电子科大讲义课堂信号与系统考卷

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
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?
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
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.
causal and stable?
(c) For the input xt 2 , compute the output y t .
(d) Determine the differential equation of this system.
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.
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
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
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
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
(a) Linear? (b) Time-invariant?Baidu Nhomakorabea(c) Memoryless? (d) Causal? (e) Stable?
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 yt related by yt x2t 1 , is this system
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 esscyrsibteemd bywtihthe diufnfeirtenicmepeuqlusaetiornesponse
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 .
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