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
(
2π
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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