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

Thus each additional bit used for quantizing increases SNR by about 6 dB, which is
a factor of 4.
Typically, the PCM scheme is refined using a technique known as nonlinear
encoding, which means, in effect, that the quantization levels are not equally spaced.
The problem with equal spacing is that the mean absolute error for each sample is the
same, regardless of signal level. Consequently, lower amplitude values are relatively
more distorted. By using a greater number of quantizing steps for signals of low amplitude
and a smaller number of quantizing steps for signals of large amplitude, a marked
reduction in overall signal distortion is achieved (e.g., see Figure 6.16).
The same effect can be achieved by using uniform quantizing but companding
(compressing-expanding) the input analog signal. Companding is a process that
compresses the intensity range of a signal by imparting more gain to weak signals
than to strong signals on input. At output, the reverse operation is performed.
Figure 6.17 shows typical companding functions. Note that the effect on the input
side is to compress the sample so that the higher values are reduced with respect to
the lower values. Thus, with a fixed number of quantizing levels, more levels are

available for lower-level signals. On the output side, the compander expands the
samples so the compressed values are restored to their original values.
Nonlinear encoding can significantly improve the PCM SNR ratio. For voice
signals, improvements of 24 to 30 dB have been achieved.