Bantu) 0'11 Ridw/
McGill University Winter 2008
MIDTERM EXAMINATION 2
Thursday, March 27, 2008
Time: 17:30 — 19:00
Instructions: 1. This is a closed book, closed notes exam.
2. Only faculty calculators are allowed.
3. Attempt all three (3) problems.
4. Ea
ECSE 306F14
Fundamentals of Signals and Systems:
D. Laplace Transform and CT LTI Systems
References:
Ch 6: The Laplace Transform (Boulet)
Ch 7: Application of the Laplace Transform to LTI Differential Systems (Boulet)
Ch 8: Time and Frequency Analysis of
17
1.2.3
The DiscreteTime Unit Impulse and Unit Step Sequences
Unit impulse sequence (or unit impulse or unit sample)
1,
0,
[n] =
n=0
n=0
(also referred to as Kronecker delta function)
[n]
0
n
Unit step sequence (unit step)
1,
0,
u[n] =
n0
n<0
u[n]
0
Lamp
ECSE 306F14
Fundamentals of Signals and Systems:
E. DiscreteTime Fourier Series and Fourier Transform
Ch 12: DiscreteTime Fourier Series and Fourier Transform (Boulet)
TOPICS:
Fourier Series Representation of DiscreteTime Periodic Signals
Properties
ECSE 306F14
Fundamentals of Signals and Systems:
F. zTransform
Ch 13: The zTransform (Boulet)
TOPICS:
Development of the TwoSided zTransform
ROC of the zTransform
Properties of the TwoSided zTransform
The Inverse zTransform
Analysis and Chara
ECSE 306F14
Fundamentals of Signals and Systems:
G. Time and Frequency Analysis of DiscreteTime LTI Systems
Ch 14: Time and Frequency Analysis of DiscreteTime Signals and Systems (Boulet)
TOPICS:
Geometric Evaluation of the DTFT from the PoleZero Plot
ECSE 306F14
Fundamentals of Signals and Systems:
B. Linear TimeInvariant Systems
Ch 2: Linear TimeInvariant Systems (Boulet)
TOPICS:
DiscreteTime LTI Systems: The Convolution Sum
ContinuousTime LTI Systems: The Convolution Integral
Properties of Linea
ECSE 306F14
Fundamentals of Signals and Systems:
C1. Fourier Series Representation of Periodic CT Signals
Ch 4: Fourier Series Representation of Periodic CT Signals (Boulet)
TOPICS:
Linear Combinations of Harmonically Related Complex Exponentials
Determin
Part 7: THE LAPLACE and Z
TRANSFORMS
If Recfw_s > a
+
X1 (s)
7.1. THE LAPLACE TRANSFORM
=
e
e
=
1 (s+a)t
e
s+a
0
=
1
s+a
0
X2 (s)
Let x(t) be a signal, then
=
est (eat )dt
+
x(t)e
e(s+a)t dt
If Recfw_s a
The Laplace transform is the sister transform of t
4.2. THE DISCRETETIME FOURIER
TRANSFORM
To see this sampling eect, consider a niteduration
sequence x[n] and construct a periodic signal x[n], for
which x[n] is one period
x[n] 0 n N 1
x[n] =
0
otherwise
DiscreteTime Fourier Transform
The FT of an di
ECE 301 Signals and Systems
Solution to Assignment 2
September 7, 2006
1
ECE 301 Solution to Homework Assignment 2
1. Indicate whether the following systems are causal, invertible, linear, memoryless, and/or time invariant by circling the correct options.
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
FALL
2014
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 1 (Due: September 25, 2014)
1) For each of the fol
1. Show that
FALL
2014
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 2 (Due: October 2, 2014)

2. Show that if a
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 4 (Due: Tuesday, November 18, 2014)
1. Determine the discrete Fouri
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
FALL
2014
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 5 (Due: Friday, November 28, 2014)
1. Find the ztransfor
FALL
2014
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 3 (Due: due Friday, October 31, 2014)
1. Sketch
 
1
2 a
FALL
2014
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
(3 credits, (324), Prerequisite: ECSE 210 and MATH 270 or MATH 271)
Cl