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Sec. 3–2 Pulse Amplitude Modulation 133
The following are the four main goals of this chapter:
• To study how analog waveforms can be converted to digital waveforms. The most
popular technique is called pulse code modulation (PCM).
• To learn how to compute the spectrum for digital signals.
• To examine how the filtering of pulse signals affects our ability to recover the digital
information at the receiver. This filtering can produce what is called intersymbol interference
(ISI) in the recovered data signal.
• To study how we can multiplex (combine) data from several digital bit streams into one
high-speed digital stream for transmission over a digital system. One such technique,
called time-division multiplexing (TDM), will be studied in this chapter. †
Another very important problem in digital communication systems is the effect of noise,
which may cause the digital receiver to produce some bit errors at the output. This problem
will be studied in Chapter 7 since it involves the use of statistical concepts that are emphasized
in the second part of this book.
3–2 PULSE AMPLITUDE MODULATION
Pulse amplitude modulation (PAM) is an engineering term that is used to describe the conversion
of the analog signal to a pulse-type signal in which the amplitude of the pulse denotes the
analog information. PAM is studied first because the analog-to-PAM conversion process is the
first step in converting an analog waveform to a PCM (digital) signal. In a few applications
the PAM signal is used directly and conversion to PCM is not required.
The sampling theorem, studied in Chapter 2, provides a way to reproduce an analog
waveform by using sample values of that waveform and (sin x)x orthogonal functions. The
purpose of PAM signaling is to provide another waveform that looks like pulses, yet contains
the information that was present in the analog waveform. Because we are using pulses, we
would expect the bandwidth of the PAM waveform to be wider than that of the analog waveform.
However, the pulses are more practical to use in digital systems. We will see, that the
pulse rate, f s , for PAM is the same as that required by the sampling theorem, namely, f s Ú 2B,
where B is the highest frequency in the analog waveform and 2B is called the Nyquist rate.
There are two classes of PAM signals: PAM that uses natural sampling (gating) and PAM
that uses instantaneous sampling to produce a flat-top pulse. These signals are illustrated
in Figs. 3–1 and 3–5, respectively. The flat-top type is more useful for conversion to PCM;
however, the naturally sampled type is easier to generate and is used in other applications.
Natural Sampling (Gating)
DEFINITION. If w(t) is an analog waveform bandlimited to B hertz, the PAM signal
that uses natural sampling (gating) is
w s (t) = w(t) s(t)
(3–1)
† Other techniques, including frequency division multiplexing, and code division multiplexing, are covered in
Chapters 5 and 8.