Graphics Programs Reference
In-Depth Information
cv
cf r
t
=
-----------
(1.17)
+
cv
cv
f r
d
=
-------------
(1.18)
+
The reflected pulse spacing is now
and the new PRF is
, where
sd
–
f r
cv
cv
f r
c
f r
sd
–
==
-----
c t
–
-------------
(1.19)
+
It follows that the new PRF is related to the original PRF by
cv
+
cv
-----------
f r
=
f r
(1.20)
–
However, since the number of cycles does not change, the frequency of the
reflected signal will go up by the same factor. Denoting the new frequency by
, it follows
f 0
cv
+
cv
-----------
f 0
=
f 0
(1.21)
–
where is the carrier frequency of the incident signal. The Doppler frequency
is defined as the difference
f 0
. More precisely,
f d
f 0
–
f 0
cv
+
cv
2 v
cv
-----------
-----------
f d
=
f 0
–
f 0
=
f 0
–
f 0
=
f 0
(1.22)
–
–
but since
and
, then
vc
«
c
=
λ f 0
2 v
c
2 v
λ
------
f d
f 0
=
------
(1.23)
Eq. (1.23) indicates that the Doppler shift is proportional to the target velocity,
and, thus, one can extract
from range rate and vice versa.
f d
The result in Eq. (1.23) can also be derived using the following approach:
Fig. 1.8 shows a closing target with velocity
. Let
refer to the range at
v
R 0
time
(time reference); then the range to the target at any time is
t 0
t
R () R 0
=
– t
(
–
)
(1.24)
0
The signal received by the radar is then given by
x r
() xt ψ ()
=
(
–
)
(1.25)
where
is the transmitted signal, and
x ()
2
--- R 0
ψ ()
=
(
–
vt
+
vt 0
)
(1.26)
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