Graphics Programs Reference
In-Depth Information
τ
τ'
sin
πτ' µτ
(
+
f
d
) 1
-----
e
j
πτ
f
d
τ
τ'
---------------------------------------------------------------
χτ
f
d
(
;
)
=
1
-----
τ '
≤
(4.17)
τ
τ'
πτ' µτ
(
+
f
d
) 1
-----
and the LFM ambiguity function is
2
τ
τ'
sin
πτ' µτ
(
+
f
d
) 1
-----
τ
τ'
)
2
χτ
f
d
(
;
=
1
-----
---------------------------------------------------------------
τ '
≤
(4.18)
τ
τ'
πτ' µτ
(
+
f
d
) 1
-----
Again the time autocorrelation function is equal to . The reader can
verify that the ambiguity function for a down-chirp LFM waveform is given by
χτ0
(
,
)
2
τ
τ'
sin
πτ' µτ
f
d
(
) 1
-----
τ
τ'
)
2
---------------------------------------------------------------
χτ
f
d
(
;
=
1
-----
τ '
≤
(4.19)
τ
τ'
πτ' µτ
f
d
(
) 1
-----
MATLAB Function Ðlfm_ambg.mÑ
The function
Ðlfm_ambg.mÑ
implements Eqs. (4.18) and (4.19). It is given
in Listing 4.4 in Section 4.6. The syntax is as follows:
lfm_ambg [taup, b, up_down]
where
Symbol
Description
Units
Status
taup
pulsewidth
seconds
input
b
bandwidth
Hz
input
up_down
up_down = 1 for up chirp
up_down = -1 for down chirp
none
input
Fig. 4.5
(a-d) shows 3-D and contour plots for the LFM uncertainty and ambi-
guity functions for
taup
b
up_down
1
10
1
These plots can be reproduced using MATLAB program
Ðfig4_5.mÑ
given in
Listing 4.5 in Section 4.6. This function generates 3-D and contour plots of an
LFM ambiguity function.
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