MAE143 A  Signals and Systems  Winter 11
Final
Instructions
(i) This exam is open book. You may use whatever written materials you choose, including
your class notes and textbook. You may use a hand calculator with no communication
capabilities
(ii) You have 3 hours
(iii) Do not forget to write your name, student number, and instructor
1.
Filtering and sampling.
The continuoustime signal
x
(
t
) = 100 sinc
2
(100
t
)
goes through an
ADC block that samples signals at a frequency
f
s
= 190
Hz. Answer the following questions
(a) (1 point) Compute the Fourier transform of
x
(
t
)
. What is its bandwidth?
(b) (1 point) Would you be able to reconstruct the original signal out of the samples taken by
the ADC block? Why?
(c) (2 points) Consider a system whose impulse response is given by
h
(
t
) = 150 sinc(150
t
)
What kind of filter is this? What is its cutoff frequency in Hz? Plot the magnitude and
phase of the transfer function.
(d) Suppose the signal
x
(
t
)
passes first through the system in (c) to produce the signal
y
(
t
)
and then goes through the ADC block to produce the samples, see Figure 1.
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 Summer '08
 MIROSLAVKRSTIC
 Fourier Series, Signal Processing, LTI system theory, ADC block

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