h n 1, 0, 2 , n 0,1, 2
5.
(20
points)
Consider
h t
sin 2 t t
cos 7 t
,
if
the
an
LTI
system
input is
x t n
with
unit
impulse
response
t n , determine the output
.
t 2
x t u t , and
h t
is illustrated in Figure 4. Please
h t
1
0
1
2
3
t
Figure 4
4. (10 points) Compute the convolution y n x n h n , where
x n 3,1, 5 , n 1, 2, 3
t n ,
determine
the
output
y t . 6. (20 points) Consider an LTI system with input
x t
t e3t u t and output
y t et u t .
(a) Determine the system function H s , then indicate the ROC of
H s .
(b) Determine the unit impulse response
y t .
2.
( 10 points ) Consider a continous-time system with input
x t
and output
y t
related by
(a)
Linear? Stable?
(b)
y t x 2t 1
, is this system
Time-invariant?
x n 3,1, 5 , n 1, 2, 3
h n 1, 0, 2 , n 0,1, 2
5.
(20
points)
Consider
h t sin 2 t
t cos 7
t,
if
the
an
LTI
input is
system
x t
n
with
unit
impulse
response
t n , determine the output
y t .
6. (20 points) Consider an LTI system with input
x t
t e3t u t and output
y t et u t .
(a) Determine the system function H s , then indicate the ROC of
y t related by
y t x 2t 1 , is this system
(a) Linear? Stable?
(b) Time-invariant?
(c) Memoryless?
(d) Causal?
(e)
3. (10 points) If we know
determine x t h t
2.
( 10 points ) Consider a continous-time system with input
x t
and output
y t
related by
(a) Linear? Stable?
(b)
y t x 2t 1
, is this system
Time-invariant?
H s .
(b) Determine the unit impulse response
h t
of this system, is this system
causal and stable?
Hale Waihona Puke (c) For the input
x t 2 , compute the output
y t .
(d) Determine the differential equation of this system.
(c)
Memoryless?
(d)
Causal?
(e)
3. (10 points) If we know
determine
x t h t
.
t 2
x t u t , and
h t
is illustrated in Figure 4. Please
h t
1
0
1
2
3
t
Figure 4
4. (10 points) Compute the convolution y n x n h n , where
x1 (t ) 1
y1 (t ) 1
0
1
t
Figure 1
0
1
2
t
Figure 2
x2 t depicted in Figure 3.
x2 (t ) 1
0
1
2
3
t
Figure 3
2.
( 10 points ) Consider a continous-time system with input x t and output
x n 3,1, 5 , n 1, 2, 3
h n 1, 0, 2 , n 0,1, 2
5.
(20
points)
Consider
h t sin 2 t
t cos 7
t,
if
the
an
LTI
input is
system
x t n
with
unit
impulse
response
1. (10 points) Consider an LTI system whose response to the signal x1 t in
Figure 1 is the signal
y1 t illustrated in Figure 2. Determine and sketch
carefully the response of the system to the input
(c)
Memoryless?
(d)
Causal?
(e)
3. (10 points) If we know
determine
x t h t
.
t 2
x t u t , and
h t
is
illustrated
h t
in
Figure
4.
Please
1
0
1
2
3
t
Figure 4
4. (10 points) Compute the convolution y n x n h n , where