Global Positioning System Reference
In-Depth Information
of 2
π
, the unambiguous bandwidth is 1/(
n
−
m
)where
n
−
m
is the delay time
between two consecutive data sets.
7.14 RESOLVING AMBIGUITY IN FINE FREQUENCY MEASUREMENTS
Although the basic approach to find the fine frequency is based on
Equation (7.22), there are several slightly different ways to apply it. If one
takes the
k
th frequency component of the DFT every millisecond, the frequency
resolution is 1 kHz and the unambiguous bandwidth is also 1 kHz. In Figure 7.7a
five frequency components are shown and they are separated by 1 kHz. If the
input signal falls into the region between two frequency components as shown
in Figure 7.7b, the phase may have uncertainty due to noise in the system.
One approach to eliminate the uncertainty is to speed up the DFT operation. If
the DFT is performed every 0.5 ms, the unambiguous bandwidth is 2 kHz. With
a frequency resolution of 1 kHz and an unambiguous bandwidth of 2 kHz, there
will be no ambiguity problem in determining the fine frequency. However, this
approach will double the DFT operations.
The second approach is to use an amplitude comparison scheme without dou-
bling the speed of the DFT operations, if the input is a cw signal. As shown in
FIGURE 7.7
Ambiguous ranges in frequency domain.
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