Digital Signal Processing Reference
In-Depth Information
Further Reading
Of course there are a good number of books on communications, which
cover the material necessary for analyzing and designing a communica-
tion system like the modem studied in this Chapter. A classic topic pro-
viding both insight and tools is J. M. Wozencraff and I. M. Jacobs's
Prin-
ciples of Communication Engineering
(Waveland Press, 1990); despite its
age, it is still relevant. More recent topics include
Digital Communications
(McGraw Hill, 2000) by J. G. Proakis;
Digital Communications: Fundamen-
tals and Applications
(Prentice Hall, 2001) by B. Sklar, and
Digital Commu-
nication
(Kluwer, 2004) by E. A. Lee and D. G. Messerschmitt.
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Exercises
Exercise 12.1: Raised cosine.
Why is the raised cosine an ideal filter?
What type of linear phase FIR would you use for its approximation?
Exercise 12.2: Digital resampling.
Usetheprogrammabledigitalde-
lay of Section 12.4.2 to design an
exact
sampling rate converter from CD to
DVD audio (Sect. 11.3). Howmany different filters
h
τ
[
are needed in total?
Does this number depend on the length of the local interpolator?
n
]
Exercise 12.3: A quick design.
Assume the specifications for a given
telephone line are
f
min
3600 Hz, and a SNR of at least
28 dB. Design a set of operational parameters for a modem transmitting on
this line (baud rate, carrier frequency, constallation size). How many bits
per second can you transmit?
=
300 Hz,
f
max
=
Exercise 12.4: The shape of a constellation.
One of the reasons for
designing non-regular constellations, or constellation on lattices, different
than the upright square grid, is that the energy of the transmitted signal is di-
rectly proportional to the parameter
σ
2
α
as in (12.10). By arranging the same
number of alphabet symbols in a different manner, we can sometimes re-
duce
2
α
and therefore use a larger amplification gain while keeping the total
output power constant, which in turn lowers the probability of error. Con-
sider the two 8-point constellations in the Figure 12.12 and Figure 12.13 and
compute their intrinsic power
σ
2
α
σ
for uniform symbol distributions. What
do you notice?
