Pulse-code modulation

Pulse-code modulation (PCM) is a digital representation of an analog signal.

The magnitude of the signal (with respect to a fixed reference) is sampled
regularly at a frequency fs. This means the value of the signal, a sample,
is captured at uniform intervals of duration T (= 1/fs). Every sample is
quantized to a series of symbols in a digital code, which is usually a
binary code.

PCM is used in digital telephone systems and for digital audio recording on
compact discs.

In conventional PCM, before being digitized, the analog data may be
processed (e.g. compressed), but once digitized, the PCM signal is not
subjected to further processing (e.g. digital compaction). In telephony,
several PCM streams may be multiplexed into a larger aggregate data stream.

Differential (or Delta) pulse-code modulation (DPCM) encodes the PCM values
as differences between the current and the previous value. For audio this
type of encoding reduces the number of bits required per sample compared to
PCM by about 25%. A variant of DPCM, Adaptive DPCM (ADPCM) varies the size
of the quantization step, to allow futher reduction of the required
bandwidth for a given signal-to-noise ratio.

Pulse-code modulation can be either Return to Zero (RZ) or
non-return-to-zero (NRZ). For a NRZ system to be synchronized using in-band
information, there must not be long sequences of identical symbols, such as
ones or zeroes. For binary PCM systems, the density of 1-symbols is called
'ones-density'.

Ones-density is often controlled using precoding techniques where the PCM
code is expanded into a slightly longer code with a guaranteed bound on
ones-density before modulation into the channel. In other cases, extra
'framing' bits are added into the stream which guarantee at least occasional
symbol transitions.

Another technique used to control ones-density is the use of a 'scrambler'
polynomial on the raw data which will tend to turn the raw data stream into
a stream that looks pseudo-random, but where the raw stream can be recovered
exactly by reversing the effect of the polynomial. In this case, long runs
of zeroes or ones are still possible on the output, but are considered
unlikely enough to be within normal engineering tolerance.

In other cases, the long term DC value of the modulated signal is important,
as building up a DC offset will tend to bias detector circuits out of their
operating range. In this case special measures are taken to keep a count of
the cumulative DC offset, and to modify the codes if necessary to make the
DC offset always tend back to zero.

Many of these codes are bipolar codes, where the pulses can be positive,
negative or absent. Typically, non-zero pulses alternate between being
positive and negative. These rules may be violated to generate special
symbols used for framing or other special purposes.

History

In the 1930s the necessity to convert analogue data to digital format for
computer use was unknown - there were no computers capable of using it.
However the idea was seen by Alec Reeves as a means of communicating with
perfect fidelity - no errors could arise in a system based on ones and
noughts. In 1938 he filed a patent in France that introduced the concept of
digital communication which he called Pulse Code Modulation. It is now
commonplace for computers, radio, television, CDs, recording and so on. More
about Alec Reeves can be found on http://www.alecharleyreeves.com, including
on line versions of his writings and lectures. There are also some Active-X
online versions of the experiments he performed in PCM.