void AnalogLowPass::design (int numPoles,
WorkspaceBase* w)
{
if (m_numPoles != numPoles)
{
m_numPoles = numPoles;
reset ();
RootFinderBase& solver (w->roots);
for (int i = 0; i < numPoles + 1; ++i)
solver.coef()[i] = reversebessel (i, numPoles);
solver.solve (numPoles);
const int pairs = numPoles / 2;
for (int i = 0; i < pairs; ++i)
{
complex_t c = solver.root()[i];
addPoleZeroConjugatePairs (c, infinity());
}
if (numPoles & 1)
add (solver.root()[pairs].real(), infinity());
}
}
void AnalogLowShelf::design (int numPoles, double gainDb)
{
if (m_numPoles != numPoles ||
m_gainDb != gainDb)
{
m_numPoles = numPoles;
m_gainDb = gainDb;
reset ();
const double n2 = numPoles * 2;
const double g = pow (pow (10., gainDb/20), 1. / n2);
const double gp = -1. / g;
const double gz = -g;
const int pairs = numPoles / 2;
for (int i = 1; i <= pairs; ++i)
{
const double theta = doublePi * (0.5 - (2 * i - 1) / n2);
addPoleZeroConjugatePairs (std::polar (std::abs(gp), theta), std::polar (std::abs(gz), theta));
}
if (numPoles & 1)
add (gp, gz);
}
}
void AnalogLowPass::design (int numPoles,
double stopBandDb)
{
if (m_numPoles != numPoles ||
m_stopBandDb != stopBandDb)
{
m_numPoles = numPoles;
m_stopBandDb = stopBandDb;
reset ();
const double eps = std::sqrt (1. / (std::exp (stopBandDb * 0.1 * doubleLn10) - 1));
const double v0 = asinh (1 / eps) / numPoles;
const double sinh_v0 = -sinh (v0);
const double cosh_v0 = cosh (v0);
const double fn = doublePi / (2 * numPoles);
int k = 1;
for (int i = numPoles / 2; --i >= 0; k+=2)
{
const double a = sinh_v0 * cos ((k - numPoles) * fn);
const double b = cosh_v0 * sin ((k - numPoles) * fn);
const double d2 = a * a + b * b;
const double im = 1 / cos (k * fn);
addPoleZeroConjugatePairs (complex_t (a / d2, b / d2),
complex_t (0, im));
}
if (numPoles & 1)
{
add (1 / sinh_v0, infinity());
}
}
}
void AnalogLowShelf::design (int numPoles,
double gainDb,
double stopBandDb)
{
if (m_numPoles != numPoles ||
m_stopBandDb != stopBandDb ||
m_gainDb != gainDb)
{
m_numPoles = numPoles;
m_stopBandDb = stopBandDb;
m_gainDb = gainDb;
reset ();
gainDb = -gainDb;
if (stopBandDb >= fabs(gainDb))
stopBandDb = fabs (gainDb);
if (gainDb<0)
stopBandDb = -stopBandDb;
const double G = std::pow (10., gainDb / 20.0 );
const double Gb = std::pow (10., (gainDb - stopBandDb) / 20.0);
const double G0 = 1;
const double g0 = pow (G0 , 1. / numPoles);
double eps;
if (Gb != G0 )
eps = sqrt((G*G-Gb*Gb)/(Gb*Gb-G0*G0));
else
eps = G-1; // This is surely wrong
const double b = pow (G/eps+Gb*sqrt(1+1/(eps*eps)), 1./numPoles);
const double u = log (b / g0);
const double v = log (pow (1. / eps+sqrt(1+1/(eps*eps)),1./numPoles));
const double sinh_u = sinh (u);
const double sinh_v = sinh (v);
const double cosh_u = cosh (u);
const double cosh_v = cosh (v);
const double n2 = 2 * numPoles;
const int pairs = numPoles / 2;
for (int i = 1; i <= pairs; ++i)
{
const double a = doublePi * (2 * i - 1) / n2;
const double sn = sin (a);
const double cs = cos (a);
addPoleZeroConjugatePairs (complex_t (-sn * sinh_u, cs * cosh_u),
complex_t (-sn * sinh_v, cs * cosh_v));
}
if (numPoles & 1)
add (-sinh_u, -sinh_v);
}
}
void AnalogLowPass::design (int numPoles,
WorkspaceBase* w)
{
if (m_numPoles != numPoles)
{
m_numPoles = numPoles;
reset ();
PolynomialFinderBase& poly (w->poly);
RootFinderBase& poles (w->roots);
poly.solve (numPoles);
int degree = numPoles * 2;
poles.coef()[0] = 1 + poly.coef()[0];
poles.coef()[1] = 0;
for (int i = 1; i <= degree; ++i)
{
poles.coef()[2*i] = poly.coef()[i] * ((i & 1) ? -1 : 1);
poles.coef()[2*i+1] = 0;
}
poles.solve (degree);
int j = 0;
for (int i = 0; i < degree; ++i)
if (poles.root()[i].real() <= 0)
poles.root()[j++] = poles.root()[i];
// sort descending imag() and cut degree in half
poles.sort (degree/2);
const int pairs = numPoles / 2;
for (int i = 0; i < pairs; ++i)
{
complex_t c = poles.root()[i];
addPoleZeroConjugatePairs (c, infinity());
}
if (numPoles & 1)
add (poles.root()[pairs].real(), infinity());
}
}
void AnalogLowPass::design (int numPoles)
{
if (m_numPoles != numPoles)
{
m_numPoles = numPoles;
reset ();
const double n2 = 2 * numPoles;
const int pairs = numPoles / 2;
for (int i = 0; i < pairs; ++i)
{
complex_t c = std::polar (1., doublePi_2 + (2 * i + 1) * doublePi / n2);
addPoleZeroConjugatePairs (c, infinity());
}
if (numPoles & 1)
add (-1, infinity());
}
}
void AnalogLowPass::design(int numPoles,
double rippleDb)
{
if (m_numPoles != numPoles ||
m_rippleDb != rippleDb)
{
m_numPoles = numPoles;
m_rippleDb = rippleDb;
reset();
const double eps = std::sqrt(1. / std::exp(-rippleDb * 0.1 * doubleLn10) - 1);
const double v0 = asinh(1 / eps) / numPoles;
const double sinh_v0 = -sinh(v0);
const double cosh_v0 = cosh(v0);
const double n2 = 2 * numPoles;
const int pairs = numPoles / 2;
for (int i = 0; i < pairs; ++i)
{
const int k = 2 * i + 1 - numPoles;
double a = sinh_v0 * cos(k * doublePi / n2);
double b = cosh_v0 * sin(k * doublePi / n2);
//addPoleZero (complex_t (a, b), infinity());
//addPoleZero (complex_t (a, -b), infinity());
addPoleZeroConjugatePairs(complex_t (a, b), infinity());
}
if (numPoles & 1)
{
add(complex_t (sinh_v0, 0), infinity());
setNormal(0, 1);
}
else
{
setNormal(0, pow(10, -rippleDb/20.));
}
}
}
void AnalogLowShelf::design (int numPoles,
double gainDb,
WorkspaceBase* w)
{
if (m_numPoles != numPoles ||
m_gainDb != gainDb)
{
m_numPoles = numPoles;
m_gainDb = gainDb;
reset ();
const double G = pow (10., gainDb / 20) - 1;
RootFinderBase& poles (w->roots);
for (int i = 0; i < numPoles + 1; ++i)
poles.coef()[i] = reversebessel (i, numPoles);
poles.solve (numPoles);
RootFinder<50> zeros;
for (int i = 0; i < numPoles + 1; ++i)
zeros.coef()[i] = reversebessel (i, numPoles);
double a0 = reversebessel (0, numPoles);
zeros.coef()[0] += G * a0;
zeros.solve (numPoles);
const int pairs = numPoles / 2;
for (int i = 0; i < pairs; ++i)
{
complex_t p = poles.root()[i];
complex_t z = zeros.root()[i];
addPoleZeroConjugatePairs (p, z);
}
if (numPoles & 1)
add (poles.root()[pairs].real(), zeros.root()[pairs].real());
}
}
