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AM, FM, and Digital Modulated Systems Chap. 5
and the PSD is
s (f) = 1 4 [ g(f - f c ) + g (-f - f c )]
(5–2b)
where G(f) = [g(t)] and g ( f) is the PSD of the complex envelope g(t).
General results that apply to both digital and analog modulating waveforms are developed
in the first half of the chapter (Secs. 5–1 to 5–8). Digital modulated signals are emphasized in
the second half (Secs. 5–9 to 5–13).
The goals of this chapter are to
• Study g(t) and s(t) for various types of analog and digital modulations.
• Evaluate the spectrum for various types of analog and digital modulations.
• Examine some transmitter and receiver structures.
• Study some adopted standards.
• Learn about spread spectrum systems.
5–1 AMPLITUDE MODULATION
From Table 4–1, the complex envelope of an AM signal is given by
g(t) = A c [1 + m(t)]
(5–3)
where the constant A c has been included to specify the power level and m(t) is the modulating
signal (which may be analog or digital). These equations reduce to the following representation
for the AM signal:
s(t) = A c [1 + m(t)] cos v c t
(5–4)
A waveform illustrating the AM signal, as seen on an oscilloscope, is shown in Fig. 5–1. For
convenience, it is assumed that the modulating signal m(t) is a sinusoid. A c [1 + m(t)] corresponds
to the in-phase component x(t) of the complex envelope; it also corresponds to the real
envelope |g(t)| when m(t) Ú -1 (the usual case).
If m(t) has a peak positive value of +1 and a peak negative value of -1, the AM signal is
said to be 100% modulated.
DEFINITION.
The percentage of positive modulation on an AM signal is
% positive modulation = A max - A c
* 100 = max [m(t)] * 100
A c
and the percentage of negative modulation is
(5–5a)
% negative modulation = A c - A min
A c
* 100 = -min [m(t)] * 100
The overall modulation percentage is
% modulation = A max - A min
2A c
* 100 =
max [m(t)] - min [m(t)]
2
* 100
(5–5b)
(5–6)
where A max is the maximum value of A c [1 + m(t)], A min is the minimum value, and A c is
the level of the AM envelope in the absence of modulation [i.e., m(t) = 0].