Digital Signal Processing Reference
In-Depth Information
sive one. The interpretation of dispersive scattering mechanisms in range is
more difficult. In Chapter 4, we shall examine how dispersive features can
be better revealed by time-frequency transforms.
1.2
Radar Signal and Noise
1.2.1
Signal Waveforms
In high range-resolution radar systems, in order to achieve high range resolu-
tion, signals having wide bandwidth are required. Widely used wideband
signals include linear frequency modulated (LFM) signals and stepped fre-
quency (SF) signals.
The LFM signal linearly changes its instantaneous carrier frequency
within a single pulse as shown in Figure 1.5(a). The LFM signal with a
Gaussian envelope can be expressed as
s
LFM
(
t
)=(
a
/
p
)
1/4
exp{
-a
t
2
/2} exp{
j
2
p
[
f
0
+
(
h
/2)
t
]
t
}
(1.6)
where
f
0
is the carrier frequency,
h
is the frequency-changing rate or chirp
rate, and
a
determines the width of the Gaussian envelope.
The frequency spectrum of the LFM signal with a Gaussian envelope
shown in Figure 1.5(b) can be derived as [36]
(
a-
j
h
)
1/2
exp
H
-
2
p
2
a
(
f
-
f
0
)
2
(1.7)
(
a
/
p
)
1/4
-
j
2
p
2
h
(
f
-
f
0
)
2
S
LFM
(
f
)=
(
a
2
h
2
)
(
a
2
h
2
)
+
+
Unlike the LFM signal, the SF signal achieves its wide bandwidth by
sequentially changing the carrier frequency step-by-step over a number of
pulses [Figure 1.6(a)]. Thus, the SF signal can be described by a sequence
of pulses with increased carrier frequencies from one pulse to the next. The
stepped carrier frequency can be expressed as
+
(
m
-
1)
D
f
f
m
=f
0
(
m
=1,2,...,
M
)
(1.8)
where
D
f
is the frequency step. The total bandwidth of the SF signal,
M
D
f
, determines the radar range resolution. Because pulses are transmitted
with a given pulse repetition interval (PRI)
T
PRI
, the SF signal can be
expressed as
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