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AM, FM, and Digital Modulated Systems Chap. 5
(f) = pA c 2
cf m a 2p (f - f c )b + f m a 2p (-f - f c )bd
2D f D f D f
where f m (·) is the PDF of the modulating signal. †
This theorem is proved in Prob. 6–60.
(5–66)
Example 5–8 SPECTRUM FOR WBFM WITH TRIANGULAR MODULATION
The spectrum for a WBFM signal with a triangular modulating signal (Fig. 5–14a) will be evaluated.
The associated PDF for triangular modulation is shown in Fig. 5–14b. The PDF is described by
f m (m) = c 1
2V p
,
|m| 6 V p
0, m otherwise
(5–67)
f m (m)
V p
m(t)
m
V p
1
2V p
t
V p
V p
V p
m
T m
(a) Triangle Modulating Waveform
(b) PDF of Triangle Modulation
p(f)
2
A c
8F
–f c -F –f c –f c +F
f c -F f c
0
f c +F
f
(c) PSD of WBFM Signal with Triangle Modulation, F=D f V p /2p
Figure 5–14
Approximate spectrum of a WBFM signal with triangle modulation.
† See Appendix B for the definition of PDF and examples of PDFs for various waveforms. This topic may be
deleted if the reader is not sufficiently familiar with PDFs. Do not confuse the PDF of the modulation, f m (·), with the
frequency variable f.