System information

telephone network will not carry frequencies below 300 Hz and above 4,000 Hz, a
sampling frequency of 8,000 samples per second will be sufficient to reproduce any
frequency within the bandwidth of an analog telephone. Keep that 8,000 samples per
second in mind; we’re going to talk about it more later.
Logarithmic companding
So, we’ve gone over the basics of quantization, and we’ve discussed the fact that more
quantization intervals (i.e., a higher sampling rate) give better quality but also require
more bandwidth. Lastly, we’ve discussed the minimum sampling rate needed to accu-
rately measure the range of frequencies we wish to be able to transmit (in the case of
the telephone, it’s 8,000 Hz). This is all starting to add up to a fair bit of data being
sent on the wire, so we’re going to want to talk about companding.
Companding is a method of improving the dynamic range of a sampling method without
losing important accuracy. It works by quantizing higher amplitudes in a much coarser
fashion than lower amplitudes. In other words, if you yell into your phone, you will
not be sampled as cleanly as you will be when speaking normally. Yelling is also not
good for your blood pressure, so it’s best to avoid it.
Two companding methods are commonly employed: μlaw
*
in North America, and alaw
in the rest of the world. They operate on the same principles but are otherwise not
compatible with each other.
Companding divides the waveform into cords, each of which has several steps. Quan-
tization involves matching the measured amplitude to an appropriate step within a
cord. The value of the band and cord numbers (as well as the sign—positive or negative)
becomes the signal. The following diagrams will give you a visual idea of what com-
panding does. They are not based on any standard, but rather were made up for the
purpose of illustration (again, in the telephone network, companding will be done at
an 8-bit, not 5-bit, resolution).
Figure A-11 illustrates 5-bit companding. As you can see, amplitudes near the zero-
crossing point will be sampled far more accurately than higher amplitudes (either pos-
itive or negative). However, since the human ear, the transmitter, and the receiver will
also tend to distort loud signals, this isn’t really a problem.
A quantized sample might look like Figure A-12. It yields the following bit stream:
00000 10011 10100 10101 01101 00001 00011 11010 00010 00001 01000 10011
10100 10100 00101 00100 00101 10101 10011 10001 00011 00001 00000 10100
10010 10101 01101 10100 00101 11010 00100 00000 01000
* μlaw is often referred to as “ulaw” because, let’s face it, how many of us have μ keys on our keyboards? μ is
in fact the Greek letter Mu; thus, you will also see μlaw written (more correctly) as “Mu-law.” When spoken,
it is correct to confidently say “Mew-law,” but if folks look at you strangely, and you’re feeling generous, you
can help them out and tell them it’s “ulaw.” Many people just don’t appreciate trivia.
Digital Telephony | 607