Global Positioning System Reference
In-Depth Information
FIGURE 6.4
Frequency aliasing for real data collection.
Figure 6.4b shows improper frequency aliasing. In Figure 6.4b, the center
frequency of the input signal does not alias to the center of the baseband. The
frequency higher than
(
2
n
+
1
)f
s
/2 and the portion of the frequency lower than
(
2
n
+
1
)f
s
/2 are aliased on top of each other. Therefore, portion of the output
band contains an overlapping spectrum, which is undesirable. When there is a
spectrum overlapping in the output, the output bandwidth is narrower than the
input bandwidth.
In order to alias the input frequency near the center of the baseband, the
following relation must hold,
f
o
=
f
i
−
≈
n(f
s
/
2
)
f
s
/
4a d
f
s
>
2
f
(
6
.
6
)
where
f
is the bandwidth of input signal. The first part of this equation is to put
the aliasing signal approximately at the center of the output band. The second
part states that the Nyquist sampling requirement must hold. If the frequency
of the input signal
f
i
is known, this equation can be used to find the sampling
frequency. Examples will be presented in Sections 6.8 and 6.9.
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