ComplexPair BandPassTransform::transform (complex_t c)
{
if (c == infinity())
return ComplexPair (-1, 1);
c = (1. + c) / (1. - c); // bilinear
complex_t v = 0;
v = addmul (v, 4 * (b2 * (a2 - 1) + 1), c);
v += 8 * (b2 * (a2 - 1) - 1);
v *= c;
v += 4 * (b2 * (a2 - 1) + 1);
v = std::sqrt (v);
complex_t u = -v;
u = addmul (u, ab_2, c);
u += ab_2;
v = addmul (v, ab_2, c);
v += ab_2;
complex_t d = 0;
d = addmul (d, 2 * (b - 1), c) + 2 * (1 + b);
return ComplexPair (u/d, v/d);
}
void DigitalRASTA::design (double pole)
{
add(ComplexPair(complex_t(0, 0), complex_t(0, 0)),
ComplexPair(complex_t(1, 0), complex_t(-1, 0)));
add(ComplexPair(complex_t(pole, 0), complex_t(0, 0)),
ComplexPair(complex_t(-0.25, sqrt(15./16.)),
complex_t(-0.25, -sqrt(15./16.))));
setNormal(0, 1);
}
ComplexPair BandStopTransform::transform (complex_t c)
{
if (c == infinity())
c = -1;
else
c = (1. + c) / (1. - c); // bilinear
complex_t u (0);
u = addmul (u, 4 * (b2 + a2 - 1), c);
u += 8 * (b2 - a2 + 1);
u *= c;
u += 4 * (a2 + b2 - 1);
u = std::sqrt (u);
complex_t v = u * -.5;
v += a;
v = addmul (v, -a, c);
u *= .5;
u += a;
u = addmul (u, -a, c);
complex_t d (b + 1);
d = addmul (d, b-1, c);
return ComplexPair (u/d, v/d);
}
