Signals and Systems
Sharif University of Technology
Dr. Ali Soltani Farani
April 23, 2013
CE 40-242
Date Due: Ordibehesht 30, 1392
Homework 7(Chapters 9&10)
Problems:
1. Determine the Laplace transforms (including the regions of convergence) of each of th
Lecture 2 (Chapter 1)
Signals & Systems
Systems
Adapted from: Lecture notes from MIT
from: Lecture notes from MIT
Ali Soltani-Farani
Spring 2012
Lecture 2 (Chapter 1)
Review on Bases of Vector Spaces
2
Sharif University of Technology, Department of Comput
1
Sharif University of technology
Department of Electrical Engineering
Spring 2015
Signals & Systems
Due Date:
26 te:
26
EE 25742-2
HW #2
x 5
.
%80
80
.
x .
x
1
Sharif University of technology
Department of Electrical Engineering
Spring 2015
Signals & Systems
Due Date: 13/02/94
EE 25742-2
HW # 10
)
. (
.
.
.
.
Lecture 5 (Chapter 3)
Signals & Systems
Systems
Fourier Series (Part I)
Adapted from: Lecture notes from MIT
MIT
Ali Soltani-Farani
Spring 2012
Lecture 5 (Chapter 3)
Transformation
General form:
x(t ) =
a (t )
i
i
i =
Basis Function
Coefficient
2
Sharif
Lecture 7 (Chapter 3)
Signals & Systems
Systems
Fourier Response and Filtering
Adapted from: Lecture notes from MIT
MIT
Ali Soltani-Farani
Spring 2012
Lecture 7 (Chapter 3)
The Eigenfunction Property of Complex Exponentials
CT:
e
st
CT
"System Function"
D
Lecture 6 (Chapter 3)
Signals & Systems
Systems
Fourier Series (Part II)
Adapted from: Lecture notes from MIT
MIT
Ali Soltani-Farani
Spring 2012
Lecture 6 (Chapter 3)
CT Fourier Series Pairs
Review
x(t ) =
a e
jk0t
2
0 =
T
k
k =
=
a e
k
k =
1
jk0t
ak =
Signals and Systems
Sharif University of Technology
Ali Soltani Farani
April 19, 2013
CE 40-242
Date Due: Ordibehesht 16, 1392
Homework 6 (Chapter 7)
Problems
1. (a) Consider the system as shown in below:
And let H () and X ( ) be as given in below:
Sketc
Signals and Systems
Sharif University of Technology
Ali Soltani Farani
April 11, 2013
CE 40-242
Date Due: Ordibehesh 2nd, 1392
Homework 5
(Chapter 5)
Problems
1. Compute the Fourier transform of the following signals.
x[n] =
ej 5 n sin( 25 n)
n
x[n] = u
Signals and Systems
Sharif University of Technology
Ali Soltani-Farani
March 3, 2013
CE 40-242
Date Due: Esfand 27, 1391
Homework 4 (Chapter 4)
Problems
1. Compute the Fourier transform of each of the following signals:
a. x(t) = e4|t| cos(5t)
1, t 1
2
2
Signals and Systems
Sharif University of Technology
Dr.Ali Soltani Farani
February 24, 2013
CE 40-242
Date Due: Esfand 13th , 1391
Homework 3 (Chapter 3)
Problems
1. Determine the Fourier series coecients for the following signal:
5
x(t) = 2 + 4cos(w0 t)
Lecture 16
Signals & Systems
Introduction to Compressed Sensing
Adapted from:
M. Davenport, M. F. Duarte, Y. C. Eldar, G. Kutyniok, Introduction to Compressed Sensing, 2011
J. Romberg, Imaging via Compressive Sampling, IEEE Signal Processing Magazine, 200
Lecture 14 (Chapter 9)
Signals & Systems
Laplace Transforms
Signals and Systems
Adapted from: Lecture notes from MIT
Ali Soltani-Farani
Spring 2012
2012
Lecture 14 (Chapter 9)
Motivation for the Laplace Transform
CT Fourier transform enables us to do a l
Lecture 11 (Chapter 6)
Signals & Systems
Time and Frequency Characterization of
Signals and Systems
Adapted from: Lecture notes from MIT and Concordia University
Ali Soltani-Farani
Spring 2012
2012
Lecture
Lecture 11 (Chapter 6)
Magnitude and Phase of FT,
Lecture 10 (Chapter 5)
Signals & Systems
The Discrete-Time Fourier Transform
Adapted from: Lecture notes from MIT, Purdue, Binghamton University, University of Rochester ,
University of Saskatchewan Sonoma State University
University of Saskatchewan, Sono
Lecture
Lecture 8 (Chapter 4)
Signals & Systems
The Continuous-Time Fourier Transform
Adapted from: Lecture notes from MIT
Ali Soltani-Farani
Spring 2012
Lecture 8 (Chapter 4)
Content
Derivation of tthe CT Fourier Transform pair
of he CT Fourier Transfor