EECS 216
SOLUTIONS TO PROBLEM SET #7
Winter 2008
1.
#4.25:
10 sketches of spectra. See next page.
2.
#4.27:
2a. The ﬁlter clips oﬀ the lower half of the modulated
M
(
ω
), leaving a right triangle.
This is called
single sideband
(SSB), since only half the spectrum is transmitted.
BUT: Note that all the information in the signal is still present (negative freqs).
ADVANTAGES: Half the bandwidth, half the power, half the noise. The problem is:
2b.
h
(
t
) =
sin(
ω
0
+
ω
f
)
t
πt

sin(
ω
0
t
)
πt
is noncausal impulse response, so it is nonrealizable.
In fact, this ﬁlter must be
very
sharp, since
ω
0
>> ω
f
. How many dB/decade needed?
So is SSB only of theoretical interest? No–there’s more than one way to do this:
3.
#4.21:
See lecture notes or #4.28 to see how to use Hilbert transforms for SSB.
3a.
H
(
ω
) =
R
e

jωt
πt
dt
=
R
cos(
ωt
)
πt
dt

j
R
sin(
ωt
)
πt
dt
(Fourier cosine and sine transforms).
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 Yagle
 Singlesideband modulation, Hilbert, positive frequencies

Click to edit the document details