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ENEE 630 Fall 2009 Homework #8
Due on Monday, 7
th
December
Problem 1
In a
normalized
lattice predictor, the forward and backward prediction errors at the
various stage of the predictor are all normalized to have
unit variance
. Such an operation
makes it possible to utilize the full dynamic range of multipliers used in the predictor, the
normalized forward and backward prediction errors are deﬁned as follows, respectively:
f
m
(
n
) =
f
m
(
n
)
P
1
/
2
m
b
m
(
n
) =
b
m
(
n
)
P
1
/
2
m
where
P
m
is the average power (or variance) of the forward prediction error
f
m
(
n
) or
that of the backward prediction error
b
m
(
n
). Show that the structure of stage
m
of the
normalized lattice predictor is as shown in Figure 1 for realvalued data.
Cos w
m
+
+
m
Csc w
m
Csc w
z
1
f
(n)
m1
w
= Cos
(
)
m
m
1
b
(n)
m
f
(n)
m
b
(n)
m1
Cos w
m
Figure 1: P1
Problem 2
Consider the problem of optimizing stage
m
of the lattice predictor. The cost
function to be used in the optimization is described by
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This note was uploaded on 10/31/2010 for the course EE 630 taught by Professor Wu during the Spring '10 term at Aarhus Universitet, Aarhus.
 Spring '10
 wu

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