Graphics Programs Reference
In-Depth Information
n
∑
1
1
---
j
2π
li
n
----------
H
l
=
X
i
exp
;
0
≤≤
ln
1
(3.58)
i
=
0
Substituting Eqs. (3.57) and (3.55) into (3.58) and collecting terms yield
n
∑
1
2
R
0
c
2
vt
i
c
1
---
2π
li
n
H
l
=
A
i
exp
j
----------
2 π
f
i
---------
---------
(3.59)
i
=
0
By normalizing with respect to
and by assuming that
and that the
n
A
i
=
1
target is stationary (i.e.,
), then Eq. (3.59) can be written as
v
=
0
n
∑
1
2
R
0
c
2π
li
n
---------
H
l
=
exp
j
----------
2 π
f
i
(3.60)
i
=
0
Using
inside Eq. (3.60) yields
f
i
=
i
∆
f
n
∑
1
2
nR
0
∆
f
c
j
2π
i
n
--------
H
l
=
exp
-------------------
+
l
(3.61)
i
=
0
which can be simplified to
sin
πχ
j
n
2
1
2πχ
n
H
l
=
---------------
exp
------------
----------
(3.62)
πχ
n
sin
------
where
2
nR
0
∆
f
χ
=
----------------------
+
l
(3.63)
c
Finally, the synthesized range profile is
sin
πχ
H
l
=
(3.64)
---------------
πχ
n
sin
------
3.6.1. Range Resolution and Range Ambiguity in SFW
As usual, range resolution is determined from the overall system bandwidth.
Assuming a SFW with
steps, and step size
, then the corresponding range
n
∆
f
resolution is equal to
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