Digital Signals and Systems - Digital Signal Processing: Fundamentals and Applications - page 82

x ( n )

1

n

5

1 0 1 2 3 4

1

FIGURE 3.27

The second digital signal in Problem 3.8.

3.9. Assume that a DS processor with a sampling time interval of 0.01 second converts the
following analog signals xðtÞ to a digital signal xðnÞ ; determine the digital sequence for each
of the analog signals.
a. xðtÞ¼e 50 t uðtÞ
b. xðtÞ¼ 5sin ð 20 ptÞuðtÞ
c. xðtÞ¼ 10cos ð 40 pt þ 30 0 ÞuðtÞ

d. xðtÞ¼ 10 e 100 t sin ð 15 ptÞuðtÞ
3.10. Determine which of the following systems is a linear system.
a. yðnÞ¼ 5 xðnÞþ 2 x

2

ðnÞ
b. yðnÞ¼xðn 1 Þþ 4 xðnÞ
c. yðnÞ¼ 4 x

3

ðn 1 Þ 2 xðnÞ
3.11. Assume that a DS processor with a sampling time interval of 0.005 second converts each of
the following analog signals xðtÞ to a digital signal xðnÞ ; determine the digital sequence for
each of the analog signals.
a. xðtÞ¼e 100 t uðtÞ
b. xðtÞ¼ 4sin ð 60 ptÞuðtÞ
c. xðtÞ¼ 7 : 5cos ð 20 pt þ 60 0 ÞuðtÞ

d. xðtÞ¼ 20 e 200 t sin ð 60 ptÞuðtÞ

3.12. Determine which of the following systems is a linear system.
a. yðnÞ¼ 4 xðnÞþ 8 x

3

ðnÞ
b. yðnÞ¼xðn 3 Þþ 3 xðnÞ
c. yðnÞ¼ 5 x

2

ðn 1 Þ 3 xðnÞ

3.13. Determine which of the following linear systems is time invariant.
a. yðnÞ¼ 5 xðn 10 Þ
b. yðnÞ¼ 4 xðn

2

Þ