Digital Signal Processing Reference
In-Depth Information
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Exercise 6.7: z-transform and magnitude response.
Consider a
causal LTI system described by the following transfer function:
1
6
+
1
2
z
−
1
1
2
z
−
2
1
6
z
−
3
+
+
H
(
z
)=
1
3
z
−
2
1
+
e
j
ω
)
(a) Sketch themagnitude response
H
from the
z
-transform. You can
use a numerical package to find the poles and the zeros of the transfer
function. What type of filter is
H
(
(
z
)
?
(b) Sketch the pole-zero plot. Is the system stable?
Now fire up your favorite numerical package (or write some C code) and
consider the following length-128 input signal:
0
n
∈
[
1 ... 50
]
x
[
n
]=
1
n
∈
[
51 . . . 128
]
