Graphics Programs Reference
In-Depth Information
T
NT
frequency
2
NT
-------
Figure 3.5. Amplitude spectrum for a coherent pulse train of finite length.
3.4. Linear Frequency Modulation Waveforms
Frequency or phase modulated waveforms can be used to achieve much
wider operating bandwidths. Linear Frequency Modulation (LFM) is com-
monly used. In this case, the frequency is swept linearly across the pulsewidth,
either upward (up-chirp) or downward (down-chirp). The matched filter band-
width is proportional to the sweep bandwidth, and is independent of the pulse-
width.
Fig. 3.6
shows a typical example of an LFM waveform. The pulsewidth
is
, and the bandwidth is
.
τ
B
The LFM up-chirp instantaneous phase can be expressed by
µ
τ
---
τ
---
---
t
2
ψ () 2π
f
0
t
=
+
≤≤
t
(3.29)
where
is the radar center frequency, and
is the LFM coeffi-
f
0
µ
=
(
2π
B
) τ
⁄
cient. Thus, the instantaneous frequency is
1
2π
d
ψ ()
f
0
τ
---
τ
---
------
f
()
=
=
+
µ
t
≤≤
t
(3.30)
d
t
Similarly, the down-chirp instantaneous phase and frequency are given, respec-
tively, by
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