Page 310 - Satellite Communications, Fourth Edition

290 Chapter Ten

large signals being quantized into coarser steps than small signals.
This is termed compression, and it is introduced to keep the signal-
to-quantization noise ratio reasonably constant over the full dynamic
range of the input signal while maintaining the same number of bits
per codeword. At the receiver (the D/A block in Fig. 10.4), the binary
codewords are automatically decoded into the larger quantized steps
for the larger signals, this being termed expansion. The expansion law
is the inverse of the compression law, and the combined processing is
termed companding.
Figure 10.4b shows how the MC145500 codec achieves compression
by using a chorded approximation. The leading bit of the digital code-
word is a sign bit, being 1 for positive and 0 for negative samples of the
analog signal. The next three bits are used to encode the chord in which
the analog signal falls, the three bits giving a total of eight chords. Each
chord is made to cover the same number of input steps, but the step size
increases from chord to chord. The chord bits are followed by four bits
indicating the step in which the analog value lies. The normalized deci-
sion levels shown in Fig. 10.4b are the analog levels at which the com-
parator circuits change from one chord to the next and from one step to
the next. These are normalized to a value 8159 for convenience in pres-
entation. For example, the maximum value may be considered to be 8159
mV, and then the smallest step would be 1 mV. The first step is shown
as 1 (mV), but it should be kept in mind that the first quantized level
−

spans the analog zero so that 0 must be distinguished from 0 . Thus
the level representing zero has in fact a step size of 1 mV.
As an example, suppose the sampled analog signal has a value 500
mV. This falls within the normalized range 479 to 511 mV, and there-
fore, the binary code is 10111111. It should be mentioned that normally
the first step in a chord would be encoded 0000, but the bits are inverted,
as noted in Fig. 10.4b. This is so because low values are more likely than
high values, and inversion increases the 1-bit density, which helps in
maintaining synchronization.
The table in Fig. 10.4b shows mu-law encode-decode characteristics.
The term mu law, usually written as -law, originated with older analog
compressors, where was a parameter in the equation describing the
compression characteristic. The -law characteristic is standard in North
America and Japan, while in Europe and many other parts of the world
a similar law known as the A-law is in use. Figure 10.5 shows the curves
for 255 and A 87.6, which are the standard values in use. These
are shown as smooth curves, which could be approached with the older
analog compression circuits. The chorded approximation approaches
these in straight-line segments, or chords, for each step.
Because of the similarity of the A-law and -law curves, the speech
quality, as affected by companding, will be similar in both systems, but