Pulse Code Modulation

Pulse Code Modulation

Pulse code modulation (PCM) is based on the sampling theorem, which states that
If a signal f(t) is sampled at regular intervals of time and at a rate higher
than twice the highest signal frequency, then the samples contain all the
information of the original signaL The function f(t) may be reconstructed
from these samples by the use of a low-pass filter.
For the interested reader, a proof is provided in a supporting document at this
book's Web site. If voice data are limited to frequencies below 4000 Hz, a conservative
procedure for intelligibility, 8000 samples per second would be sufficient to
characterize the voice signal completely. Note, however, that these are analog samples,
called pulse amplitude modulation (PAM) samples. To convert to digital, each
of these analog samples must be assigned a binary code.
Figure 6.15 shows an example in which the original signal is assumed to be
bandlimited with a bandwidth of B. PAM samples are taken at a rate of 2B, or
once every Ts = 1/2B seconds. Each PAM sample is approximated by being
quantized into one of 16 different levels. Each sample can then be represented by
4 bits. But because the quantized values are only approximations, it is impossible
to recover the original signal exactly. By using an 8-bit sample, which allows 256
quantizing levels, the quality of the recovered voice signal is comparable with
that achieved via analog transmission. Note that this implies that a data rate of
(8000 samples per second) X (8 bits per sample) = 64 kbps is needed for a single
voice signaL
Thus, PCM starts with a continuous-time, continuous-amplitude (analog)
signal, from which a digital signal is produced. The digital signal consists of blocks of
n bits, where each n-bit number is the amplitude of a PCM pulse. On reception, the
process is reversed to reproduce the analog signaL Notice, however, that this process