ECE 310 Discrete and Continuous Signals and Systems ...vahe/summer2012/ece310/q5.pdf · ECE 310...
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ECE 310 Discrete and Continuous Signals and Systems
Quiz #5University of Illinois at Chicago
Summer 2012
Name (print): UIN:
1. (2 points) Given x(t) as shown in the figure below, find its Fourier transform X(ω).Hint: Consider decomposing x(t) into two simpler functions x1(t) and x2(t).
t
x(t)
0 1
1
2
2 3−1−2−3
Dr. Vahe Caliskan 1 of 5 Handed out: July 18, 2012
ECE 310 Discrete and Continuous Signals and Systems
Quiz #5University of Illinois at Chicago
Summer 2012
2. (2 points) Given x(t) = u(t)− u(−t), find its Fourier transform X(ω).Hint: Consider sketching x(t) first.
Dr. Vahe Caliskan 2 of 5 Handed out: July 18, 2012
ECE 310 Discrete and Continuous Signals and Systems
Quiz #5University of Illinois at Chicago
Summer 2012
3. (3 points) Given the Fourier transform X(ω) as shown below, find x(t). Also determine x(0).
233
4 8−4−8
X(ω)
ω
Dr. Vahe Caliskan 3 of 5 Handed out: July 18, 2012
ECE 310 Discrete and Continuous Signals and Systems
Quiz #5University of Illinois at Chicago
Summer 2012
4. (2 points) Given that x(t) = rect
(
t+ 1.5
2
)
rect
(
t− 1.5
2
)
, find X(ω).
Hint: Consider sketching x(t) first.
Dr. Vahe Caliskan 4 of 5 Handed out: July 18, 2012
ECE 310 Discrete and Continuous Signals and Systems
Quiz #5University of Illinois at Chicago
Summer 2012
5. (1 point) Given x(t) shown below, find X(0).
2
2
31
1
4−2−4 −1−3
x(t)
t
Dr. Vahe Caliskan 5 of 5 Handed out: July 18, 2012
