Frequency response from biquad coefficients

notes
Here is a formula for plotting the frequency response of a biquad filter. Depending on the
coefficients that you have, you might have to use negative values for the b- coefficients.
code
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//w = frequency (0 < w < PI)
//square(x) = x*x

y = 20*log((sqrt(square(a0*square(cos(w))-a0*square(sin(w))+a1*cos(w)+a2)+square(2*a0*cos(w)*sin(w)+a1*(sin(w))))/
                          sqrt(square(square(cos(w))-   square(sin(w))+b1*cos(w)+b2)+square(2*   cos(w)*sin(w)+b1*(sin(w))))));

Comments

this formula can have roundoff errors with frequencies close to zero... (especially a problem
with high samplerate filters)

here is a better formula:

from RBJ @ http://groups.google.com/group/comp.dsp/browse_frm/thread/8c0fa8d396aeb444/a1bc5b63ac56b686

 20*log10[|H(e^jw)|] =
 10*log10[ (b0+b1+b2)^2 - 4*(b0*b1 + 4*b0*b2 + b1*b2)*phi + 16*b0*b2*phi^2 ]
-10*log10[ (a0+a1+a2)^2 - 4*(a0*a1 + 4*a0*a2 + a1*a2)*phi + 16*a0*a2*phi^2 ]

where phi = sin^2(w/2)