Digital Signal Processing Reference
In-Depth Information
Plot of y1
=
cos(0.1
p
n)
Plot of y2
=
cos(0.3
p
n)
1
1
0.5
0.5
0
0
−
0.5
−
0.5
−
1
−
1
0
20
40
60
0
20
40
60
Value of n
Value of n
Plot of y3
=
cos(
p
n)
Plot of y4
cos(1.8
p
n)
=
1
1
0.5
0.5
0
0
−
0.5
0.5
−
−
1
−
1
0
20
40
60
0
20
40
60
Value of n
Value of n
Figure 1.10
Plot of cos
(ω
0
n)
for different values of
ω
0
between 0 and 2
π
.
frequency. In Figure 1.10 we have plotted the DT sequences as
ω
0
attains a few
values between 0 and 2
π
, to illustrate this property. We will elaborate on this
property in later chapters of the topic.
Since frequencies separated by 2
π
are the same, as
ω
0
increases from 2
π
to
3
π
, the frequency of oscillation increases in the same manner as the frequency
of oscillation when it increases from 0 to
π
. As an example, we see that the
frequency of
v
0
(n)
=
cos
(
0
.
1
πn)
is the same as that of
v
1
(n)
=
cos
(
2
.
1
πn)
.It
is interesting to note that
v
2
(n)
=
cos
(
1
.
9
πn)
also has the same frequency of
oscillation as
v
1
(n)
because
v
2
(n)
=
cos
(
1
.
9
πn)
=
cos
(
2
π
−
0
.
1
πn)
(1.20)
=
cos
(
2
πn)
cos
(
0
.
1
πn)
+
sin
(
2
πn)
sin
(
0
.
1
πn)
(1.21)
=
cos
(
0
.
1
πn)
=
v
0
(n)
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