Laplace Transforms
Practice Session
PROBLEM 1. Find the Laplace Transform of the
following signal: i.) using definition
ii.) using properties
a) A causal signal,
= 5 4 + 3 2 2 4
b) = 18 4|
c) = 3 3 ()
d) = 2 , where is any real number
e) = 2
f)
1
= 2
2

EEE35 LQ2 Reviewer
March 1, 2013
Disclaimer: This reviewer is lacking in comparison to the slides because, to be honest, I have no idea which parts of the slides
will be included or not. I just included here what I assume to be the bare essentials and the

38
EEE 35: Signals & Systems
Exercise 10: Impulse Response & Frequency Response
Exercise 10: Impulse Response & Frequency Response
Objective: To understand the relationship between the impulse response and
the frequency response
A. Impulse response to pro

EEE 35: Signals & Systems
Exercise 5: Bode Plots
Exercise 5: Bode Plots
Objective: To be able to create Bode plots using MATLAB.
Bode plot is a way of interpreting how a system responds to sinusoidal input responses.
In this case, it is a means of describ

EEE 35: Signals and Systems
Quiz 3.1.1
This is a CLOSED NOTES, CLOSED BOOKS exercise. Encircle
the letter of the correct answer. (2 POINTS EACH)
(FOR QUESTIONS 1 TO 3) The Fourier series expresses a
real-valued and periodic signal as a linear combination

EEE35 Lab08: Spectrogram and convolution
For this exercise, you may repeat running the program as much as you can. This is good for two
weeks. At each step, you may press Ctrl+C (windows) to stop the script and check for generated
variables. For all the i

EEE 35: Signals & Systems 1
Exercise 7: Applications of DFT on DT Signals
Lab Exercise 07: Applications of DFT on DT Signals
Objectives:
1. To produce the magnitude and phase response of any given signal.
2. To observe and characterize the frequency respo

Exercise 6: Fourier Series for Continuous-Time Signals
Objective: At the end of this exercise, the student should be able to analyze and
synthesize periodic signals.
A. Synthesis
Recall from the lecture the following signal synthesized from sinusoidal har

EEE 35: Signals and Systems
Quiz 3.1.2
This is a CLOSED NOTES, CLOSED BOOKS exercise. Encircle the
letter of the correct answer. (2 POINTS EACH)
The Fourier transform enables us to generate a representation of
aperiodic signals in the frequency domain. Fo

IDFT using IFFT for Signal Recovery - Tuesday
Instead of generating a sinusoidal signal, generate a square wave
(of at least 15 harmonics) with a frequency of 150 Hz. Calculate
the DFT and the inverse Fourier transform.
1. Can you still recover the origin

EEE 35: Signals and Systems
Quiz 3.4.1
This is a CLOSED NOTES, CLOSED BOOKS exercise. NO
CALCULATORS allowed. Write the letter of the correct answer. (2
POINTS EACH)
1.
6.
2.
7.
3.
8.
4.
9.
5.
10.
1. Discrete-time non-periodic signals have a spectrum whic

EEE 35: Signals & Systems
Exercise 9: Inverse DFT using IFFT for Signal Recovery
Exercise 9: Inverse DFT using IFFT for Signal Recovery
Objectives: At the end of this exercise, the student should be able to compute the inverse DFT and
recover a discrete-t

EEE 35 Sample Problems for January 9-16, 2012 (Source: van Valkenburg,
Network Analysis, 2nd edition)
1. In the network shown below, the elements are chosen such that L = CR12 and
R1 = R2. If vs(t) is a voltage pulse of 1-volt amplitude and T sec duration

EEE 35 DC4
* Convolution Sum
* Solution to Difference Equations
Electrical and Electronics Engineering Institute - EEE 35
1
Problem 1
The impulse response of an LTI system is
hn=cfw_1, 2, 1, 1
Determine the response of the system to the input
x n=cfw_1, 2

EEE 35 Sample Problems for January 9-16, 2012 (Source: van Valkenburg,
Network Analysis, 2nd edition)
1. In the network shown below, the elements are chosen such that L = CR12 and
R1 = R2. If vs(t) is a voltage pulse of 1-volt amplitude and T sec duration

Laplace Transform and
Properties
DC 05
Laplace Transform Definition:
Bilateral transform (for non-causal systems):
Lcfw_x(t) =
+
()
Unilateral Transform (for causal systems):
Lcfw_x(t) =
+
()
0
s = + ; ;
Must have set of values for s where the integr

EEE 35 Signals and Systems
2nd Semester 2013-2014
Problem Set 1
Due: December 9, 2013
WORK INDEPENDENTLY!
Set 1
On the 75th Quarter Quell Hunger Games, the arenas design is a 12-hour clock as shown in the
N
figure below:
1st force field activation: 1 tick

EEE 35: Signals & Systems
Lecture 1B
Signals as Functions
EEE 35: Signals & Systems
Component
Type
Process
Some Applications
Signals
Continuous-time,
Continuous-valued
(Analog)
Analysis
Discrete-time,
Discrete-valued
(Digital)
Synthesis
Electric and
elec

EEE 35 DC2
* Signals as functions
* Signal manipulation
* Sampling theorem
Electrical and Electronics Engineering Institute - EEE 35
1
Review on Singularity Functions
Electrical and Electronics Engineering Institute - EEE 35
2
Problem 1
Determine the func

EEE 35 Signals and Systems
2nd Semester 2013-2014
Problem Set 2
Due:
January 27, 2014, 7AM
WORK INDEPENDENTLY!
Set 1
The signal x(t) is a periodic triangular waveform shown below:
A. (5 POINTS) Provide the time domain mathematical expression for a single

EEE 35 DC 1.1
EEE 33 Review
Natural and Forced responses
Steady-state and Transient responses
Zero-input and Zero-state responses
Electrical and Electronics Engineering Institute - EEE 35
Linear Differential Equations
A linear ordinary differential equati

EEE 35 DC3
* Systems as functions
* Convolution integral
Electrical and Electronics Engineering Institute - EEE 35
1
Problem 1
Draw the block diagram for the following system
equations
t
d
d
y t =x t 2 x t 3 x d
dt
dt
0
d2
d
d2
y t 0.5 y t 0.01 y t =2 2

Laplace Transform and Properties
EEE 35: DC 2.1 Practice Session
Signals and Systems
2S 2013 2014
DC 2.1: Laplace Transform and Properties
EEE 35: Signals and Systems
1
Laplace Transform and Properties
EEE 35: DC 2.1 Practice Session
Signals and Systems
2

More Exercises on ILT,
Solutions to Differential Equations
DC 07
Solving DEs using Laplace
Recall:
()
0+ ;
2 ()
2 0 + (0+) ;
2
(Method 1)
We can represent differential equations in the
time-domain as polynomial expressions in the
s-domain.
Example:
U

EEE 35 Signals and Systems
Due: March 3, 2014, 7AM
2nd Semester 2013-2014
WORK INDEPENDENTLY!
Problem Set 3
Set 1
1. Shown below is a basic multiplier block commonly used for digital communication systems.

Laplace Transforms
Practice Session
PROBLEM 1. Find the Laplace Transform of the
following signal: i.) using definition
ii.) using properties
a) A causal signal,
= 5
b) =
+ 3
2
4
| |
c) = 3 ()
d) = , where is any real number
e) = 2
f)
=
( + 2)
(
)
(

Inverse Laplace Transform
EEE 35: DC 2.2 Practice Session
Signals and Systems
2S 2013 2014
DC 2.2: Inverse Laplace Transform
EEE 35: Signals and Systems
1
Reference
Chapter 09, Signals and Systems 2nd ed. by Alan V.
Oppenheim, Alan S. Willsky and S. Hami

Pole Zero Diagram
Bode Plots
DC 08
Example 1
Draw the Pole-Zero Diagram for the given
system functions.
a. H1(s) =
s2 + s 6
2s2 + 7s + 5
b. H2(s) =
s2 + 2s + 2
2s3 - 3s2 + 2s 3
Solution 1a
(s + 3)(s 2)
(2s + 5)(s + 1)
j
j2
j1
OX
X
-3 -2 -1
-j1
-j2
1
O
2

EEE 35 Signals and Systems
Due: March 22, 2014, 7AM
2nd Semester 2013-2014
WORK INDEPENDENTLY!
Problem Set 4
Set 1
Consider the sequence x(n) = 2nu(n).
a. Is x(n) absolutely summable?
b. Does the Fouri