Graphics Programs Reference
In-Depth Information
r ô ô ô ô 3
ô 2 u
2
ô u 2
2
ô s 2
2
----- r ô ô u
--------
--------
--------
,
,
r ô uu
,
r ô ss
,
(12.86)
6
-------- r t ô ô t ô 2
r uss us 2
-------- r stu stu r suu su 2
------- r utt ut 2
------- r uuu u 3
,
,
,
,
,
-----
2
2
2
2
6
are small and can be neglected. Thus, the range
r n
is approximated by
ô 2
2
rtsu ô
ô ô
r ô u ô u
(
,,,
;
D n
)
=
r
+++
r u u
-----
+
+
(12.87)
ô ô
s 2
----
t 2
----
u 2
2
r ô st ô st
-----
r ss
+++ +
r st st
r tt
r uu
Consider the following two-way path: the element transmitting, scatterer
reflecting, and the element receiving. It follows that the round trip
delay corresponding to this two-way path is
n th
C i
n th
1
--- r n 1
tsu ô
tsu ô
τ n 1 n 2
=
(
(
,,,
;
D n 1
)
+
r n 2
(
,,,
;
D n 2
)
)
(12.88)
where
c
is the speed of light.
12.9.5. Signal Synthesis
The observation interval is divided into subintervals of width
. During each subinterval, the real array is operated in
sequential mode, and an array length of is synthesized. The number of sub-
intervals is computed such that is large enough to allow sequential
transmission for the real array without causing range ambiguities. In other
words, if the maximum range is denoted as
M
t
=
(
÷
M
)
ob
2 N
M
t
R mx
then
tN 2 R mx
c
>
------------
(12.89)
Each subinterval is then partitioned into
N
sampling subintervals of width
2 R mx
c
. The location
t mn
represents the sampling time at which the
n th
ele-
ment is transmitting during the
m th
subinterval.
The normalized transmitted signal during the
m th
subinterval for the
n th
element is defined as
s n
(
t mn
)
=
cos
(
f o t mn
+
ζ
)
(12.90)
where
ζ
denotes the transmitter phase, and
f o
is the system operating fre-
quency. Assume that there is only one scatterer,
C i
, within the
k th
range cell
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