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Sec. 3–13 Study-Aid Examples 225
(a) Find and sketch the magnitude spectrum for the PAM signal.
(b) Find a numerical value for the first null bandwidth of the PAM signal.
Solution.
(a) Using W(f ) = 2 (fB) in Eq. (3–10), MATLAB computes and plots the spectrum shown
in Fig. 3–47. The plot shows how W(f) is repeated at harmonics of the sampling
sin pt f
frequency and weighted by the ta function (caused by the rectangular pulse
pt f
b
shape).
1.6
Magnitude Spectrum of Flat-Topped PAM
1.4
1.2
1
|W s (f)|
0.8
0.6
0.4
0.2
0
–5
–4 –3 –2 –1 0 1 2 3 4 5
f
Figure 3–47 Solution for SA3-1. (See SA3_1.m.)
(b) The spectrum first goes to zero at B = 3 kHz. For this spectrum, 3 kHz is not a good
measure of bandwidth, because the spectral magnitude becomes large again at higher
frequencies. In examples like this, engineers use the envelope of the spectrum to specify
the null bandwidth. Thus, the first null bandwidth of the spectral envelope, t 2
B null = 1 t = 1100 µs = 10 kHz.
sin pt f
2 , is
pt f
SA3–2 PCM Signal Bandwidth and SNR In a communications-quality audio system,
an analog voice-frequency (VF) signal with a bandwidth of 3,200 Hz is converted into a PCM
signal by sampling at 7,000 sampless and by using a uniform quantizer with 64 steps. The
PCM binary data are transmitted over a noisy channel to a receiver that has a bit error rate
(BER) of 10 -4 .