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Sec. 3–3 Pulse Code Modulation 141
loss in the recovered analog waveform due to the filtering effect, H( f), caused by the flat-top
pulse shape. This loss, if significant, can be reduced by decreasing t or by using some
additional gain at the high frequencies in the low-pass filter transfer function. In that case, the
low-pass filter would be called an equalization filter and have a transfer function of 1H(f).
The pulse width t is also called the aperture since tT s determines the gain of the recovered
analog signal, which is small if t is small relative to T s . It is also possible to use product
detection similar to that shown in Fig. 3–4, except that now some prefilter might be needed
before the multiplier (to make the spectrum flat in a band centered on f nf s ), to compensate
for the spectral loss due to the aperture effect. Once again, f s needs to be selected so that
Ú 2B in order to prevent aliasing.
f s
Example 3–2 THE SPECTRUM OF A FLAT-TOP 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 flat-top sampling this
analog signal. See Example3_02.m for the solution.
The transmission of either naturally or instantaneously sampled PAM over a channel
requires a very wide frequency response because of the narrow pulse width, which imposes
stringent requirements on the magnitude and phase response of the channel. The bandwidth
required is much larger than that of the original analog signal, and the noise performance of
the PAM system can never be better than that achieved by transmitting the analog signal
directly. Consequently, PAM is not very good for long-distance transmission. It does provide
a means for converting an analog signal to a PCM signal (as discussed in the next section).
PAM also provides a means for breaking a signal into time slots so that multiple PAM signals
carrying information from different sources can be interleaved to transmit all of the information
over a single channel. This is called time-division multiplexing and will be studied in
Sec. 3–9.
3–3 PULSE CODE MODULATION
DEFINITION. Pulse code modulation (PCM) is essentially analog-to-digital conversion
of a special type where the information contained in the instantaneous samples of an
analog signal is represented by digital words in a serial bit stream.
If we assume that each of the digital words has n binary digits, there are M 2 n unique
code words that are possible, each code word corresponding to a certain amplitude level.
However, each sample value from the analog signal can be any one of an infinite number of
levels, so that the digital word that represents the amplitude closest to the actual sampled
value is used. This is called quantizing. That is, instead of using the exact sample value of the
analog waveform w(kT s ), the sample is replaced by the closest allowed value, where there
are M allowed values, each corresponding to one of the code words. Other popular types of
analog-to-digital conversion, such as delta modulation (DM) and differential pulse code modulation
(DPCM), are discussed in later sections.