重邮 信号与系统考试答案 考研必备

t

2h(t) ecos (t) sint (t)

22

t

2

(3) y'' 2y' y f' 2f

H(p)

p 2p 211

222

p 2p 1(p 1)(p 1)(p 1)

h(t) (e t te t) (t)

(4) y''' 6y'' 11y' 6y f' 2f H(

p 21

32

p 6p 11p 6(p 1)(p 2)(p 3)(p 1)(p 2)

p 2

=

h(t)=

pt

p 3p 1

pt

p 3

p 1

(

1 t1 3t

e) (t) e22

2.10 求h(k)

(1) y(k)+2y(k-1)=f(k-1)

解：H(E)=1 2E 1

1

1

h(k) ( 2)k 1 (k 1)

E 2

(2) y(k+2)+3y(k+1)+2y(k)=f(k+1)+f(k) H(E)=

E 1E 11

2

E 3E 2(E 1)(E 2)E 2

h(k) ( 2)k 1 (k 1)

(3) y(k)+y(k-1)+

1

y(k-2)=f(k) 4

E2

解： H(E)= 11

E2 E (E )2

42

h(k)=

E2

d12k 1

(E )H(E)EdE2

E

=1

2

dk 1

(E)dE

E

12

(k)

=(k+1)Ek

E

k

1 (k) (k 1)( ) (k). 2

12

(4) y(k)-4y(k-1)+8y(k-2)=f(k) 解: h(k)-4y(k-1)+8y(k-2)= (k)