重邮 信号与系统考试答案 考研必备

1.7试证明 (t)=lim

0

( t)

2

2

.

( 2 t2)

(t)lim22

0( t)

0

lim

t 0

0 t 0

1.8 (1)f(t) sin( t ) (t) sin( ) (t)

1 11

(2) f(t) sin( t) (t ) sin( ) (t ) 0.707 (t )

4444

(3) f(t) sin( t ) '(t) sin( ) '(t) cos( ) (t)

1 1 1

(4) f(t) sin( t) '(t ) sin( ) '(t ) cos( ) (t )

44444

1.9 (1) sin(t) (t )dt sin 0.70744 sin5t

(2) (t)dt 5Sa(5t) (t)dt 5

t

(3) e 2t (t) '(t) dt 1 2e 2t

2

t 0

3

t

(4) (t t 1) ()dt (t2 t 1)|2| (t)dt 2

2

3

(5) (t2 2) (t 5)dt 0

100

(6) (t2 2) (t 5)dt (52 2) (t 5)dt 27

10

(7) sin ( 5)d sin5 (t 5)

0t

t

(8) ( 2 1) ()d ( 2 1)2 ( )d 2 (t)

21

(9) (2t2 t 5) (t )dt [2t2 t 5]

104

10

t

1

4

t

t

14

[4t 1] 0

(10)

t

(1 ) ( )d [ ( ) ( )]d (t) (t)

t

k 1

1.13: f1(k) k k ,f2(k) ( ) k 1 .

(1)f1(k) f2(k) k k (a)

k 1

k 1 .