EE 301  Signals & Systems
Homework #2
Due: October 30, 2008
Problem 1
Using the given inputoutput relations where x and y denote the input and output of the
system respectively, determine with full justification, whether each of the following systems
is
EE 301  Signals & Systems
Homework #9
December 14, 2006
Due: December 21, 2006
Problem 1 (MATLAB)
(a)
(b)
Calculate analytically the DTFT of the rectangular pulse defined by x [ n ] = u[ n] u[ n 11] . Also
create a vector x containing the nonzero samples
EE 301  Signals & Systems I
Homework 4
(Due: October 26, 2006)
October 19, 2006
Problem 1
a ) Determine the impulse response h(t ) of a causal LTI continuoustime system whose inputoutput relationship is described by the differential equation given below
EE 301 Signals & Systems
Homework 3
Due: October 12, 2006
Problem 1
Determine whether each one of the following statements is TRUE or FALSE and fully
justify your answer (i.e., prove if true and disprove or give a counter example if false.
However, if we
Middle East Technical University
Electrical & Electronics Engineering Department
EE301 MATLAB Assignment
Prepared by Umut Orguner
(Please read the notes at the end of the assignment
for information on preparation and submission)
Under the content of the
Middle East Technical University
Department of Electrical and Electronics Engineering
301: Signals and Systems
Fall 2011
Homework 10
Due: January 06, 2012
1. Let X () be the DTFT of the discrete time sequence x[n] where x[n] = n2n , 2 n 2, and x[n] = 0
fo
EE 301 Signals & Systems I
Homework 9
Due: Dec. 29, 2011
1. The discretetime signal [ ] is defined as
[ ]
cfw_
]. Without explicitly
The periodic signal [ ] is obtained as [ ]
[
[ ], determine whether the following are true for
evaluating the DTFS repre
EE 301 Signals & Systems
Homework 8
Due: Nov. 13, 2011
Problem 1
The ztransform of
()
What is
(
is given as ( )
)
(

, and
).
?
Problem 2
Consider a system response
()
. The impulse response can be found through regular
polynomial division.
i.
The divis
EE 301 Signals & Systems
Homework 3
Due: Oct. 25, 2011
Problem 1
()
()
.
Find
ii.
Find
iii.
iv.
Show that if
then
Let the nonzero widths of the signals
and
nonzero duration of their convolution is equal to
v.
for
.
i.
for
Show that
by
.
respectively. Show
EE 301 Signals & Systems
Homework 6
Due: Nov. 29, 2011
Q.1) The magnitude and phase responses of an ideal bandlimited differentiator are given by
the expressions


cfw_


cfw_
a. Plot the magnitude and phase responses and explain why this system is n
MIDDLE EAST TECHNICAL UNIVERSITY
Department of Electrical and Electronics Engineering
EE 301 Signals & Systems
Homework 7
Due: December 6, 2011
1. Find the Laplace transforms of:
a)
d
3e 5(t ) u (t ) ,
dt
b) e
3 t
,
c) te 2t cos(5t ) u(t )
2. A linear, ti
MIDDLE EAST TECHNICAL UNIVERSITY
Electrical and Electronics Engineering Department
EE 301 Signals and Systems I
Homework # 7
DUE : 23 November 2006, Thursday
Q.1. Determine the Fourier transform of the triangular function, shown below, by
(a) multiplying
EE 301 Signals & Systems
Homework 4
Due: Nov. 1, 2011
Problem 1
The impulse response of an LTI system is h(t ) (t ) (t 1) .
i. What is the action of the system for an arbitrary input
? Propose a block diagram
representation for this system.
ii. Evaluate a
MIDDLE EAST TECHNICAL UNIVERSITY
Department of Electrical and Electronics Engineering
EE 301 Signals & Systems
MATLAB Homework 1
Due: Oct. 11, 2011
The purpose of this homework assignment is to introduce you to MATLAB. It is a very popular
numerical softw
MIDDLE EAST TECHNICAL UNIVERSITY
Department of Electrical and Electronics Engineering
EE 301 Signals & Systems
Homework 2
Due: Oct. 18, 2011
Problem 1: The following equalities describe various DT and CT systems where x and y denote the
input and output o
Middle East Technical University
Electrical and Electronics Engineering Department
EE 301 Signals & Systems
Homework 5
Due(*) November 10, 2011
Consider the periodic signal x(t ) with a fundamental period 2 seconds, that is defined
over one period by
sin
Q1. (16 pts) a) a k
1
T0
T0
x p (t )e
jk
2
t
T0
dt
0
1
T0
x(t )e
jk
2
t
T0
dt
1
2
X (k
)
T0
T0
k
(1)
b) Since the overall period is now 2T0, x p (t ) has the coefficients
1
ak
2T0
2T0
0
jk
x p (t )e
2
t
2T0
1
dt
2T0
x(t ) x(t T ) e
jk
2
t
2T0
0
1
MORE MATLAB INSTRUCTIONS
1. Plotting functions
In this section, the basics of plotting functions in MATLAB are described. Throughout we work
with the example of two functions, f (t) = (2t + 1)et sin(t), and g (t) = (t 1)et cos(t).
Step 1, Specify the doma
Fall 20089
EE 301 Signals & Systems
Homework 5
Due: Jan. 16, 2008
1. Consider a real signal x(t ) with a triangular spectrum given below.
c
2 50
a. Draw the spectrum of y (t ) = x(t ) cos(2 1000t ) .
b. What is the minimum sampling rate for y (t ) in ord
EE301 Homework 7
Solutions
1. a)
,
b)
, by using timeshifting and differentiation in time properties.
,
.
c)
,
, by using shifting and differentiation in the sdomain
properties.
2. a) H ( s)
1
1/ 4 1/ 4
, and t he ROC is 2 Recfw_s , so that h(t ) is ri
EE301 Signals & Systems
Homework IV
Answers
Q1. (1p)
i. The system delays its current input by 1 sec. and then subtracts it from the
current input signal.
ii. Unit step response, g ( t ) , is
g ( t ) = u ( t ) u ( t 1)
g ( t ) is plotted in Figure1.
Unit
EE 301 Signals & Systems
Fall 2006
Exercise Problem Set
(Not to be returned)
Problem 1
Determine the Laplace transform and the corresponding ROC for the following
signals:
a. x(t ) = e t cos(2t )u(t ) + e t u(t ) + e t / 2u (t )
b. x(t ) = cos(3t )u ( t )
EE 301 Signals & Systems I
MATLAB Tutorial with Questions
Under the content of the course EE301, this semester, some MATLAB questions will
be assigned in addition to the usual theoretical questions. This MATLAB tutorial has
been prepared to serve as a me
1. (3 points)
Linea
r
Caus
al
Stabl
e
Invertibl
e
Memoryles
s
Yes
TimeInvarian
t
Yes
No
Yes
No
No
Yes
No
Yes
No
Yes
Yes
Yes
No
No
Yes
No
No
Yes
No
No
Yes
Yes
No
Yes
No
No
Yes
No
No
No
Yes
No
Yes
Yes
No
No
No
Yes
Yes
No
Yes
No
Yes
Yes
Yes
No
Yes
2. (6 poin