The z-Transform - Digital Signal Processing: Fundamentals and Applications - page 159

z
ðz þ 0 : 3 Þðz 0 : 5 Þ

b. XðzÞ¼

5 z
ðz 0 : 75 Þðz

c. XðzÞ¼

2

z þ 0 : 5 Þ

2 zðz 0 : 4 Þ
ðz 0 : 2 Þ

d. XðzÞ¼

2

ðz þ 0 : 8 Þ
5.12. A system is described by the difference equation

yðnÞþ 0 : 2 yðn 1 Þ¼ 4 ð 0 : 3 Þ n uðnÞ

Determine the solution when the initial condition is yð 1 Þ¼ 1.

5.13. A system is described by the difference equation

yðnÞ 0 : 5 yðn 1 Þþ 0 : 06 yðn 2 Þ¼ð 0 : 4 Þ n 1

uðn 1 Þ

Determine the solution when the initial conditions are yð 1 Þ¼ 1, and yð 2 Þ¼ 2.

5.14. Given the following difference equation with the input e output relationship of a certain
initially relaxed system (all initial conditions are zero),

yðnÞ 0 : 7 yðn 1 Þþ 0 : 1 yðn 2 Þ¼xðnÞþxðn 1 Þ
a. find the impulse response sequence yðnÞ due to the impulse sequence dðnÞ ;
b. find the output response of the system when the unit step function uðnÞ is applied.
5.15. A system is described by the difference equation

yðnÞ 0 : 6 yðn 1 Þþ 0 : 08 yðn 2 Þ¼ð 0 : 5 Þ n 1 uðn 1 Þ

Determine the solution when the initial conditions are yð 1 Þ¼ 2, and yð 2 Þ¼ 1.

5.16. Given the following difference equation with the input e output relationship of a certain
initially relaxed system (all initial conditions are zero),

yðnÞ 0 : 6 yðn 1 Þþ 0 : 25 yðn 2 Þ¼xðnÞþxðn 1 Þ

a. find the impulse response sequence yðnÞ due to the impulse sequence dðnÞ ;
b. find the output response of the system when the unit step function uðnÞ is applied.
5.17. Given the following difference equation with the input e output relationship of a certain
initially relaxed DSP system (all initial conditions are zero),

yðnÞ 0 : 4 yðn 1 Þþ 0 : 29 yðn 2 Þ¼xðnÞþ 0 : 5 xðn 1 Þ

a. find the impulse response sequence yðnÞ due to the impulse sequence dðnÞ ;
b. find the output response of the system when the unit step function uðnÞ is applied.