Digital Signal Processing Reference
In-Depth Information
the exhaustive search procedure for the motion parameters. This problem
becomes especially severe when higher-order motions are involved. Recently,
genetic algorithms [16] have been attempted as a way to reduce the computa-
tional complexity and speed up the search procedure.
9.5
Moving Target Detection
In Chapter 7, we discussed SAR imaging of moving targets and how to
detect moving targets in clutter. Especially in a high clutter environment,
it is difficult to detect moving targets by using conventional methods. In
[17], the WVD was used to detect a moving target and estimate motion
parameters. Combined with the Hough transform as we described in Section
7.4.1, the WVD works well for single target detection, but not for multiple
targets owing to the cross-term interference. A combined Wigner-Hough
transform extended to the analysis of multicomponent LFM signals was
suggested in [18-20].
Another approach to detecting multiple LFM signals in clutter is the
fractional Fourier transform (FRFT) [21]. For any real angle
a
, the FRFT
of a signal
s
(
t
) is defined by
FRFT
a
(
u
) =
(9.1)
cot
a
¥
-¥
5
S
1
-
j
cot
a
D
1/2
e
j
u
2
s
(
t
)
e
j
t
2
cot
a
e
-
jut
csc
a
dt
2
(
a¹
n
p
)
2
p
(
a
=n
2
p
)
s
(
u
)
s
(
-
u
)
(
a+
p
=n
2
p
)
where
n
is an integer.
The FRFT depends on an angle parameter
a
and can be interpreted
as a rotation of the time-frequency plane by the angle
a
. In [22] relationships
between the FRFT and the WVD and the STFT are derived in a simple
and natural form. For the WVD, the relationship is
WVD
(
t
,
v
) = 2 exp{2
j
v¢
t
¢
}
¥
-¥
FRFT
a
(
z
)
FRFT
*
(2
v¢-
z
) exp{
-
2
jt
¢
z
}
dz
(9.2)
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