Digital Signal Processing Reference
In-Depth Information
By integrating (8.14) over the length of the blade
L
, the total baseband
signal becomes the following [6]:
s
L
(
t
)=
L
0
exp
H
j
4
l
l
cos
b
sin(
V
t
+
u
0
)
J
dl
(8.15)
=L
exp
H
j
4
l
u
0
)
J
sinc
H
4
l
u
0
)
J
L
2
cos
b
sin(
V
t
+
L
2
cos
b
sin(
V
t
+
For a rotor with
N
blades, there will be
N
different initial rotation
angles
u
k
=
u
0
+
k
2
p
/
N
,(
k
=0,1,2,...
N
-
1)
(8.16)
and the total received signal becomes
s
S
(
t
)=
N
-
1
k=
0
s
Lk
(
t
)
(8.17)
L
sinc
H
4
l
+
k
2
p
/
N
)
J
exp{
j
F
k
(
t
)}
=
N
-
1
k=
0
L
2
cos
b
sin(
V
t
+
u
0
where
F
k
(
t
)=
4
p
L
2
cos
b
sin(
V
t
+
u
0
+
k
2
p
/
N
)
k
=0,1,2,...
N
-
1)
l
(8.18)
8.2.3
Time-Domain Signatures of Rotation-Induced Modulations
Rotor blades in a helicopter are in rotational motion that will impart a
periodic modulation on radar returned signals as shown in (8.17). The
rotation-induced Doppler shifts relative to the Doppler shift of the fuselage
(or body) occupy unique locations in the frequency domain. The modulation
in the frequency domain as well as the time-domain signal have been used
as radar signatures for target identification [8, 9].
The time-domain signature of rotor blades is defined by the magnitude
in (8.17)
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