musicdsp.org source code archive - WSInf

Another 4-pole lowpass... (click this to go back to the index)
Type : 4-pole LP/HP
References : Posted by fuzzpilz [AT] gmx [DOT] net
Notes :
Vaguely based on the Stilson/Smith Moog paper, but going in a rather different direction from others I've seen here.
The parameters are peak frequency and peak magnitude (g below); both are reasonably accurate for magnitudes above 1. DC gain is 1.
The filter has some undesirable properties - e.g. it's unstable for low peak freqs if implemented in single precision (haven't been able to cleanly
separate it into biquads or onepoles to see if that helps), and it responds so strongly to parameter changes that it's not advisable to update the
coefficients much more rarely than, say, every eight samples during sweeps, which makes it somewhat expensive.
I like the sound, however, and the accuracy is nice to have, since many filters are not very strong in that respect.
I haven't looked at the HP again for a while, but IIRC it had approximately the same good and bad sides.
Code :
double coef[9];
double d[4];
double omega; //peak freq
double g; //peak mag
// calculating coefficients:
double k,p,q,a;
double a0,a1,a2,a3,a4;
k=(4.0*g-3.0)/(g+1.0);
p=1.0-0.25*k;p*=p;
// LP:
a=1.0/(tan(0.5*omega)*(1.0+p));
p=1.0+a;
q=1.0-a;
a0=1.0/(k+p*p*p*p);
a1=4.0*(k+p*p*p*q);
a2=6.0*(k+p*p*q*q);
a3=4.0*(k+p*q*q*q);
a4= (k+q*q*q*q);
p=a0*(k+1.0);
coef[0]=p;
coef[1]=4.0*p;
coef[2]=6.0*p;
coef[3]=4.0*p;
coef[4]=p;
coef[5]=-a1*a0;
coef[6]=-a2*a0;
coef[7]=-a3*a0;
coef[8]=-a4*a0;
// or HP:
a=tan(0.5*omega)/(1.0+p);
p=a+1.0;
q=a-1.0;
a0=1.0/(p*p*p*p+k);
a1=4.0*(p*p*p*q-k);
a2=6.0*(p*p*q*q+k);
a3=4.0*(p*q*q*q-k);
a4= (q*q*q*q+k);
p=a0*(k+1.0);
coef[0]=p;
coef[1]=-4.0*p;
coef[2]=6.0*p;
coef[3]=-4.0*p;
coef[4]=p;
coef[5]=-a1*a0;
coef[6]=-a2*a0;
coef[7]=-a3*a0;
coef[8]=-a4*a0;
// per sample:
out=coef[0]*in+d[0];
d[0]=coef[1]*in+coef[5]*out+d[1];
d[1]=coef[2]*in+coef[6]*out+d[2];
d[2]=coef[3]*in+coef[7]*out+d[3];
d[3]=coef[4]*in+coef[8]*out;
Comments
from : Christian@savioursofsoul.de
comment : Yet untested object pascal translation: