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Baseband Pulse and Digital Signaling Chap. 3
The spectrum of the PAM signal with natural sampling is given by Eq. (3–3) as a function of
the spectrum of the analog input waveform. This relationship is illustrated in Fig. 3–3 for the case
of an input waveform that has a rectangular spectrum, where the duty cycle of the switching
waveform is d = t>T s = 1>3 and the sampling rate is f s 4B. As expected, the spectrum of the
input analog waveform is repeated at harmonics of the sampling frequency. This is similar to the
spectrum for impulse sampling that was studied in Sec. 2–7—for example, compare
Fig. 2–18 with Fig. 3–3. For this example, where d = 1>3, the PAM spectrum is zero for ; 3f s ,
; 6f s , and so on, because the spectrum in these harmonic bands is nulled out by the (sin x)x function.
From the figure, one sees that the bandwidth of the PAM signal is much larger than the
bandwidth of the original analog signal. In fact, for the example illustrated in Fig. 3–3b, the null
bandwidth for the envelope of the PAM signal is 3f s 12B; that is, the null bandwidth of this PAM
signal is 12 times the bandwidth of the analog signal.
Example 3–1 THE SPECTRUM OF A NATURALLY SAMPLED PAM SIGNAL
Assume that a baseband analog signal has a rectangular-shaped spectrum with a bandwidth of
5 Hz. Calculate and plot the spectrum of a PAM signal that is obtained by naturally sampling this
analog signal. See Example3_01.m for the solution.
Figure 3–3
Spectrum of a PAM waveform with natural sampling. (See Example3_01.m.)