Digital Signal Processing Reference
In-Depth Information
0
1
−0.25
p
0.8
−0.5
p
0.6
0.4
−0.75
p
0.2
−
p
w
w
0
0
1
2
3
4
5
6
0
1
2
3
4
5
6
(a)
(b)
Fig. 5.19. Magnitude and phase spectra of LTIC system with impulse response
h
(
t
)=1.25
e
−0.6
t
sin(0.8
t
)
u
(
t
). (a) Magnitude spectrum; (b) phase spectrum.
20
0
0
−0.25
p
−20
−0.5
p
−40
−0.75
p
−60
−
p
w
−80
w
10
−2
10
−1
10
0
10
1
10
2
10
−2
10
−1
10
0
10
1
10
2
(a)
(b)
Bode plots
In Bode plots, the magnitude
H
(
ω
)
in decibels and phase
<
H
(
ω
)
are plotted as functions of frequency
ω
using a logarithmic scale. Use of a loga-
rithmic scale, with base 10, on the frequency
ω
-axis offers two main advantages.
Fig. 5.20. Bode plots for the
LTIC system considered in
Example 5.31. (a) Magnitude
plot; (b) phase plot.
(1) Compared to a linear scale, the use of a logarithmic scale allows a wider
range of frequencies to be plotted, with the lower frequencies represented
at a higher resolution.
(2) The asymptotic approximations of the magnitude and phase spectra can
easily be sketched graphically by hand.
Figure 5.20 illustrates the Bode plots of the LTIC system considered in
Example 5.31 using a logarithmic scale on the frequency axis. Figure 5.20(a)
shows the magnitude Bode plot, where the magnitude
H
(
ω
)
is expressed in
decibels (dB) as 20 log
10
H
(
ω
)
and plotted as a function of log
10
(
ω
). Figure
5.20(b) shows the phase Bode plot, where the phase <
H
(
ω
) is plotted as a
function of log
10
(
ω
).
5.10 M
ATLAB
exercises
In this section, we will consider two applications of M
ATLAB
. First, we
illustrate the procedure for calculating the CTFT of a CT signal
x
(
t
) using
M
ATLAB
. In our explanation, we consider an example,
x
(
t
)
=
4 cos(10
π
t
)
,
and write the appropriate M
ATLAB
commands for the example at each step.
Second, we list the procedure for plotting the Bode plots in M
ATLAB
.
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