I'm trying to find the equation of a shelving filter of the second order. I easily found the equation for a first order filter on wikipedia with a transition region which have a 6db per octave slope. The equations are :
coef^2 * (1 + (f / (coef * f0))^2) / (1 + (f/f0)^2) for the lowshelf
(1 + (f / (coef * f0))^2) / (1 + (f/f0)^2) for the highshelf
coef = multiplicator coef (gain = 10 log10 (coef))
f = frequency
f0 = cutoff frequency
But now, how can I use a kind of Q factor to modify the slope of the transition region ?
Of course, as I'm using already a frequency signal and not a temporal signal, I can't use the equations made for the z transform...
Thank you for all your answers