The signal flow graph for the general two-zero filter is given in Fig.10.8, and the derivation of frequency response is as follows:
The parameters and are called the numerator coefficients, and they determine the two zeros. Using the quadratic formula for finding the roots of a second-order polynomial, we find that the zeros are located at
Forming a general two-zero transfer function in factored form gives
from which we identify and , so that
The approximate relation between bandwidth and given in Eq. (10.5) for the two-pole resonator now applies to the notch width in the two-zero filter.
Figure 10.9 gives some two-zero frequency responses obtained by setting to 1 and varying . The value of , is again . Note that the response is exactly analogous to the two-pole resonator with notches replacing the resonant peaks. Since the plots are on a linear magnitude scale, the two-zero amplitude response appears as the reciprocal of a two-pole response. On a dB scale, the two-zero response is an upside-down two-pole response.