Digital Signal Processing Reference
In-Depth Information
f
est
. For every
period of the incoming signal that is received, that signal is correlated with a sine
wave that has a phase slightly larger and slightly smaller than
To determine this maximum, begin with an initial estimate of
f
est
. This yields two
values for the correlation coefficient, one at
. The dif-
ference between these two values gives an approximation of the derivative of the
correlation coefficient. Using the difference between the correlation coefficients at
f
est
+e
f
est
+e
and the other at
f
est
-e
and
f
est
-e
as an estimate of the derivative, a new value for
f
est
is calculated
using
(
)
ff
=+ -
YY
est
est
+
e
-
e
where
2
p
Ú
(
)
◊
(
)
Y
=
sin
t
◊
wf
+
sin
t
◊
wf
++
e
+
e
carrier
est
0
2
p
Ú
(
)
◊
(
)
Y
=
sin
t
◊
wf
+
sin
t
◊
wf
+-
e
-
e
carrier
est
0
This process is repeated every time a full period of the incoming sine wave is
received. Eventually,
f
est
will be equal and the derivative estimated by the
difference in the correlation coefficient
f
carrier
and
f
est
+e
and
f
est
-e
will be 0. When this occurs,
the receiver is considered locked onto the signal.
Implementation
1.
Figure 10.27 shows the C source program
sine8_phase_shift.c
used to
generate a 1-kHz sine wave with eight unique phase shifts as the output of the
first DSK. This output sine wave has varying phases but a constant frequency.
Build this project as
sine8
_
phase
_
shift
. Verify that the DSK output connected
to a scope is as shown in Figure 10.28. Every 50 periods of the sine wave, the
loop index in the program is incremented by 1 to skip one of the lookup values
set in
sine_table
. This results in a transmitted sine wave with eight differ-
ent phase values. Connect the output of the DSK into the input of the second
DSK.
2.
Figure 10.29 shows the C source program
bpsk_demod.c
(on the CD) that
implements a PLL demodulator on the second DSK. Note that the first DSK
is still running even though the USB port is unplugged and reconnected to the
second DSK. See also the example
scrambler
in Chapter 4. Figure 10.30
a
shows a CCS plot of the demodulator output. Note that eight different ampli-
tude values are shown for each period of the received input sinusoid. This plot
is obtained within CCS using
phiBuf
as the starting address, with 500 points
as the acquisition and display size. You can readily change the demodulator
program so that the phase shift is every five periods of the sine wave. You can
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