Errata for
Principles of Signal Detection and
Parameter EstimationChapter 1
1. On page 1, lines 12 and 13, the hyphenated word theses should be replaced by these(no s, no hyphenation).2. On page 4, line 3, replace give by given.3. On page 4, line 9, a period is missing after observations.
Chapter 2
1. On page 18, line 11, replace
Y
1
by
Y
1
.2. On page 29, line 1 just below Fig. 2.1, replace SouthWest by SouthEast.3. On page 35, equation (2.67) should be
P
D
=
...
. The change replaces
P
F
by
P
D
.4. On page 53, the summation on the last line of equation (2.130) should be
M
−
1
i
=0
(sumwith respect to
i
instead of
j
).
Chapter 3
1. On page 81, 5 lines from the bottom, a closing parenthesis is missing in min(
I
0
(
γ
)
,I
1
(
γ
)).2. On page 93, equation (3.77) should be
δ
B
n
(
y
1
,...,
y
n
) =
1 for
L
n
(
y
1
,...,
y
n
)
≥
B
0 for
L
n
(
y
1
,...,
y
n
)
≤
A,
i.e., exchange
A
and
B
on the right hand side of the equation.
Chapter 4
1. On page 119, line 2 should be:
C
(
x
,
ˆ
x
) =

x
−
ˆ
x

1
,
i.e., a hat is missing on top of the second
x
on the right hand side of the equation.1
2. On page 119, equation (4.25), integrations should be over
dx
i
, not
d
y
.3. On page 120, in the equation 8 lines from the bottom, the second equality should be
···
=
m
X
+
K
XY
K
−
1
Y
(
Y
−
m
Y
)The change is that the minus sign after
m
X
should be replaced by a plus sign.4. In the equation appearing on the second line of p. 129, replace (
Y
−
m
y
)
T
by (
Y
−
m
Y
)
T
, i.e. the
Y
subscript of
m
should be in capital bold font instead of lower casebold font.5. Equation (4.77) on p. 131 should be
G
=
K
LLS
H
T
R
−
1
,
i.e.,
R
should be replaced by
R
−
1
.6. On page 135, Case 3, a closing parenthesis is missing on the right hand side of theﬁrst line of the ﬁrst equation, which should be
L
(
y
,m,v
)
△
= ln(
f
Y
(
y

m,v
))7. On page 137, 5 lines from the bottom, the equation should be
b
(
S
,
x
) = exp(
x
T
S
−
t
(
x
))The change is that
v
(
x
) should be replaced by
t
(
x
) to maintain consistency with theexponential canonical form (4.80).8. On line 6 of page 139, replace ”where
O
T
...” by ”where
0
T
...” The change consists of replacing a bold face capital O by a bold face capital zero.9. On page 143, in the equation 10 lines from the bottom, a hat is missing on top of
θ
ML
, which should be replaced by ˆ
θ
ML
.10. On the last line of page 150, replace ”... at the most ...” by ”... at most ...” i.e., delete”the”.
Chapter 5
1. On page 177, on the right hand side of equation (5.21), replace
A
by
A
, i.e. the
A
should be capital italic, not capital calligraphic.2. On page 187, in the equations on line 3 and on line 7, the product should be from
k
= 1 to
N
−
2 (instead of
N
−
1).3. On page 192, the right hand side of the ﬁrst line of equation (5.56) should be
P
[
R
≥
η

A
] and on the second line , the integral should be
∞
η
, i.e. the limits of integrationshould be
η
and
∞
.2
Chapter 7
1. On page 304, equation (7.76), the element in the third row and second column of matrix
C
(
t
) should be
K
(
t
+ 1
,t
) (a ”1” is missing).2. On page 318, on the fourth line of Problem 7.4, replace ”... and since
X
(0) =
−
X
(
T
),...” by ”... and since
K
(0) =
−
K
(
T
),...”
Chapter 9
1. On page 411, equation (9.204) should be:
h
(
t,ω
0
) =
ℜ{
˜
s
∗
(
T
−
t
)exp(
j
(
ω
c
+
ω
0
)
t
)
}
=
c
(
T
−
t
)cos((
ω
c
+
ω
0
)
t
−
ψ
(
T
−
t
))
.
The changes consist of inserting a closing bracket
}
at the end of the ﬁrst line, andreplacing
c
(
t
−
t
) by
c
(
T
−
t
) after the equality sign on the second line.2 On page 413, the ﬁrst line of equation (9.208) should be
<
˜
s
1
,
˜
s
2
>
=
∞−∞
˜
s
(
t
−
d
1
)˜
s
∗
(
t
−
d
2
)exp(
j
(
ω
1
−
ω
2
)
t
)
dt
The change consists of inserting
dt
at the end of the equation.3. On page 424, the ﬁrst sentence of Problem 9.5 should be:Consider the CT version of Problem 5.9.4. On page 424, 10th line of Problem 9.5, replace ”intefering” by ”interfering” (an ’r’ ismissing).
Chapter 11
1. On page 503, the ﬁrst line of equation (11.84) should be:
Q
(
θ
,
θ
k
) =
−
12tr
Q
−
1
Φ
k
−
AΨ
k
−
Ψ
T k
A
T
+
AΘ
k
A
T
The change consists of replacing
Ω
k
by
Θ
k
in the last term of this equation.2. On page 505, replace lines 15 and 16 by:Then by taking the conditional expectation with respect to
Y
on both sides of (11.93)and using the repeated conditioning identity (11.90), ...The change consists of inserting ”conditional” in front of expectation on line 15, andreplacing (11.89) by (11.90) on line 16.3
3. On page 508, the ﬁrst subequation of equation (11.108) should beˆ
X
k
(
t
) =
a
sk
(
t
) ˆ
X
k
(
t
+ 1) +
P
ck
(
t
) ˆ
X
fk
(
t
)
/P
fk
(
t
)The change consists of exchanging
P
ck
(
t
) and
P
fk
(
t
) in the last term of the equation.4. On page 509, line 8,
ψ
k
is deﬁned as
ψ
k
=
T
t
=1
ˆ
X
k
(
t
) ˆ
X
k
(
t
−
1) +
P
k
(
t,t
−
1)A subscript
k
was omitted in ˆ
X
(
t
−
1).5. On page 512, the left hand side of equation (11.115) should be2ln
L
G
(
Y
) =
···
The Latex source code for this equation contained a minor error.6. On page 516, line 3 of Problem 11.1 should be:
H
1
:
Y
(
t
) =
Z
(
t
) +
V
(
t
)In other words, replace
H
0
by
H
1
.7. On page 518, the equation on the second line from the bottom should be
q
= (1
−
a
2
)
P .
8. In the ﬁrst line of page 521, replace 1
< ℓ < N/
2 by 1
≤
ℓ < N/
2.9. On page 521, the equation appearing on the 6th line from the bottom should be
m
kℓ
=
P
kℓ
v
[ˆ
Y
1
(
e
jω
ℓ
) +
A
k
e
jω
ℓ
D
k
ˆ
Y
2
(
e
jω
ℓ
)]Compared to the srcinal equation, this requires replacing the opening parenthesis (on the right hand side of the equation by a square bracket [, inserting a hat on top of
Y
2
, and inserting a closing bracket ].
Chapter 12
1. The left hand side of equation (12.174) on page 577 should be
L
k
=0
h
k
D
(
t
−
k
) =
···
Instead of starting from
k
= 1, the summation should start from
k
= 0.4