For digital communications it is necessary to transform the signals from the analog source of information into signals that are compatible with the digital processing they will undergo. This transformation is known as formatting the signal: Based on the information generated by the source, digital symbols are obtained. Formatting the information involves three processes: sampling, quantification and coding.
Nyquist demonstrated that an analog
signal could be completely reconstructed without any loss of information
based on a set of its periodic discrete samples, provided the following
criterion is met:
where B is the analog bandwidth [B]: Hz,
and fm the sampling frequency [fm]: samples/s.
When sampling, values are taken from the analog signal every 1/fm seconds (sampling period). Quantification assigns these analog values a digital value by approximation and in accordance with the curves defined by the ITU. Finally, each quantified value is assigned a binary code (a series of zeros and ones) that constitutes the symbol to be transmitted. This process is called pulse code modulation (PCM).
PCM technology was patented and developed in France in the 30s (1938) but could not be used because the suitable technology was not available until during the Second World War. The first commercial PCM system was set up in 1962 by Bell Labs (USA). Its initial goal was that of converting an analog voice telephone channel to digital.
A telephone channel admits frequencies of between 300 Hz and 3400 Hz. Bearing in mind that it is necessary to establish margins (known as guard bands) in the channel that allow the correct recovery of the analog signal at the receiving end through a filtering process, the bandwidth to be considered is greater than 3.1 kHz. It is set at 4 kHz. According to the Nyquist criterion, if we take this value as the minimum bandwidth, the maximum rate of symbols that can be transmitted by the channel will be 8000 symbols/s to avoid Inter-Symbol Interference. At the same time, if we apply the relative criterion to the sampling, we have to sample at a minimum frequency of 8000 samples per second.
In the European PCM system, 256 levels of digital quantification (law
A of quantification) are assigned to the sampled values, which remain
analog after sampling. In order to codify 256 levels in binary, 8 bits
per level (8 bits per symbol or sample) are needed. This means that a
rate of 8000 samples per second means a bit rate of 64000 bit/s. That
is why the capacity of the digital telephone channel is 64 kbit/s.
