Answers to Selected Problems - Digital Signal Processing: Fundamentals and Applications - page 834

3.5.

(a)

10

5

0

-5

-8 -6 -4 -2 0 2 4 6 8

n

(b)

6

4

2

0

-2

-8 -6 -4 -2 0 2 4 6 8

n

3.6. a. xðnÞ¼ 3 dðnÞþdðn 1 Þþ 2 dðn 2 Þþdðn 3 Þþdðn 5 Þ

b. xðnÞ¼dðn 1 Þdðn 2 Þþdðn 4 Þdðn 5 Þ

xðnÞ¼e 0 : 5 n uðnÞ¼ð 0 : 6065 Þ n uðnÞ 3.9. a.

b. xðnÞ¼ 5 sin ð 0 : 2 pnÞuðnÞ

c. xðnÞ¼ 10 cos ð 0 : 4 pn þ p= 6 ÞuðnÞ

xðnÞ¼ 10 e n sin ð 0 : 15 pnÞuðnÞ¼ 10 ð 0 : 3679 Þ n sin ð 0 : 15 pnÞuðnÞ
3.10. a. nonlinear system
b.

d.

linear system

c. nonlinear system

3.13. a. time-invariant

3.15. a. causal system

b. noncausal system

c. causal system

3.16. a. hðnÞ¼ 0 : 5 dðnÞ 0 : 5 dðn 2 Þ

hðnÞ¼ð 0 : 75 Þ n , n 0 b.

hðnÞ¼ 1 : 25 dðnÞ 1 : 25 ð 0 : 8 Þ n , n 0 c.

3.19. a. hðnÞ¼ 5 dðn 10 Þ

hðnÞ¼dðnÞþ 0 : 5 dðn 1 Þ
3.20. Since

b.

hðnÞ¼ 0 : 5 dðnÞþ 100 dðn 2 Þ 20 dðn 10 Þ and S ¼ 0 : 5 þ 100 þ 20 ¼ 120 : 5 ¼

finite number, the system is stable.
3.23. a. hðnÞ¼ð 0 : 75 Þ n uðnÞ , S ¼ P k ¼ 0 ð 0 : 75 Þ k ¼ 1 =ð 1 0 : 75 Þ¼ 4 ¼ finite, the system is stable.

S ¼ P k ¼ 0 ð 2 Þ k ¼ 1 þ 2 þ 2 2 hðnÞ¼ð 2 Þ n uðnÞ , b. þ / ¼ N ¼ infinite, the system is

unstable.