Digital Signal Processing Reference
In-Depth Information
T
0
C
k
TV
2
T
1
0
0
2
T
(a)
T
0
C
k
TV
2
T
2
0
0
2
T
(b)
TV
0
2
T
(c)
Figure 5.2
Frequency spectra of rectangular pulse trains.
where The magnitude of each harmonic is seen to vary according to the
sinc function as shown in Figure 5.2(a), in which
sinc(x) = sin(x)/x.
T
0
C
k
is plotted versus the frequency
v.
The
reason for plotting will become evident later.
Now consider the effect of increasing the period of the signal from to
Because the components of the spectrum become closer together
along the frequency axis as the period increases; therefore,
T
0
C
k
T
0
= T
1
T
0
= T
2
= 4T
1
.
v
0
= 2p/T
0
,
¢v = v
0
decreases. This is
illustrated in Figure 5.2(b).
