Digital Signal Processing Reference
In-Depth Information
3(z + 0.8)
z(z - 0.8)(z - 2)
(ii)
H(z) =
3(z - 0.8)
z(z + 0.8)(z + 2)
(iii)
H(z) =
3(z - 1)
2
(iv)
H(z) =
z
3
- 1.6z
2
+ 0.64z
2z - 1.5
(v)
H(z) =
z
3
- 2z
2
+ 0.99z
Use MATLAB where required.
(b)
For each system that is unstable, give a bounded input for which the output is
unbounded.
(c)
Verify the results in part (b) by finding the unbounded term in the response for
that input.
11.24.
Label each of the following
z
-transforms as a lowpass, highpass, bandpass, or bandstop
filter. Also label each filter as BIBO stable or unstable.
(a)
z
2
z
2
- 1
, |z| 7 1
H
1
(z) =
(b)
z
2
z
2
+ .81
, |z| 7 .9
H
2
(z) =
(c)
1
1 + 1.1z
- 1
, |z| 7 1.1
H
3
(z) =
(d)
z
2
z
2
- 4.25z + 1
, |z| 7 4
H
4
(z) =
11.25.
Given the discrete-time function
f[n] = a
n
u[n] - b
2n
u[-n - 1].
(a)
What condition must hold on
a
and
b
for the bilateral
z
-transform to exist?
(b)
Assuming that the preceding condition holds, find the bilateral
z
-transform and
region of convergence of
f[n]
.
11.26.
Find the bilateral
z
-transforms and the regions of convergence for the following functions:
0.7
n
u[n]
(a)
(b)
(c)
(d)
0.7
n
u[n - 7]
0.7
n
u[n + 7]
-0.7
n
u[-n - 1]
