Databases Reference
In-Depth Information
1.0
0.9
0.8
a
1
= 0.6
a
1
= 0.99
0.7
0.6
R
(
k
)
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
14
16
18
20
k
F I GU R E 8 . 8
Autocorrelation function of an AR(1) process with two values of
a
1
.
4
3
2
1
x
n
0
−
1
−2
−3
−
4
−5
0 0 0 0 0 0 0 0 0 0 0
n
F I GU R E 8 . 9
Sample function of an AR(1) process with
a
1
= 0.99.
From this we can see that the autocorrelation will decay more slowly for larger values of
a
1
. Remember that the value of
a
1
in this case is an indicator of how closely the current sample
is related to the previous sample. The autocorrelation function is plotted for two values of
a
1
in
Figure
8.8
. Notice that for
a
1
close to 1, the autocorrelation function decays extremely slowly.
As the value of
a
1
moves farther away from 1, the autocorrelation function decays much faster.
Sample waveforms for
a
1
=
6 are shown in Figures
8.9
and
8.10
. Notice
the slower variations in the waveform for the process with a higher value of
a
1
. Because the
waveform in Figure
8.9
varies more slowly than the waveform in Figure
8.10
, samples of this
waveform are much more likely to be close in value than the samples of the waveform of
Figure
8.10
.
0
.
99 and
a
1
=
0
.
