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Morris WL040/Bidgoli-Vol III-Ch-53 September 15, 2003 12:23 Char Count= 0
COMMUNICATIONSTHEORY:BITS OFTRANSMITTEDINFORMATION 649Original Analog Voice SignalStep 2:
One of 256 Level
Values Is Assigned
to Each Sample
(Resulting in Quantization
Error Noise")Step 3:
Binary Value of the Level of Each Sample
Make Up Transmitted "Digitized" Version of
Original Analog SignalQuantization Error "Noise"
(difference between
sample and actual value)100,130,140,150,150,140,1301100100 10000010 10001100 10010110 10010110 10001100 10000010TimeDigitizer TimeStep 1:
Signal Sampled
at Regular Intervals
(8,000 per second)
("Pulse Amplitude
Modulated Signal")Figure 2: Digitization of a voice signal.(Newton, 1998) and (Truxal, 1990). A digitizer takes
samples of the height (i.e., amplitude) of the incoming
analog signal at regular time intervals (e.g., 8,000 times
per second). For each of these regularly timed measure-
ments, the digitizer outputs a fixed length digital number
(expressed in terms of logical 0s and 1s) that corresponds
to the size of the signal height measured for each sample.
See, e.g., Figure 2.
Depending on the digitizer, the number of bits that are
used to represent each level of signal amplitude can vary. If
eight bits are used to represent the measurements of each
sample’s height, then 256 height levels can be represented.
The use of eight bits to represent each sample of a voice
signal is fairly typical. The rounding error or difference
between the actual height of each sample and the true
height of the sampled signal at the sampled point is called
“quantization error.”
More bits could be used to represent each sample’s am-
plitude, allowing more discrete levels to digitize a signal
and, in turn, reducing the amount of quantization (or
rounding error) noise. However, the additional bits for
each sample would require additional transmission ca-
pacity with little offsetting benefit. Experience has shown
that the human ear cannot easily detect the noise cre-
ated by quantization error with eight bits sample encod-
ing.
The minimum rate at which a CODEC must sample a
voice signal is the Nyquist rate. Nyquist determined that
in order for a sampled representation of a signal to ac-
curately capture the entire range of frequencies in theoriginal signal, the samples must be taken at a rate that is
more than two times the highest frequency component of
the original signal. Thus, in order to transmit a voice sig-
nal digitally and achieve the same performance as conven-
tional analog telephony networks, the transmitted voice-
band signal, with its highest frequency assumed to be
3,400 cycles per second, must be sampled at more than
6,800 samples per second. It is common to oversample
a voice signal using a sample rate of 8,000 samples per
second.
With eight bit encoding per sample, the digital equiva-
lent of a voiceband signal that is sampled 8,000 times per
second requires 64,000 bits per second (8,000 samples per
second×8 bits per sample). This is known as the G.711
standard.
CODECs often incorporate techniques for reducing the
transmitted bit rate from the base amount of 64,000 bits
per second. Some of those techniques include (1) using
nonlinear (logarithmic) sampling levels, (2) transmitting
only changes in signal levels, or (3) removing redundant
information while maintaining signal quality and mini-
mizing processing delay (Castelli, 2002). Using nonlinear
sampling levels is known as “companding.” Compand-
ing has the effect of decreasing the number of sample
levels required by proportionately increasing the sample
levels in the most relevant height range for the signal.
Companding also has the secondary effect of reducing
the quantization noise in the relevant amplitude range,
compared to that in noncompanded digitized signals, for
a given number of bits per sample. Differential pulse