)) / Functions.AGM(1, k));
return(1.0 / Math.Sqrt(k) * Functions.JacobiTheta1(z, y)
/ Functions.JacobiTheta0(z, y));
}
/// <summary>
/// discremination factor L_N(Ωs)
/// </summary>
private static double L_N(double Ωs, int N)
{
#if false
// Analog Electronic Filters pp.178
// Equation 4.36
double k = 1.0 / Ωs;
double numer = Math.Pow(Ωs, N);
double denom = 1;
double Kk = Functions.CompleteEllipticIntegralK(k);
int η = N & 1;
double x = Math.Exp(-Math.PI * Functions.AGM(1, Math.Sqrt(1.0 - k * k)) / Functions.AGM(1, k));
for (int m = 1; m <= (N - η) / 2; ++m)
{
denom *= Math.Pow(Functions.EllipticSine(((2.0 * m - 1 + η) / N + 1) * Kk, k), 4);
}
return(numer / denom);
#else
// Analog Electronic Filters pp.178
// Equation 4.37
int η = N & 1;
double k = 1.0 / Ωs;
double r = 1.0;
if (η == 1)
{
r = 1.0 / k;
}
for (int m = 1; m <= (N - η) / 2; ++m)
{
double z = (2.0 * m - 1 + η) / 2 / N + 1.0 / 2.0;
double y = Math.Exp(-Math.PI * Functions.AGM(1.0, Math.Sqrt(1.0 - k * k))
/ Functions.AGM(1.0, k));
var θ04 = Math.Pow(Functions.JacobiTheta0(z, y), 4);
var θ14 = Math.Pow(Functions.JacobiTheta1(z, y), 4);
r *= θ04 / θ14;
}
return(r);
#endif
}