Digital Signal Processing Reference
In-Depth Information
|
s
S
(
t
)
|
=
|
N
-
1
+
k
2
p
/
N
)
J
exp{
j
F
k
(
t
)}
|
(8.19)
L
sinc
H
4
l
L
2
cos
b
sin(
V
t
+
u
0
k=
0
where
F
k
(
t
) is defined by (8.18).
Assume a radar is operating at S-band with a wavelength of 0.1m,
and a helicopter has 2 rotor blades at a constant rotation rate of 5 revolu-
tions/sec (rev/sec). If the distance of the blade roots from the rotor center
is 0.3m, the distance of the blade tips from the rotor center is 6.7m, and
the elevation angle of the rotor
b
= 0, the time-domain signature of the
rotor blades in (8.19) is shown in Figure 8.7(a). The frequency spectrum
of the same signal is shown in 8.7(b), which we will discuss in Section 8.2.4.
The rotor blade's return has a short flash when the blade has specular
reflection at the advancing as well as at the receding point of rotation [9].
The interval between flashes is related to the rotation rate of the rotor. The
duration of the flash is determined by the length of the blade
L
, the wave-
length
l
, and the rotation rate
V
as described by the sinc function in (8.19).
Figure 8.7
(a) The magnitude of the radar-returned signal from two rotor blades; and
(b) the frequency spectrum of the radar-returned signal.
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