Global Positioning System Reference
In-Depth Information
6.7 SAMPLING FREQUENCY AND BAND ALIASING FOR REAL DATA
COLLECTION
(
10
)
If only one ADC is used to collect digitized data from one RF channel, the output
data are often referred to as real data (in contrast to complex data). The input
signal bandwidth is limited by the sampling frequency. If the sampling frequency
is
f
s
, the unambiguous bandwidth is
f
s
/2. As long as the input signal bandwidth
is less than
f
s
/2, the information will be maintained and the Nyquist sampling
rate will be fulfilled. Although for many low-frequency applications the input
signal can be limited to 0 to
f
s
/2, in general, the sampling frequency need not
be twice the highest input frequency.
If the input frequency is
f
i
, and the sampling frequency is
f
s
, the input
frequency is aliased into the baseband and the output frequency
f
o
is
f
o
=
f
i
−
nf
s
/
2a d
f
o
<f
s
/
2
(
6
.
5
)
where
n
is an integer. The relationship between the input and the output frequency
is shown in Figure 6.3.
When the input is from
nf
s
to
(
2
n
+
1
)f
s
/2, the frequency is aliased into
the baseband in a direct transition mode, which means a lower input frequency
translates into a lower output frequency. When the input is from
(
2
n
+
1
)f
s
/2 to
(n
+
1
)f
s
, it is aliased into the baseband in an inverse transition mode, which
means a lower input frequency translates into a higher output frequency. Either
case can be implemented if the frequency translation is properly monitored.
If the input signal bandwidth is
f
, it is desirable to have the minimum sam-
pling frequency
f
s
higher than the Nyquist requirement of 2
f
. Usually, 2
.
5
f
is used because it is impractical to build a filter with very sharp skirt (or a brick
wall filter) to limit the out-of-band signals. Thus, for the C/A code the required
minimum sampling rate is about 5 MHz. This sampling frequency is adequately
separated from the undesirable frequency of 5.115 MHz. The sampling frequency
must be properly selected. Figure 6.4a shows the desired frequency aliasing. The
input band is placed approximately at the center of the output band and the input
and output bandwidths are equal.
FIGURE 6.3
Input versus output frequency of band aliasing.
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