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EE661 Modulation Theory
Spring 2008
Practice Midterm Exam #2
The following problems were taken from previous exams.
They were not given all in the same
year so do not interpret the set of problems as representative of a complete exam, but rather take
each problem as a representative problem.
Problem 1.
(40 points)
(a) For a full response CPFSK modulation format with a modulation index,
,
prove
that the
asymptotic relative power efficiency is bounded by
.
(b) Since
optimizes the above expression, suppose we choose
as our modu
lation index (since it is a simple rational number close to the optimal value).
Prove that for
this case, the upper bound in (a) is tight, that is, for
,
.
Partial Answer:
For part (a) see the soultion to HW7, problem 1.
To prove that the bound is
tight, you simply want to make an argument that any other choice of paths to compare must
lead to at least as great a distance.
Details of the proof will vary.
Problem 2.
(25 points)
An IID sequence of data symbols
are precoded such that
. A PAM sig
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 Spring '08
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