/// <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;
}
public IirFilter(IirFilterCoefficients coefficients)
{
Debug.Assert(coefficients != null);
Debug.Assert(coefficients.A.Length > 0 && coefficients.B.Length > 0 && coefficients.A[0] == 1.0);
IsEnabled = true;
_a = coefficients.A;
_b = coefficients.B;
_nb = _b.Length - 1;
_na = _a.Length - 1;
_buf1 = new double[_nb];
_buf2 = new double[_na];
}
public BiquadFilter(IirFilterCoefficients coefficients)
{
Debug.Assert(coefficients != null);
Debug.Assert(coefficients.B != null && coefficients.B.Length == 3);
Debug.Assert(coefficients.A != null && coefficients.A.Length == 3);
IsEnabled = true;
// From http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt:
//
// b0 + b1*z^-1 + b2*z^-2
// H(z) = ------------------------ (Eq 1)
// a0 + a1*z^-1 + a2*z^-2
//
// This shows 6 coefficients instead of 5 so, depending on your architechture,
// you will likely normalize a0 to be 1 and perhaps also b0 to 1 (and collect
// that into an overall gain coefficient). Then your transfer function would
// look like:
//
// (b0/a0) + (b1/a0)*z^-1 + (b2/a0)*z^-2
// H(z) = --------------------------------------- (Eq 2)
// 1 + (a1/a0)*z^-1 + (a2/a0)*z^-2
//
// or
// 1 + (b1/b0)*z^-1 + (b2/b0)*z^-2
// H(z) = (b0/a0) * --------------------------------- (Eq 3)
// 1 + (a1/a0)*z^-1 + (a2/a0)*z^-2
//
//
// The most straight forward implementation would be the "Direct Form 1"
// (Eq 2):
// y[n] = (b0/a0)*x[n] + (b1/a0)*x[n-1] + (b2/a0)*x[n-2]
// - (a1/a0)*y[n-1] - (a2/a0)*y[n-2] (Eq 4)
_b0 = coefficients.B[0] / coefficients.A[0];
_b1 = coefficients.B[1] / coefficients.A[0];
_b2 = coefficients.B[2] / coefficients.A[0];
_a1 = coefficients.A[1] / coefficients.A[0];
_a2 = coefficients.A[2] / coefficients.A[0];
}
private static IOnlineFilter Create(IirFilterCoefficients coefficients)
{
return new IirFilter(coefficients);
}
private static IOnlineFilter CreateCascade(int order, IirFilterCoefficients coefficients)
{
return(new FilterCascade(Enumerable.Range(0, order).Select(_ => new BiquadFilter(coefficients)).ToArray()));
}