Digital telephone
CODECs
G.9 have historically used (for land-line switching
networks) a simple 8-bit format called
-law (or simply
``mu-law'') that compresses large amplitudes in a manner loosely
corresponding to human
loudness perception.

Given an input sample

represented in some internal format, such as a
short, it is converted to 8-bit mu-law format by the formula
[
58]
where
![$ Q_\mu[]$](http://www.dsprelated.com/josimages_new/mdft/img2024.png)
is a
quantizer which produces a kind of
logarithmic
fixed-point number with a 3-bit characteristic and a 4-bit mantissa, using
a small table lookup for the mantissa.
As we all know from talking on the telephone, mu-law sounds really quite
good for voice, at least as far as
intelligibility is concerned.
However, because the telephone
bandwidth is only around 3 kHz (nominally
200-3200 Hz), there is very little ``
bass'' and no ``highs'' in the
spectrum above 4 kHz. This works out fine for intelligibility of voice
because the first three
formants (
envelope peaks) in typical speech
spectra occur in this range, and also because the difference in spectral
shape (particularly at high frequencies) between consonants such as
``sss'', ``shshsh'', ``fff'', ``ththth'', etc., are sufficiently preserved
in this range. As a result of the narrow bandwidth provided for speech, it
is sampled at only 8 kHz in standard CODEC chips.
For ``wideband audio'', we like to see
sampling rates at least as high as
44.1 kHz, and the latest systems are moving to 96 kHz (mainly because
oversampling simplifies
signal processing requirements in various areas,
not because we can actually hear anything above 20 kHz). In addition, we
like the low end to extend at least down to 20 Hz or so. (The lowest note
on a normally tuned bass guitar is E1 = 41.2 Hz. The lowest note on a
grand
piano is A0 = 27.5 Hz.)
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