Digital Signal Processing Reference
In-Depth Information
may have a value of zero]
.
If the function is evaluated with
s = z
i
, 1 … i … m,
we
find
H(z
i
) = 0.
Therefore, the
z
i
are called
zeros
of the transfer function. If
H(s)
is
evaluated with
s = p
i
, 1 … i … n,
we find that this causes a divide by zero and
H(p
i
)
is undefined. Because
H(p
i
)
becomes undefined, the
p
i
are called
poles
of the
transfer function.
Poles and zeros of a transfer function
EXAMPLE 7.13
A transfer function is given in the form of (7.49) as
4s + 8
2s
2
+ 8s + 6
.
H(s) =
The transfer function is rewritten in the form of (7.50) as
2(s + 2)
(s + 1)(s + 3)
.
H(s) =
We now see that this transfer function has one zero at and two poles located at
and The poles and the zero of the transfer function are plotted in the
s
-
plane in Figure 7.10. It is standard practice to plot zeros with the symbol
s =-2
s =-1
s =-3.
and poles with
the symbol *.
S
Im (
s
)
j
Re (
s
)
3
2
1
Figure 7.10
■
