1. Name: UIN:
Texas A&M University, College Station
Electrical Engineering/Computer Engineering
ECEN 314, Spring 2011
Wednesday, February 2, 2011
Quiz #1
Dr. Deepa Kundur
Duration: 20 minutes
• All work must be performed within the space provided. You may use the back of sheets if
necessary.
• No aids such as calculators or cheat sheets allowed.
• Answer all questions.
• If a particular question seems unclear, please explicitly state any reasonable assumptions and
proceed with the problem.
• Please properly label all points of interest on sketches and graphs that you are requested to
draw.
• For full points, show all steps and present results clearly.
Question Earned Grade
1
/10
2
/10
Total
/20
1

2. 1. Find the even and odd components of the following signal:
x(t) = t2
sin3
(5t)
Note: Double and triple check your work to avoid “silly” mistakes.
Solution:
xe(t) =
x(t) + x(−t)
2
=
t2 sin3
(5t) + (−t)2 sin3
(5(−t))
2
=
t2 sin3
(5t) + t2 sin3
(−5t)
2
=
t2 sin3
(5t) + t2(−1)3 sin3
(5t)
2
=
t2 sin3
(5t) − t2 sin3
(5t)
2
= 0
xo(t) =
x(t) − x(−t)
2
=
t2 sin3
(5t) − (−t)2 sin3
(5(−t))
2
=
t2 sin3
(5t) − t2 sin3
(−5t)
2
=
t2 sin3
(5t) − t2(−1)3 sin3
(5t)
2
=
t2 sin3
(5t) + t2 sin3
(5t)
2
= t2
sin3
(5t)
2

3. 2. Consider the following signal:
t
x(t)
A
-A
-T1
T1
Figure 1: Signal of interest in Question 2. You must find the total energy, the time-averaged power
and classify the signal either has an energy signal or a power signal.
(a) (4 points) What is the total energy of the signal in Fig. 1?
(b) (4 points) What is the time-averaged power of the signal in Fig. 1?
(c) (2 points) Categorize the signal of Fig. 1 as an energy signal or a power signal?
Solution:
(a) The total energy is given by
E =
∞
−∞
x2
(t)dt
= area under the rectangular signal x2(t)
= A2
(2T1) = 2A2
T1
(b) The time-averaged power is given by
P = lim
T→∞
1
T
∞
−∞
x2
(t)dt
= lim
T→∞
1
T
area under the rectangular signal x2(t)
= lim
T→∞
1
T
A2
(2T1) = lim
T→∞
1
T
2A2
T1 = 0
(c) Since 0 < E < ∞ for an energy signal and 0 < P < ∞ for a power signal, x(t) is an
energy signal.
3