Graphics Programs Reference
In-Depth Information
f
r
2πσ
t
2
C
i
C
o
CA
==
------
------------
(7.47)
It follows that the improvement factor for a single canceler is
f
r
2πσ
t
S
o
S
i
2
------------
-----
I
=
(7.48)
The power gain ratio for a single canceler is (remember that
H
()
is periodic
with period
f
r
)
f
r
⁄
∫
2
S
o
S
i
1
f
r
π
f
f
r
2
H
()
2
---
-----
=
=
4
sin
-----
d
f
(7.49)
f
r
⁄
2
)
2
Using the trigonometric identity
(
22 2ϑ
cos
)
=
4
(
sin
ϑ
yields
f
r
⁄
∫
2
1
f
r
2π
f
f
r
d
H
()
2
=
---
22
cos
--------
=
2
(7.50)
f
r
⁄
2
It follows that
f
r
2πσ
t
2
------------
I
=
2
(7.51)
The expression given in Eq. (7.51) is an approximation valid only for
. When the condition is not true, then the autocorrelation func-
tion needs to be used in order to develop an exact expression for the improve-
ment factor.
σ
t
«
f
r
σ
t
«
f
r
Example:
A certain radar has
f
r
=
800
Hz
. If the clutter rms is
σ
v
=
6.4
Hz
(wooded
hills with
σ
w
=
1.16311
Km
⁄
hr
), find the improvement factor when a single
delay line canceler is used.
Solution:
In this case
σ
t
=
σ
v
. It follows that the clutter attenuation CA is
f
r
2πσ
t
2
2
800
2()6.4
------------
------------------------
CA
=
=
=
395.771
=
25.974
dB
(
)
and since
S
o
⁄
S
i
==
2
dB
we get
.
I
dB
=
(
CA
+
S
o
⁄
S
i
)
dB
=
3
+
25.97
=
28.974
dB
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