第三章考题第3章考题电子科技大学信号与系统858期末复习

(d)
✓
a k e
jkw0
5. x1(t) e t [u(t 1) u(t 1)],

x(t) x1(t) (t 4k ), x(t) may be ( ). k

a).x(t )
✓

a0

k 1
2ak
c os (kt
/
2)

b).x(t) 2ak cos(kt / 2) k 1
2
2
y( t ) x(t) h(t).
Determine the valueof 0 which insures that y(0) 0.
6. x[n] cosn,h[n] ( 1 )n u[n], y[n] ?
2
2 cosn
3
7. x(t)* etu(t) 1 e2t , x(t) ?
(a) 1 e2t u(t ) 4
(c) 1 e2t u(t ) 4
(b) 1 e2t ✓4 (d) 1 e2t
4
4. ( 2 e2t ) etu(t) ?
2012
2 1 e2t 3
5. x(t) e j0t ,
h(t) u(t 1 ) u(t 1 ),

8. x1(t) e t , x(t) x1(t) (t 4k), k
The Fourier series coefficients of x(t) may be ( ).
a✓).ak ak , Im{ak } 0 b).ak ak , Im{ak } 0 c).ak ak , Re{ak } 0 d ).ak ak , Re{ak } 0
(a) x(-t)=-x(t) 0 with fundmental period T=8
✓
(b) x(-t)=-x(t) 0 with fundmental period T=32 (✓c) x(-t)=-x(t) 0 with fundmental period T=16 (d) x(-t)=x(t) 0 with fundmental period T=16

(a) x(t ) a0 2ak cos(kw0t ) k 1

(b) x(t ) 2 jak sin(kw0t )
✓
k 1

(c) x(t ) 2ak cos(kw0t )
k 1

(d) x(t ) 2 ak sin(kw0t )
✓
k 1
7. x1(t) t[u(t 1) u(t 1)],
The eigenfunction of the system
1. y(t) 2 etu(t) ?
a) 2e-tu(t) ✓b) 2 c) e-t d) 1
2. The convolution integral y(t)=cost*e-tu(t)
may be ( )
(a) cos(t / 4) (✓c) 1 cos(t / 4)
signal x(t) with fundamental period T=1 and FS coefficients ak , it is found y(t)=x(t), the FS coefficients akmust satisfy( )
H(jw) 1
-5π -3π
w 3π 5π
(a) ak 0, k 2
(a) ak 2
(c)
✓
ak e
j 3kw0
(b)
1 2
ak
e

j
3 kw0
(d) 2ak e j 3kw0
4. the Fourier series coefficients of x(1 t) is ( )
(a) ak e jkw0 (c) -ak e jkw0
(b)ak e jkw0
2
(b) 1 cos(t / 4)
2
(d) cos(t / 4)
x(t) cos0t H( j) y(t) H ( j0) cos[0t H ( j0)] H ( j) H ( j) e jH ( j)
3. the convolution interal y(t)=e2t*e-2tu(t) may be ( )
2. The input of an LTI systemis
x(t) 2 cost cos3t,
then y(t) ?
H(j)
j
-2 0
2

-j
3. Consider a CT LTI system which frequency response is
illustrated in fig. when the input to this system is a periodic

x(t) x1(t) (t 8k), x(t) may be ( ). k
a).ak ak , Im{ak } 0 b).ak ak , Im{ak } 0 c).ak ak , Re{ak } 0 d✓).ak ak , Re{ak } 0
w
-3π
3π
✓(a)
H(jw) 1
-4π -π
π (b)
H(jw) 1
w 4π
w
-4π
4π
(c)
w
-4π -3π
3π 4π
(✓d)
5. The output of system( ) to the input x(t)=cos2 t+sin5 t+cos10t
is not periodic
H(jw) 1

c).x(t) a0 2ak sin(kt / 2) k 1

d ).x(t) 2ak sin(kt / 2) k 1
6. let x(t) be a real periodic signal, and x(-t)=-x(t), the Fourier series of x(t) may be ( )
Chapte 3
1. let x(t) be a periodic signal with fundamental
frequency w0 , and Fourier series coefficients ak , the Fourier series coefficients of dx(t - 1) is ( )
(✓b) ak 0, k 2
(c)
ak

0
0
k 2 k 2
(d)
ak



0
0
k 3 k 3
5. The output of system( ) to the input x(t)=cos2 t+sin10t
is periodic
H(jw) 1
H(jw) 1
(a) w0 2 (b)w0
✓
(c)w0 3 (✓d)w0 4
7. Consider an LTI systemwhosefrequency
responseis H ( j) sin( / 2) ,
if the output y(t) 0,
then thefundamental period of
H(jw) 1
w
-3π
(a)
3π
w
-4π -3π
3π 4π
(b)
H(jw) 1
w
-4π
4π
(✓c)
H(jw) 1
w
-3π
3π
(✓d)
6. Consider a continuous-time LTI system whose frequency response is H ( jw) sin(w / 2) . When w the input to this system is x(t ) e jw0t , it is found y(t) 0. Which of the following statements is true( )
2013
1 3e2t
2013期末
8. e4t e2tu(t) ? does not exist
FS and LTI system

1. The input signal of an LTI system is x(t) (-1)n (t - n) n-
if the output y(t) cos 5 t cos 7 t, the unit impuse
the input x(t) may be (
).
a).T 1 b).T 2 c).T 0.5 d).T 3
✓
✓
8. Consider a continuous-time LTI system whose frequency response is H( jw) sin(8w) . If the w periodic input signal x(t) satisfy ( ), the output y(t) 0.
of the system may be( )
(a✓)
h(t )

1
2
t
(sin 8 t

sin 4
t)
(b) h(t ) 1 (sin 8 t sin 4 t) t
(c) h(t ) 1 (sin10 t sin 4 t) 2 t
(d) h(t ) 1 (sin 8 t sin 2 t) 2 t
the Fourier series coefficients of x(3t) is ( )