Signals and Systems
Sharif University of Technology
Dr. Hamid Reza Rabiee
December 10, 2010
CE 40-242
Date Due: Dey 4, 1389
Homework 7 (Chapter 9)
Problems
1. Determine the Laplace transform and the associated region of convergence and pole-zero plot
for each of the following functions of time:
9-21. a
9-21. b
9-21. c
9-21. d
9-21. f
9-21. j
9-21. h
1.
2.
2. Determine the function of time, x(t), for each of the following Laplace transforms and their
associated regions of convergence:
9-22. a
9-22. b
9-22. c
9-22. e
9-22. g
−s
1. X(s) = ( 1−es
2
)
3. Problem 9-6
4. Problem 9-10
5. Problem 9-27
6. Problem 9-34
1
7. Determine which of the following pole-zero diagrams could represent Laplace transforms of even
functions of time. Determine expressions for the time functions of those that can represent even
functions of time. For those that cannot, explain why they cannot.
How can you determine if a signal is even or not by looking at its Laplace transform and region
of convergence?
Practical Assignment
(a) Use partial fraction expansion to find the inverse Laplace transform of each of the following.
For each case, find all finite poles and zeros and plot their location in the s-plane. Use
Matlab to plot the time functions. Qualitatively, how does the zero location affect the time
response?
1. X(s) =
2. X(s) =
2. X(s) =
8(s+9)
(s+2)(s+10)
1
s2 +2s+2
3s2 +3s+1
s(s+1)2
2