Biquad Transfer Function

Transfer function with two poles and two zeros. It is the highest degree of polynomial in denominator or both is quadratic.

For LPF, 

$T(s) = \frac{-G \cdot \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}$

For HPF, 

$T(s) = \frac{G \cdot s^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}$

For BPF, 

$T(s) = \frac{G \cdot s}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}$

For BSF, 

$T(s) = \frac{s^2 + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}$

For APF, 

$T(s) = \frac{s^2 - \frac{\omega_0}{Q}s + \omega_0^2}{s^2 + \frac{\omega_0}{Q}s + \omega_0^2}$

Zeros of All Pass Filter must be mirror images of poles and vice versa.