Digital Signal Processing Reference
In-Depth Information
1.5
1.5
Input sinusoid
Ideal shift of 60 deg
Hilbert shifted by 60 deg
Input signal
Ideal shift of 90 deg
Hilbert phase shifted by 90 deg
(
b
)
(
a
)
1
1
0.5
0.5
0
0
-0.5
-0.5
-1
-1
failure points
-1.5
-1.5
0
20
40
60
0
50
100
150
200
250
Time / Sampling Period
Time / Sampling Period
Figure 7.20
(a) Phase-shifting a sinusoid by 60
o
. (b) Phase-shifting a modulated signal through 90
o
when carrier frequency is 0.04, modulation frequency is 0.025, and depth of modulation is also 60
o
.
small number of Bessel components; see Figure 7.21. From this perspective, we
consider a signal to be within the confines of a narrowband when only a few
Bessel components (if not one) are important, or correspondingly, a very small
number of Fourier coefficients are sufficient. In fact, Boashash [10,11] suggests
2
250
(
a
)
(
b
)
Input Signal
Ideal Phase Shited by 60 deg
Hilbert Phase Shifted by 60 deg
Shifted
1.5
200
1
0.5
150
0
100
-0.5
-1
50
-1.5
-2
0
0
20
40
60
80
100
0
0.25
0.5
0.75
1
Time / Sampling Period
Normalized Frequency
Figure 7.21
Phase-shifted modulated signals at higher frequencies beyond the Hilbert transition edges
give better results. (a) Carrier frequency is 0.1, modulation frequency is 0.05, and depth of modulation
is also 60
o
. (b) FFT of the signal in (
a
).
