Graphics Programs Reference
In-Depth Information
where
φ
0
=
V
n
(
N
1
) φ 2
⁄
.
Define
{
=
exp
(
j
∆φ
n
) ;
=
0 1 …
N
,, ,
1
}
. It follows that
e
j
φ
0
w
()
w
()
V
1
)
V
N
1
E
(
sin
ψ
)
=
[
+
+
…
wN
1
+
(
]
(8.49)
N
∑
1
e
j
φ
0
w
()
V
n
=
n
=
0
The discrete Fourier transform of the sequence
w
()
is defined as
N
∑
1
(
j
2π
nq
)
--------------------
N
W
()
=
w
()
e
;
q
=
01…
N
,, ,
1
(8.50)
n
=
0
The set
{
sin
ψ
q
}
which makes
V
1
equal to the DFT kernel is
λ
q
Nd
sin
ψ
q
=
-------
;
q
=
01…
N
,, ,
1
(8.51)
Then by using Eq. (8.51) in Eq. (8.50) yields
e
j
φ
0
W
()
E
(
sin
ψ
)
=
(8.52)
The one-way array pattern is computed as the modulus of Eq. (8.52). It follows
that the one-way radiation pattern of a tapered linear array of circular dishes is
G
(
sin
ψ
)
=
G
e
W
()
(8.53)
where
G
e
is the element pattern.
In practice, phase shifters are normally implemented as part of the Transmit/
Receive (TR) modules, using a finite number of bits. Consequently, due to the
quantization error (difference between desired phase and actual quantized
phase) the sidelobe levels are affected.
MATLAB Function Ðlinear_array.mÑ
The function
Ðlinear_array.mÑ
computes and plots the linear array gain pat-
tern as a function of real sine-space (sine the steering angle). It is given in List-
ing 8.3 in Section 8.8. The syntax is as follows:
[theta, patternr, patterng] = linear_array(Nr, dolr, theta0, winid, win, nbits)
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