THE STATE UNIVERSITY OF NEW JERSEY
RUTGERS
College of Engineering
Department of Electrical and Computer Engineering
332:322
Principles of Communications Systems
Spring 2004
Problem Set 7
Haykin section 3.6
Web notes on convexity
Web notes on quantization
1.
Quantization:
Show that a nonuniform quantizer with sufficiently small bin sizes
∆
i
, has
meansquare quantization error of approximately
1
12
∑
i
∆
2
i
p
i
, where
p
i
is the probability that
the input signal amplitude lies within the
i
th interval.
HINT: You may assume that for
∆
i
sufficiently small, you have an approximately uniform
distribution given that
x
lies in the i
th
bin.
SOLUTION:
First we invoke LloydMax. Since we assume the conditional distribution in
any bin is approximately uniform, we must have the associated level q
i
as the midpoint of the
bin. If the bin starts at x
i
1
, it must end at x
i
x
i
1
∆
i
. Then we must have q
i
x
i
1
∆
i
2
(or q
i
x
i
∆
i
2
).
Let’s talk only in terms of the q
i
.
Then we know that the i
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 Spring '08
 Rose
 Probability theory, bin, 1 j, 4 bit, College of Engineering Department of Electrical and Computer Engineering, 1 30 16 j

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