SYSC3501 Communication Theory
Assignment #3
Due: 4:00pm Wednesday March 15
th
2011
Question 1
Suppose a signal m(t) (shown in the figure below) is transmitted using frequency
modulation.
(a)
Write the expression of f
i
(t), the instantaneous frequency, in terms of m(t) for
modulated signal, where
() ( )
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
=
∫
∞
−
t
c
d
m
k
t
f
A
t
s
λ
π
2
2
cos
, with f
c
=100Hz, A = 2 and k
= 3.
(b)
Sketch f
i
(t),
θ
(t), the phase deviation, and the modulated signal s(t). Provide
appropriate labels on the sketch x and yaxes.
(c)
What is the maximum frequency deviation and maximum phase deviation for this FM
signal?
Question 2
Let
()
)
t
40
(
Sa
40
t
w
=
.
(a) Find the Fourier transform
( )
f
W
and sketch
( )
f
W
.
(b)
If
()
t
w
is sampled with a sampling frequency of
Hz
75
f
s
=
(we assume ideal
sampling, i.e. the sampling waveform is a unitweight impulse train), plot the magnitude
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 Spring '11
 fewrf
 Digital Signal Processing, Signal Processing, PAM signal, original analog signal

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