Digital Signals and Systems - Digital Signal Processing: Fundamentals and Applications - page 83

3.14. Determine which of the following linear systems is causal.
a. yðnÞ¼ 0 : 5 xðnÞþ 100 xðn 2 Þ 20 xðn 10 Þ
b. yðnÞ¼xðn þ 4 Þþ 0 : 5 xðnÞ 2 xðn 2 Þ
3.15. Determine the causality for each of the following linear systems.
a. yðnÞ¼ 0 : 5 xðnÞþ 20 xðn 2 Þ 0 : 1 yðn 1 Þ
b. yðnÞ¼xðn þ 2 Þ 0 : 4 yðn 1 Þ
c. yðnÞ¼xðn 1 Þþ 0 : 5 yðn þ 2 Þ
3.16. Find the unit-impulse response for each of the following linear systems.
a. yðnÞ¼ 0 : 5 xðnÞ 0 : 5 xðn 2 Þ ; for n 0, xð 2 Þ¼ 0, xð 1 Þ¼ 0
b. yðnÞ¼ 0 : 75 yðn 1 ÞþxðnÞ ; for n 0, yð 1 Þ¼ 0
c. yðnÞ¼ 0 : 8 yðn 1 Þþxðn 1 Þ ; for n 0, xð 1 Þ¼ 0, yð 1 Þ¼ 0
3.17. Determine the causality for each of the following linear systems.
a. yðnÞ¼ 5 xðnÞþ 10 xðn 4 Þ 0 : 1 yðn 5 Þ
b. yðnÞ¼ 2 xðn þ 2 Þ 0 : 2 yðn 2 Þ
c. yðnÞ¼ 0 : 1 xðn þ 1 Þþ 0 : 5 yðn þ 2 Þ

3.18. Find the unit-impulse response for each of the following linear systems.
a. yðnÞ¼ 0 : 2 xðnÞ 0 : 3 xðn 2 Þ ; for n 0, xð 2 Þ¼ 0, xð 1 Þ¼ 0
b. yðnÞ¼ 0 : 5 yðn 1 Þþ 0 : 5 xðnÞ ; for n 0, yð 1 Þ¼ 0
c. yðnÞ¼ 0 : 6 yðn 1 Þxðn 1 Þ ; for n 0, xð 1 Þ¼ 0, yð 1 Þ¼ 0
3.19. For each of the following linear systems, find the unit-impulse response, and draw the block
diagram.
a. yðnÞ¼ 5 xðn 10 Þ
b. yðnÞ¼xðnÞþ 0 : 5 xðn 1 Þ
3.20. Determine the stability of the following linear system.
yðnÞ¼ 0 : 5 xðnÞþ 100 xðn 2 Þ 20 xðn 10 Þ

3.21. For each of the following linear systems, find the unit-impulse response, and draw the block

diagram.
a. yðnÞ¼ 2 : 5 xðn 5 Þ
b. yðnÞ¼ 2 xðnÞþ 1 : 2 xðn 1 Þ

3.22. Determine the stability for the following linear system.
yðnÞ¼ 5 xðnÞþ 30 xðn 3 Þ 10 xðn 20 Þ

3.23. Determine the stability for each of the following linear systems.
a. yðnÞ¼ P k ¼ 0 0 : 75 k xðn kÞ
b. yðnÞ¼ P k ¼ 0 2 k xðn kÞ