/// <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>
/// Returns the IIR filter coefficients for a transfer function.
/// Normalizes the coefficients so that a[0] is 1.
/// </devdoc>
private static IirFilterCoefficients ComputeIirFilterCoefficients(Polynomials.RationalFraction tf, double gain)
{
// Note that compared to the original C code by Tony Fisher the order of the A/B coefficients
// is reverse and the A coefficients are negated.
double scale = tf.Bottom[0];
var coefficients = new IirFilterCoefficients();
coefficients.A = tf.Bottom.Select(x => x / scale / gain).ToArray();
coefficients.A[0] = 1;
coefficients.B = tf.Top.Select(x => x / scale / gain).ToArray();
return coefficients;
}
private static double ComputeGain(Polynomials.RationalFraction tf, FilterKind type, double fcf1, double fcf2)
{
switch (type)
{
case FilterKind.LowPass:
return ComputeGainAt(tf, Complex.One); // At DC
case FilterKind.HighPass: // At Nyquist
return ComputeGainAt(tf, new Complex(-1, 0));
case FilterKind.BandPass: // At center frequency
return ComputeGainAt(tf, Mathx.Expj(2 * Math.PI * ((fcf1 + fcf2) / 2)));
case FilterKind.BandStop: // At sqrt( [gain at DC] * [gain at samplingRate/2]
return Math.Sqrt(ComputeGainAt(tf, Complex.One) * ComputeGainAt(tf, new Complex(-1, 0)));
default:
throw new System.ComponentModel.InvalidEnumArgumentException("type", (int)type, typeof(FilterKind));
}
}
private static double ComputeGainAt(Polynomials.RationalFraction tf, Complex w)
{
return Complex.Abs(Polynomials.Evaluate(tf, w));
}
