causal and stable?
(c) For the input xt 2 , compute the output y t .
(d) Determine the differential equation of this system.
a
5
xn 3,1,5,n 1,2,3
hn 1,0,2,n 0,1,2
(d) Draw a block diagram representation of this system.the system function H s , then indicate the ROC of H s .
(b) Determine the unit impulse response ht of this system, is this system
a
4
causal and stable?
ht sin 2t cos 7t , if the input is
t
x t t n , determine the output n
y t .
6. (20 points) Consider an LTI system with input xt t e3tu t and output
7. (20 points) A causal LTI system is described by the difference equation
yn 1 yn 1 xn 1 xn 1
2
2
(a) Find the system function H z , sketch the pole-zero pattern of H z , then
x1(t) 1
y1(t) 1
x2 (t) 1
01
t
Figure 1
01 2
Figure 2
t
01 2 3
t
Figure 3
2. ( 10 points ) Consider a continous-time system with input xt and output
y t related by
indicate the ROC of H z .
(b) Determine the unit impulse response hn , is this system stable?
(c) Compute the output of this system, if the input signal is xn cos n .
yt x2t 1
a
, is this system
1
2. ( 10 points ) Consider a continous-time system with input xt and output
yt related by yt x2t 1 , is this system
(a) Linear? (b) Time-invariant? (c) Memoryless? (d) Causal? (e) Stable?
ht sin 2t cos 7t , if the input is
t
x t t n , determine the output n
y t .
6. (20 points) Consider an LTI system with input xt t e3tu t and output
1. (10 points) Consider an LTI system whose response to the signal x1t in
Figure 1 is the signal y1t illustrated in Figure 2. Determine and sketch
carefully the response of the system to the input x2 t depicted in Figure 3.
the the
convolution convolution
yynn
xxnnhhnn,,
where where
xxnn33,,11,,55,,nn
1, 2,3 1, 2,3
hhnn 11,,00,,22,,nn00,,11,,22
57.. (2(200poipnotisn)tAs)cauCsoanlsLidTeIrsyastnemLisTdI essacyrsibteemd bywtihthe diufnfeirtenicmepeuqlusaetiornesp3onse
4. (10 points) Compute the convolution yn xnhn, where
xn 3,1,5,n 1,2,3
hn 1,0,2,n 0,1,2
5. (20 points) Consider an LTI system with unit impulse response
y t etu t .
(a) Determine the system function H s , then indicate the ROC of H s .
(b) Determine the unit impulse response ht of this system, is this system
3. (10 points) If we know xt ut , and h t is illustrated in Figure 4. Please
determine xt ht .
ht
t2
1
0 1 23
t
Figure 4
4. (10 points) 4. (10 points)
Compute Compute
3. (10 points) If we know xt ut , and h t is illustrated in Figure 4. Please
determine xt ht .
ht
t2
1
0 1 23
t
Figure 4
a
2
(a) Linear? (b) Time-invariant? (c) Memoryless? (d) Causal? (e) Stable?