Graphics Programs Reference
In-Depth Information
When coherency is maintained between the consecutive pulses, then an expres-
sion for the normalized train is
N
∑
1
1
N
--------
s
()
=
s
1
(
tiT
)
(4.24)
i
=
0
The output of the matched filter is
∞
∫
)
e
j
2π
f
d
t
s
()
s
∗
t
χτ
f
d
(
;
)
=
(
+
τ
d
(4.25)
∞
Substituting Eq. (4.24) into Eq. (4.25) and interchanging the summations and
integration yield
N
∑
1
N
∑
1
∞
∫
1
----
)
e
j
2π
f
d
t
)
s
1
∗
tjT
τ
χτ
f
d
(
;
)
=
s
1
(
tiT
(
d
(4.26)
i
=
0
j
=
0
∞
Making the change of variable
t
1
=
tiT
yields
N
∑
1
N
∑
1
∞
∫
1
----
e
j
2π
f
d
iT
)
e
j
2π
f
d
t
1
t
()
s
1
∗
t
1
χτ
f
d
(
;
)
=
s
1
(
[
τ
(
ij
)
T
]
d
t
1
(4.27)
i
=
0
j
=
0
∞
The integral inside Eq. (4.27) represents the output of the matched filter for a
single pulse, and is denoted by
χ
1
. It follows that
N
∑
1
N
∑
1
1
----
e
j
2π
f
d
iT
χτ
f
d
(
;
)
=
χ
1
[
τ
(
ij
)
T
;
f
d
]
(4.28)
i
=
0
j
=
0
is used, then the following relation is true:
1
When the relation
qi
=
j
N
∑
N
∑
0
∑
N
∑
1
q
N
∑
1
N
∑
1
q
=
+
(4.29)
i
=
0
m
=
0
q
=
(
N
1
)
i
=
0
q
=
1
j
=
0
for j
=
i
q
for i
=
j
+
q
Using Eq. (4.29) into Eq. (4.28) gives
1. Rihaczek, A. W.,
Principles of High Resolution Radar
, Artech House, 1994.
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