The basic processes in digital transmission of analog information are sampling, quantizing and encoding.

Sampling:

The sampling theorem states that the signal may be reconstructed without any error from regularly spaced samples taken at the rate fs (samples/second) which is at least twice the maximum frequency fm present in the signal. Common telephone system practice is to use a sampling frequency of 8000 Hz. While transmitting the original waveform, the time between samples of one signal may be used to transmit samples of other signals. This is time division multiplexing

(TDM).

The samples to which the sampling theorem refers are analog pulses whose amplitudes are equal to that of original waveform at the time of sampling. The original signal may be reconstructed without error by passing the samples through an ideal low-pass filter whose transfer function is appropriate to the sampling pulse shape. A communication system that samples an input waveform and transmits analog pulses is said to use pulse amplitude modulation.

Quantization and Encoding:

Analog pulses are subjected to amplitude distortion so pulse amplitude modulation is not used over satellite links. The analog samples are quantized –resolved into one of a finite number of possible values – and the quantized values are binary encoded and transmitted digitally. Thus each sample is converted into a digital word that represents the quantization value closest to the original analog sample. Quantization may be uniform or non-uniform depending on whether or not the quantized voltage levels are uniform or non-uniformly spaced. At the receiver a digital-to-analog (D/A) converter converts each incoming digital word back into an analog sample; these analog samples are filtered and the original input waveform is reconstructed. A communication system that transmits digitally encoded quantized values is called pulse code modulation (PCM). The quantization process shown in figure prevents exact reconstruction of the digitized waveform. The error introduced is called quantization error, and a person listening to a reconstructed speech signal perceives the quantization error as an added noise called quantization noise.

Companding:

Uniform quantization introduces more noise when a signal is small. Improved noise performance can be obtained by using non-uniform quantization in which the step size of the quantization intervals increases in proportion to the signal value being quantized. The same effect can be obtained from a uniform quantizer if the input signal is compressed before quantization. The distortion introduced by the compressor must be removed at the receiver by an expander. The transfer functions of the compressor and expander are complementary, that is, their product is a constant and the amplitude distribution of a signal that has passed through both a compressor and expander is unchanged.

Companding was first employed on terrestrial telephone systems using analog compressors that had logarithmic transfer functions. These were the so-called mu-law and A-law compressors. Later developments in digital technology allowed digital implementation of the compression and expansion functions and permitted the sampling, compression quantization and encoding operations to be combined into one equipment called a coder.