Graphics Programs Reference
In-Depth Information
τ
1
=
τ′
⁄
N
(4.37)
and the frequency for the
ith
subpulse is
f
i
=
f
0
+
i
∆
f
;
i
=
1
N
,
(4.38)
where
f
0
is a constant frequency and
f
0
»
∆
f
. It follows that the time-band-
width product of this waveform is
N
2
∆
f
τ′
=
(4.39)
Costas signals (or codes) are similar to SFW, except that the frequencies for
the subpulses are selected in a random fashion, according to some predeter-
mined rule or logic. For this purpose, consider the matrix shown in Fig.
4.13b. In this case, the rows are indexed from and the columns
are indexed from . The rows are used to denote the
subpulses and the columns are used to denote the frequency. A
ÐdotÑ
indicates
the frequency value assigned to the associated subpulse. In this fashion, Fig.
4.13a shows the frequency assignment associated with a SFW. Alternatively,
the frequency assignments in Fig. 4.13b are chosen randomly. For a matrix of
size
NN
×
i
=
12…
N
,, ,
j
=
012…
N
,,, ,
(
1
)
NN
×
, there are a total of
N
!
possible ways of assigning the
ÐdotsÑ
(i.e.,
N
!
possible codes).
0
1
2
3
4
5
6
7
8
9
8
0
1
2
3
4
5
6
7
9
10
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
(a)
(b)
Figure 4.13. Frequency assignment for a burst of N subpulses. (a) SFW (stepped
LFM); (b) Costas code of length Nc = 10.
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