Graphics Programs Reference
In-Depth Information
main lobe widening. Table 13.1 gives a summary of some windows with the
corresponding impact on main beam widening and peak reduction.
TABLE 13.1.
Common windows.
Null-to-null Beamwidth. Rectangular
window is the reference.
Peak
Reduction
Window
Rectangular
1
1
Hamming
2
0.73
Hanning
2
0.664
Blackman
6
0.577
2.76
0.683
β
=
6 )
Kaiser (
1.75
0.882
β
=
3 )
Kaiser (
The multiplication process defined in Eq. (13.131) is equivalent to cyclic
convolution in the frequency domain. It follows that is a smeared (dis-
torted) version of . To minimize this distortion, we would seek windows
that have a narrow main lobe and small side lobes. Additionally, using a win-
dow other than a rectangular window reduces the power by a factor
X
w
()
X
()
P
w
, where
N
∑
1
N
∑
1
1
----
w
2
W
()
2
P
w
=
()
=
(13.132)
n
=
0
k
=
0
It follows that the DPS for the sequence
x
w
()
is now given by
1
P
w
N
2
P
w
-------------
X
()
2
=
1
P
w
N
2
12…
N
P
k
w
X
()
2
)
2
=
-------------
{
+
XN k
(
}
;
k
=
,, ,
----1
(13.133)
1
P
w
N
2
w
)
2
-------------
X
N
2
P
N
=
(
⁄
⁄
2
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