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
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 st
ECSE 306F14
Fundamentals of Signals and Systems:
E. Discrete-Time Fourier Series and Fourier Transform
Ch 12: Discrete-Time Fourier Series and Fourier Transform (Boulet)
TOPICS:
Fourier Series Repres
ECSE 306F14
Fundamentals of Signals and Systems:
F. z-Transform
Ch 13: The z-Transform (Boulet)
TOPICS:
Development of the Two-Sided z-Transform
ROC of the z-Transform
Properties of the Two-Sided z
ECSE 306F14
Fundamentals of Signals and Systems:
G. Time and Frequency Analysis of Discrete-Time LTI Systems
Ch 14: Time and Frequency Analysis of Discrete-Time Signals and Systems (Boulet)
TOPICS:
Ge
ECSE 306F14
Fundamentals of Signals and Systems:
B. Linear Time-Invariant Systems
Ch 2: Linear Time-Invariant Systems (Boulet)
TOPICS:
Discrete-Time LTI Systems: The Convolution Sum
Continuous-Time LT
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 Combination
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
4.2. THE DISCRETE-TIME FOURIER
TRANSFORM
To see this sampling eect, consider a nite-duration
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
ot
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,
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
FALL
2014
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 1
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
ASS
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 4 (Due: Tuesday,
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
FALL
2014
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 5 (D
FALL
2014
Department of Electrical & Computer Engineering
McConnell Engineering Building
3480 University, Montral, Qubec, H3A 0E9
ECSE306: FUNDAMENTALS OF SIGNALS AND SYSTEMS
ASSIGNMENT 3 (Du
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