Biquad Type-II Coefficient Generation

Question

I have a Biquad II filter implementation in my embedded environment and I'm trying to find some equations to generate the coefficients for it.

I have already found the Audio Eq Cookbook, which simply describes how to calculate all of the coefficients for Type I.

LPF: (Taken from Audio Eq Cookbook, Type I Equations)

omega = 2*PI*frequency/sampleRate
sin   = sin(omega)
cos   = cos(omega)
alpha = sin/(2Q)                                     (if Q is specified)
      = sinsinh[ ln(2)/2 * bandwidth * omega/sin ]   (if bandwidth is specified)
        b0 =  (1 - cos)/2
        b1 =   1 - cos
        b2 =  (1 - cos)/2
        a0 =   1 + alpha
        a1 =  -2*cos
        a2 =   1 - alpha

What are the equations for type II coefficients?

hay, i didn't see this until now, 2 weeks later. the coefficients for the Direct Form 1 and Direct Form 2 are the same. but these coefficients have to be massaged a bit if your implementation is a form like Lattice or Ladder or some other State Variable Forms. — robert bristow-johnson, Apr 05 '19 at 22:01
@robertbristow-johnson hey robert, please elaborate since I'm desperately wanting to implement a ladder filter. Can you lead me to a reading source? or even better, a math like this simple? — Can Uysal, Apr 05 '19 at 23:24
@robertbristow-johnson lol, robert it is you! you are the author of audio eq cookbook, huge fan! such an honour! :) thank you for this lovely source, It saved me like a years work maybe. Thank you! Your page in musicdsp is down by the way, is there any other sites hosting your original writing?
While I find you here, would like to ask another question. When my filter drops down below 200-300 hz, some distortion/noise begin to rumble in low end, especially with high Q. Is there a way to eliminate this? Using direct form II transposed. — Can Uysal, Apr 05 '19 at 23:38
for the lattice, i got this answer for how to calculate the coefficients from the Direct Form and this answer for how to code it. — robert bristow-johnson, Apr 05 '19 at 23:56
that musicdsp is often down. looks like you can find the cookbook text here. — robert bristow-johnson, Apr 06 '19 at 00:04
thank you, i will try to implement that. any idea about that low end rumble? — Can Uysal, Apr 06 '19 at 10:14

Biquad Type-II Coefficient Generation

0 Answers0