Graphics Programs Reference
In-Depth Information
∞
∞
τ
f
r
frequency
∞
∞
f
0
f
0
(
1 τ
⁄
)
f
0
+
(
1 τ
⁄
)
Figure 3.4. Amplitude spectrum for a coherent pulse train of infinite length.
∞
∑
F
3
() 2π
=
F
n
δω 2
n
π
f
r
(
)
(3.26)
n
=
∞
The amplitude spectrum of
is shown in Fig. 3.4. In this case, the spectrum
f
3
()
has a
envelope that corresponds to
. The spacing between the spec-
sin
x
⁄
x
F
n
tral lines is equal to the radar PRF,
.
f
r
Finally, define the function
as
f
4
()
N
∑
f
4
()
=
f
2
(
tnT
)
(3.27)
n
=
0
Note that
is a limited duration of
. The FT of
is
f
4
()
f
3
()
f
4
()
∞
∑
Sinc
ω
NT
2
-------
F
4
()
AN
τ
=
•
Sinc n
πτ
f
r
(
)δω2
n
π
f
r
(
)
(3.28)
n
=
∞
where the operator indicates convolution. The spectrum in this case is
shown in
Fig. 3.5.
The envelope is still a
(
•
)
which corresponds to the
sin
x
⁄
x
pulsewidth. But the spectral lines are replaced by
spectra that corre-
sin
x
⁄
x
spond to the duration
.
NT
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