信号与系统期末复习Exercise3

Problem8
The system diagram of a DT LTI system is indicated in figure (1) Please find out system function H(z), depict the zero-pole plots, and mark the ROC (2) Find out the system unit impulse response h[n], and determine whether the system is causal (3) Determine the system differential function (4) If the input signal is x[n]=1, n , find out the system output y[n]
1 1 y n 3 2 u n 3 2
n n
and find out the expressions (4) If the FT in question 3 converges, what input signal we should take?
?
2
1
0
1
2



x t
sin 2 t
t
e
j 2t
?
Problem3
A continuous LTI system is illustrated in the figure,
Where h t 1
is x t
1
3 s in t 2

0
1
1
2
3
t

X
2

j e
j
d
Problem2
The spectrum of x t X j is indicated in the figure, please Find:
X
j


x t dt ?
1
dx t dt
t0
h1 t
x t h2 t


y t
Problem4
Find out the time domain signal x(t) represents at given region of convergence
X
s
1 e e
s s
Re{s} >0
Problem5
d t dt
Suppose input x t 1 2 sin 2 t co s 1 0 t ,Determine the Output y(t)

x t
h1 t
h2 t h3 t

h4 t
y t
Problem 10
Determine the function x(t), for the Laplace transform X(s) and its associated ROC
1 10 e , t
t
Please determine the H(s), depict the zero-pole plots, and mark the ROC Calculate the system unit impulse reponse h(t) Determine the differential equation for the system
x[ n ]
1
z
5/2
z
1
y[n ]
1
Problem 9
Consider the system illustrated in Figure, where
h1 t e
10 t
u t
h2 t
s in 4 t
t
h3 t
s in 3 t
t
h4 t
j

Problem6
A causal continuous time LTI system got the diagram in the figure where K is the constant. (1)Please determine the range of K to guarantee the stable system (2) If the input signal is x t e t , t while the ouput is y t
t
s in t 2 ,if the input signal h2 t t
x t 2n

where, x t u t 0 .5 u t 0 .5 1
please find out the system output y(t)
A causal continuous LTI system got the rational system function, whose zeros and poles plot are showed in figure (1) Find out the H(s) and its ROC (2) Calculate the unit impulse h(t) and judge whether the system is stable t x t e u t (3) If the input signal is find the system output y(t) 3 2 1 (4) Depict the system diagram
x t
1 s3
1 s2
y t
K
Problem7
A stable DT LTI system can be descripted by the 5 1 differential equation: y n y n 1 y n 2 x n x n 1 6 6 where is the constant. The system output is y n 3 c o s n 2 When input is x n c o s n (1)Please determine the H(z), depict the zero-pole plots, and mark the ROC (2)Find out the system unit impulse response and judge the causality. (3) How many input signal will generate the output of
u n 1
(a)Find the system function H(z), indicate the ROC
(b)Determine the unit impulse response h[n], is this system stable
(c)Compute the output of this system, if the input signal Is x n c o s n
Problem 12
The input x(t) and output y(t) of a stable LTI system are related through the block-diagram representation shown in Figure (a) Determine the system function H(s), then indicate the ROC (b) Determine the unit impulse response h(t) of this system, is this system causal? (c) For the input x t e 2 t ,compute the output y(t)
1 s2
x t
1 s
y t
3
X s
e e
s
s s
e e
s
Problem 11
Consider an LTI system with input x n n 1 / 4 n 2
and output y n n 1 / 2
n 1
Exercise
Problem1
The signal x(t) is indicated in the figure, and x t X j
Please find the Phase of
X
x t
j
X
j
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