Digital Signal Processing Reference
In-Depth Information
10.3.
Given the LTI system of Figure P10.3, with the input
x
[
n
] and the impulse response
h
[
n
], where
1,
1 F n F 6
2,
-2 F n F 1
b
x[n] =
b
otherwise
h[n] =
0,
0,
otherwise.
Parts (a), (b), and (c) are to be solved without finding
y
[
n
] for all
n
.
(a)
Solve for the system output at that is, find
y
[5].
(b)
Find the maximum value for the output
y
[
n
].
(c)
Find the values of
n
for which the output is maximum.
(d)
Verify the results by solving for
y
[
n
] for all
n
.
(e)
n = 5;
Verify the results of this problem using MATLAB.
x
[
n
]
y
[
n
]
h
[
n
]
Figure P10.3
h[n] = a
n
u[n],
10.4.
Given the LTI system of Figure P10.3, with the impulse response
where
x[n] = b
n
u[n],
a
is a constant. This system is excited with the input
with
b Z a
and constant.
b
(a)
Find the system response
y
[
n
]. Express
y
[
n
] in closed form, using the formulas for
geometric series in Appendix C.
(b)
Evaluate
y
[4], using the results of part (a).
(c)
Verify the results of part (b) by expanding the convolution sum for
y
[4], as in
(10.15).
10.5.
Consider the LTI system of Figure P10.3, with the input
x
[
n
] and the impulse response
h
[
n
], where
2,
- 1 F n F 3
b
x[n] =
0,
otherwise
1,
-6 F n F-1
h[n] =
b
0,
otherwise.
Parts (a), (b), and (c) are to be solved without finding
y
[
n
] for all
n
.
(a)
Solve for the system output at that is, find
y
[4].
(b)
Find the maximum value for the output
y
[
n
].
(c)
Find the values of
n
for which the output is maximum.
(d)
Verify the results by solving for
y
[
n
] for all
n
.
(e)
n = 4;
Verify the results of this problem using MATLAB.
10.6.
Consider the discrete-time LTI system of Figure P10.3. This system has the impulse
response
h[n] = u[n + 2] - u[n - 2],
