Digital Signal Processing Reference
In-Depth Information
N
-
Â
1
[]
=◊
[]
=
(
[
]
)
yk
mr
T
k
mr
◊
k
-
i
i
i
=
0
where
m
is a weight vector,
r
a vector of delayed samples selected from the input
signal, and
N
the number of samples in
m
and
r
. The adaptive algorithm computes
the weights based on the correlation matrix and a direction vector:
[
]
◊
[]
=
C
k
,
d
=
0
m
k
l
D
where
C
is a correlation matrix,
D
a direction vector, and
a scale factor. The cor-
relation matrix
C
is computed as an average of the signal correlation over several
samples:
l
-
Â
n
1
1
(
)
kk
T
[
]
=
[]
ƒ-
[
]
C
k
,
d
r
r
d
N
AV
i
=
0
where
N
AV
is the number of samples included in the average. The direction vector
D
indicates the signal desired:
T
[
(
)
]
[
(
)
]
D
=
1
exp
j
wt
◊◊◊
exp
j
w
N
-
1
t
T
T
where
the delay between samples
that create the output, and
N
the order of the correlation matrix.
This procedure minimizes the undesired-to-desired ratio (UDR) [70]. UDR is
defined as the ratio of the total signal power to the power of the signal desired, or
w
T
is the angular frequency of the signal desired,
t
T
[]
◊
[
]
◊
[]
P
P
mC m
kk k
,0
1
total
UDR =
=
=
(
)
(
)
2
T
[]
◊
T
Pk
mD
[]
◊
d
Pk
mD
d
d
where
P
d
is the power of the signal desired.
MATLAB is used to simulate the ATA, then ported to the C6x for real-time
implementation. Figure 10.67 shows the test setup using a fixed desired signal of
1416 Hz and an undesired signal of 1784 Hz (which can be varied). From MATLAB,
and optimal value of
t
is found to minimize UDR. This is confirmed in real time,
since for that value of
with a GEL file), the undesired signal (initially
displayed from an HP3561A analyzer) is greatly attenuated.
t
(varying
t
10.23.5 FSK Modem
This project implements a digital modulator/demodulator. It generates 8-ary FSK
carrier tones. The following steps are performed in the program.
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