/// <devdoc>
/// Evaluates the transfer function of a Bessel filter. The gain is normalized to 1 for DC.
/// It returns a complex number that corresponds to the gain and phase of the filter output.
/// </devdoc>
private static Complex TransferFunction(double[] besselPolynomialCoefficients, Complex frequency)
{
var f = new Polynomials.RationalFraction
{
Top = new double[] { besselPolynomialCoefficients[besselPolynomialCoefficients.Length - 1] }, // to normalize gain at DC
Bottom = besselPolynomialCoefficients
};
return(Polynomials.Evaluate(f, frequency));
}
/// <devdoc>
/// Given the z-plane poles and zeros, compute the rational fraction (the top and bottom polynomial coefficients)
/// of the filter transfer function in Z.
/// </devdoc>
private static Polynomials.RationalFraction ComputeTransferFunction(PolesAndZeros zPlane)
{
var topCoeffsComplex = Polynomials.Expand(zPlane.Zeros);
var bottomCoeffsComplex = Polynomials.Expand(zPlane.Poles);
// If the GetRealPart() conversion fails because the coffficients are not real numbers, the poles
// and zeros are not complex conjugates.
return new Polynomials.RationalFraction
{
Top = topCoeffsComplex.Select(x => GetRealPart(x)).ToArray(),
Bottom = bottomCoeffsComplex.Select(x => GetRealPart(x)).ToArray(),
};
}
private static double ComputeGainAt(Polynomials.RationalFraction tf, Complex w)
{
return Complex.Abs(Polynomials.Evaluate(tf, w));
}
