Review of Analog Signal Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 803

g. xðtÞ¼ 3 e 2 t cos ð 3 tÞuðtÞ
h. xðtÞ¼ 10 t

5

uðtÞ
B.8. Determine the inverse transform of the analog signal xðtÞ for each of the following functions
using Table B.5 and partial fraction expansion.

10
s þ 2

a. XðsÞ¼

100
ðs þ 2 Þðs þ 3 Þ

b. XðsÞ¼

100 s

c. XðsÞ¼

2

s þ 7 s þ 10

25

d. XðsÞ¼

s

2

þ 4 s þ 29

B.9. Solve the following differential equation using the Laplace transform method:

2 dxðtÞ
dt

þ 3 xðtÞ¼ 15 uðtÞ with xð 0 Þ¼ 0

a. Determine XðsÞ .
b. Determine the continuous signal xðtÞ by taking the inverse Laplace transform of XðsÞ .

B.10. Solve the following differential equation using the Laplace transform method:

2

þ 2 xðtÞ¼ 10 u t with

d xðtÞ

dt

þ 3 dxðtÞ
dt

x 0 ð 0 Þ¼ 0 and xð 0 Þ¼ 0

2

a. Determine XðsÞ .
b. Determine xðtÞ by taking the inverse Laplace transform of XðsÞ .

B.11. Determine the locations of all finite zeros and poles in the following functions. In each case,
make an s-plane plot of the poles and zeros, and determine whether the given transfer
function is stable, unstable, or marginally stable.

ðs 3 Þ

a. HðsÞ¼

ðs

2

þ 4 s þ 4 Þ

2

sðs þ 5 Þ

b. HðsÞ¼

ðs

2

þ 9 Þðs

2

þ 2 s þ 4 Þ

2

ðs þ 1 Þðs þ 1 Þ

c. HðsÞ¼

sðs

2

þ 7 s 8 Þðs þ 3 Þðs þ 4 Þ