重邮 信号与系统考试答案 考研必备

信号与系统习题解答

1.1

(1) f(t)= (t)1

解 P lim

2

2

|f(t)|dt

11

lim dt 2 20

2

E总 lim |f(t)|dt lim dt

f(t) (t)为功率信号。(2) f(t)= (t)- (t-1)

解 f(t)是矩形脉冲信号，故为能量信号。

(3)f(t) 6t (t)

解：书中已作证明斜坡信号为非公非能信号。

(4)f(t) 5ej( 0t )解 |f(t)| 5

1 P lim

T T

2

|f(t)|dt

2

2

1 limT T

2

2

25dt 25

2

2

2

T

E总 lim

T

|f(t)|dt lim 25dt

2

2

f(t)为功率信号

(5) f(t) e tsin2t (t)

2

解：E总 lim |f(t)|dt lim (e tsin2t)2dt

e 2t(ej2t e j2t)1 2tj4t j4t

lim ( )lim e(e e 2)dt2 (2j)400

1

( )lim [e (2 j4)t e (2 j4)t]dt

4 0