EECE 340 Homework, Fall 2007
American University of Beirut · Signals and Systems · 3 pages
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American University of Beirut
Department of Electrical and Computer Engineering
EECE 440 Signals and Systems
Homework 1: Due February 26, 2007 at 12:00
Problem 1
Determine if each of the following signals is an energy signal or a power signal by
deriving the energy or the time averaged power of the signal:
a) x(t) = A[u(t+2a) – u(t-4a)]
a > 0;
b) x(t) = sin(wt)
Problem 2
Determine if the following systems are:
1. Memoryless
2. Time-invariant
3. Linear
4. Causal
5. Stable
Justify your answers.
a.
2)
x t(
)1
x t(
1
x )t(
y )t(
−
−
−
−
=
b.
x )t(
e
)t(
y
= −kt
with k>0.
Problem 3
Check whether or not the following signals are periodic. Determine the fundamental
periods T for the periodic ones.
a) ( )
3cos(2
)sin(8
)
x t
t
t
π
π
=
b) ( )
cos(5
)
sin(3
)
x t
t
t
π
π
=
+
c) ( )
t
x t
= e−
Problem 4
Compute and Graph the derivatives of the following functions:
a)
b)
Problem 5
Evaluate the following integrals:
a)
cos(
t) ( )
e
t dt
π δ
+∞
−∞∫
b)
cos(
)
5
(
2)
t
e
t
dt
π δ
+∞
−
∫
t
x(t)
A
4a
t
x(t)
A
-2a
4a
Matlab
Problem 1
Sketch the following functions using Matlab:
a)
[
]
1( )
4sin(3
)
( )
(
6)
x t
t
u t
u t
π
=
−
−
b)
2( )
(
5) (
5)
2(
2) (
2)
4(
5) (
5)
x t
t
u t
t
u t
t
u t
= −
+
+
−
−
−
+
−
−
Problem 2
Sketch on the same figure, the following functions using Matlab:
a)
1( )
4sin(3
)
x t
πt
=
b)
2( )
2cos(5
)
x t
πt
=
c)
1
2
( )
( )
( )
y t
x t
x t
=
+
Determine the period of y(t).