###
One-Zero

Figure

B.1 gives the

signal flow graph for the general one-zero
filter. The

frequency response for the one-zero filter may be found by
the following steps:

By factoring out

from the frequency response, to
balance the exponents of

, we can get this closer to polar form as
follows:

We now apply the general equations given in
Chapter

7 for filter gain

and filter phase

as a function of frequency:

A plot of

and

for

and various
real values of

, is given in Fig.

B.2. The filter has a zero
at

in the

plane, which is always on the
real axis. When a point on the unit circle comes close to the zero of
the

transfer function the filter gain at that frequency is
low. Notice that one real zero can basically make either a highpass
(

) or a

lowpass filter (

). For the phase
response calculation using the

graphical method, it is necessary to
include the

pole at

.

**Next Section:** One-Pole**Previous Section:** Phasor Analysis: Factoring a Complex Sinusoid into Phasor Times Carrier