Graphics Programs Reference
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frequency
frequency
B
B
f
0
f
0
time
time
τ
τ
(a)
(b)
Figure 3.6. Typical LFM waveforms. (a) up-chirp; (b) down-chirp.
µ
τ
---
τ
---
---
t
2
ψ () 2π
f
0
t
=
≤≤
t
(3.31)
1
2π
τ
---
τ
---
d
ψ ()
f
0
------
f
()
=
=
µ
t
≤≤
t
(3.32)
d
t
A typical LFM waveform can be expressed by
µ
---
t
2
j
2π
f
0
t
+
t
-
e
s
1
()
Rect
=
(3.33)
where
denotes a rectangular pulse of width
. Eq. (3.33) is then
Rect t
τ
(
⁄
)
τ
written as
()
e
j
2π
f
0
t
s
()
s
1
=
(3.34)
where
-
e
j
πµ
t
2
t
s
()
Rect
=
(3.35)
is the complex envelope of
.
s
1
()
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