Digital Signal Processing Reference
In-Depth Information
200
o
= 0.001
o
175
φ
150
125
100
o
= 90
o
φ
75
50
F
m
25
0
0
0.2
0.4
0.6
0.8
1
Normalized Frequency,
F
10
−3 o
. Filter
length and cut-off frequency for Hilbert and low-pass filters were 155 and 0.7, respectively. Carrier
frequency = 0.4. Modulation frequency
F
m
= 0.05.
ϕ
o
= 90
o
and 1
Figure 7.12
Bessel components of input signal into demodulator for
×
considerable number of Bessel components in contrast to the latter. Note that the
spacing between the components is equal to the modulation frequency
F
m
. For
relatively small
o
, the modulation frequency
F
m
could be relatively large without
their product being significant in comparison to the carrier frequency
F
. This
explains the observation (see Figure 7.11) that for small amplitudes
ϕ
o
, the
apparent stable error range is more extended than for larger modulation
amplitudes. Further discussion on these issues in relation to narrowband and
wideband FM demodulation are to be found in Carlson [4] and Hahn [8]. We will
discuss the influence of the carrier frequency on filter bandwidth in the following
sections.
ϕ
7.6.3
AC Phase Error and Demodulation Bandwidth
From our previous discussion it is not too difficult to see that if the carrier
frequency
F
is increased, then for a given modulation index, the condition
o
F
m
<<
F
allows for a greater range on
F
m
. While this is true in general, the cut-off
frequencies of both the Hilbert and low-pass filter and the band-pass nature of the
demodulation process itself limit the overall demodulation bandwidth. Figure 7.13
shows how the peak-to-peak error responds to changes in carrier frequency for a
range of modulation frequencies. Although the shape of the response remains
essentially the same, it is nevertheless shifted along the modulation frequency axis
for various carrier frequencies
F
. The loss in bandwidth for
F
> 0.6 and < 0.2 in
ϕ
