北邮考研信号与系统专业课试卷及答案B

14.
x(n)=sin(0.3n)
15.
z
X (z) = 1+ 2z−1 + 3z−2 + 4z−3 + 5z−4
16. x(n) = {−3 2 3} ↑
h(n) = {2 −4 1} ↑
17.
x(n) = (−0.8)n u(n − 2) z
6
48
1.
f1 øt÷, f2 øt÷
2.1
f øt÷ ã f1øt÷\ f2 øt÷ f ø0÷=
=1 T1
F0
=n
=
1
1 jn
1
Sa
n 4
1
e
−
j
n 4
1
=
1 j2n
Sa n
e
−
j
n 2
2
FT (
)= 2
∑∞ 1
−∞ j2n
Sa n
e
−
j
n 2
⋅
(
2
− 2n )
8
2
1
B
∫ R( ) = lim 1 T E 2 cos
T T →∞ 0
0t ⋅ cos
0 (t −
)u(t −
)dt
> 0 , f (t)⋅ f (t − )
yøt ÷
F( ) H( ) Y( )
H( ) ( ) = 00
2.3 4. f (t) = sin(2t) ⋅ u(t −1)
5.
F
(s)
=
(
s
+
s+6
2)(s
+
5)
6.
x(n)
=
1 2
|n|
z
7. X (z) =
z
1< z <1
z
−
1 2
z
+
1 4
4
2
z x(n)
8.
∫∞ −∞
sin t
f1(t )
2 1
01 2 3 4 t
f2 (t )
2
1
01 2 3 4 t
2.1
2
6
2.
2.2
f (t)
(B )
F ( ) = R( )+ jX ( ) y(t ) ⇔ Y ( )=?
f (t )
2
y(t )
2
1
1
0 1 2 t −4 −2
02
4t
2.2
3.
H ø ÷ 2.3
f øt÷= 1 õ cos t
x(t)
y(t)
8
4.1
m(t)
H(j )
x(t)
s=3 m
y(t) y(t)
1
x(t)
2
y(t)
3
H1(j )
c
c
5
M(j )
4.2
H1(j ) r(t)
x(t) r(t)=x(t)
4
6
(B )
4.1
6
8
7
1
H (s) = V2 (s)
V1(s)
2K
8
y(-2)=0.5
10
1 2 3
s s2 + 4s + 4
t
2
dt
8
3
fT (t)
FT ( )
F (n 1 )
3
6
(B )
fT (t )
1
1
L
2
L
− 3 − 5 −2 − 3 −1 − 1 0 1 1 3 2 5 3
t
2
2
2
2
2
2
3
8
f (t) = E cos( 0t)u(t)
8
5
− rad 2
H( j
)=
− e
j
2
e
j
2
>0 <0
a
h(t)
b
x(t ) = cos 1t + sin 2t
16
17
6
48
9.
12 15 18
1 f ø0÷=
4.
7.
8
2 y( j ) = F(2 ) + F(− 2 ) = 2R(2 )
5.
8.
3 yøt÷ ã 3 õ 2 cos t
6.
T1 = 1 1 = 2
fo (t ) → F0 (
)= 1
j
Sa e − j 4 4
[ ] ( ) ( ) F n
1
2(t )
e2(t )
−
−
10
6
6
B
B
1. 1 u t − 1 2 2
2. 1
3. (t + 1)u(t + 1) − (t − 1)u(t − 1)
4. 1 t [− u(− t )+ u(t )] 5. e − t u(t ) 6.
2
7. 1 F −
e
−
j
1 2
8.
2 2
10
11
13
14
(B )
B
17
2
36
1.
∫ t (2t −1)dt =_______ −∞
2.
.{
sin
0ó
t
7 65
9: t ó 1 )* õ 8 2(
9: t 8
õ
1 2
)(*&%'
dt
=
3.
f1 (t) = u(t) f2 (t) = u(t + 1) − u(t −1) g(t) = f1 (t)∗ f2 (t)=
7
x(n)=(0.5)n, n 0
H(z) h[n]
(H e j )
y(n)+3y(n-1)+2y(n-2)=x(n) y(n)
9
y(-1)=0,
5
6
(B )
4
ab
0 rad/s 1
rad/s 0
8
10
9
r1(t) r2(t)
1(t) L
+ r2 (t) −
e1 (t )
R2 +C+
R1 r1(t)
∫ R( ) = lim 1
T →∞ T
T + E 2 cos2
0t ⋅ cos
0 + E 2 sin
0
⋅ 1 sin 2 2
0 t dt
∫ ∫ =
lim
T →∞
1 T
T+
E 2 cos
0
1 + cos 2 2
0t dt +
T+
E 2 sin
0
⋅ 1 sin 2 2
0
tdt
∫ = lim 1
T →∞ T
0 1
1 2
(t (t
) )
+
R1 0
0 e1(t) −1e2(t )
2
2
4.
t u(t )
5.
g(t) = (1− e− t )u(t)
6.
x(t )
y(t) = x2 (t)
7. F [ f (t )] = F ( ) F[ f (− 2t + 1)]
8.
f(t)
F(s) te−at f (t )
9.
1.1
t0
vc(0-)=-E
s
1.2
1.2
A
B
1 sC
1.1
1.2
1
T + E 2 cos
0
1 dt = E 2 cos 22
0
E2 2
[(
−
0 )+
(
+
0 )]
8
8
8
8
10
8
&&12((tt))
=
−
R1
L 1
C
−1 L
−1
1 (t ) 2 (t )
+
R1 L
0
R2C
0 1
e1 e2
(t (t
) )
R2C
r1 (t ) r2 (t )
=
Βιβλιοθήκη Baidu
− R1 0
6
10.
11.
f(t)
H (s) = 1 s + 0.5
(B )
F
(
s)
=
(s
+
0
a)2
+
2 0
(
>-a a
)
12.
LTI
H(j
) = 9 + j3 8 + j6 −
2
13.
e(t) = E1 sin ( 1t ) + E2 sin (2 1t )
r(t) = KE1 sin ( 1t − 1 ) + KE2 sin (2 1t − 1 )