Although humans are well equipped for analog communications, analog
transmission is not particularly efficient. When analog signals become weak
because of transmission loss, it is hard to separate the complex analog
structure from the structure of random transmission noise. If you amplify
analog signals, it also amplifies noise, and eventually analog connections
become too noisy to use. Digital signals, having only "one-bit" and "zero-bit"
states, are more easily separated from noise. They can be amplified without
corruption. Digital coding is more immune to noise corruption on long-distance
connections. Also, the world's communication systems have converted to a
digital transmission format called pulse code modulation (PCM). PCM is a type
of coding that is called "waveform" coding because it creates a coded form of
the original voice waveform. This document describes at a high level the
conversion process of analog voice signals to digital signals.
There are no specific requirements for this document.
This document is not restricted to specific software and hardware
versions.
For more information on document conventions, refer to the
Cisco
Technical Tips Conventions.
PCM is a waveform coding method defined in the ITU-T G.711
specification.
The first step to convert the signal from analog to digital is to
filter out the higher frequency component of the signal. This make things
easier downstream to convert this signal. Most of the energy of spoken language
is somewhere between 200 or 300 hertz and about 2700 or 2800 hertz. Roughly
3000-hertz bandwidth for standard speech and standard voice communication is
established. Therefore, they do not have to have precise filters (it is very
expensive). A bandwidth of 4000 hertz is made from an equipment point if view.
This band-limiting filter is used to prevent aliasing (antialiasing). This
happens when the input analog voice signal is undersampled, defined by the
Nyquist criterion as Fs < 2(BW). The sampling frequency is less than the
highest frequency of the input analog signal. This creates an overlap between
the frequency spectrum of the samples and the input analog signal. The low-pass
output filter, used to reconstruct the original input signal, is not smart
enough to detect this overlap. Therefore, it creates a new signal that does not
originate from the source. This creation of a false signal when sampling is
called aliasing.
The second step to convert an analog voice signal to a digital voice
signal is to sample the Filtered input signal at a constant sampling frequency.
It is accomplished by using a process called pulse amplitude modulation (PAM).
This step uses the original analog signal to modulate the amplitude of a pulse
train that has a constant amplitude and frequency. (See Figure 2.)
The pulse train moves at a constant frequency, called the sampling
frequency. The analog voice signal can be sampled at a million times per second
or at two to three times per second. How is the sampling frequency determined?
A scientist by the name of Harry Nyquist discovered that the original analog
signal can be reconstructed if enough samples are taken. He determined that if
the sampling frequency is at least twice the highest frequency of the original
input analog voice signal, this signal can be reconstructed by a low-pass
filter at the destination. The Nyquist criterion is stated like this:
Fs > 2(BW)
Fs = Sampling frequency
BW = Bandwidth of original analog voice signal
Figure 1: Analog Sampling
After you filter and sample (using PAM) an input analog voice signal,
the next step is to digitize these samples in preparation for transmission over
a Telephony network. The process of digitizing analog voice signals is called
PCM. The only difference between PAM and PCM is that PCM takes the process one
step further. PCM decodes each analog sample using binary code words. PCM has
an analog-to-digital converter on the source side and a digital-to-analog
converter on the destination side. PCM uses a technique called quantization to
encode these samples.
Figure 2: Pulse Code Modulation - Nyquist
Theorem
Quantization is the process of converting each analog sample value into
a discrete value that can be assigned a unique digital code word.
As the input signal samples enter the quantization phase, they are
assigned to a quantization interval. All quantization intervals are equally
spaced (uniform quantization) throughout the dynamic range of the input analog
signal. Each quantization interval is assigned a discrete value in the form of
a binary code word. The standard word size used is eight bits. If an input
analog signal is sampled 8000 times per second and each sample is given a code
word that is eight bits long, then the maximum transmission bit rate for
Telephony systems using PCM is 64,000 bits per second. Figure 2 illustrates how
bit rate is derived for a PCM system.
Each input sample is assigned a quantization interval that is closest
to its amplitude height. If an input sample is not assigned a quantization
interval that matches its actual height, then an error is introduced into the
PCM process. This error is called quantization noise. Quantization noise is
equivalent to the random noise that impacts the signal-to-noise ratio (SNR) of
a voice signal. SNR is a measure of signal strength relative to background
noise. The ratio is usually measured in decibels (dB). If the incoming signal
strength in microvolts is Vs, and the noise level, also in microvolts, is Vn,
then the signal-to-noise ratio, S/N, in decibels is given by the formula S/N =
20 log10(Vs/Vn). SNR is measured in decibels (dB). The higher the SNR, the
better the voice quality. Quantization noise reduces the SNR of a signal.
Therefore, an increase in quantization noise degrades the quality of a voice
signal. Figure 3 shows how quantization noise is generated. For coding purpose,
an N bit word yields 2N quantization labels.
Figure 3: Analog to Digital Conversion
One way to reduce quantization noise is to increase the amount of
quantization intervals. The difference between the input signal amplitude
height and the quantization interval decreases as the quantization intervals
are increased (increases in the intervals decrease the quantization noise).
However, the amount of code words also need to be increased in proportion to
the increase in quantization intervals. This process introduces additional
problems that deal with the capacity of a PCM system to handle more code words.
SNR (including quantization noise) is the single most important factor
that affects voice quality in uniform quantization. Uniform quantization uses
equal quantization levels throughout the entire dynamic range of an input
analog signal. Therefore, low signals have a small SNR (low-signal-level voice
quality) and high signals have a large SNR (high-signal-level voice quality).
Since most voice signals generated are of the low kind, having better voice
quality at higher signal levels is a very inefficient way of digitizing voice
signals. To improve voice quality at lower signal levels, uniform quantization
(uniform PCM) is replaced by a nonuniform quantization process called
companding.
Companding refers to the process of first compressing an analog signal
at the source, and then expanding this signal back to its original size when it
reaches its destination. The term companding is created by combining the two
terms, compressing and expanding, into one word. At the time of the companding
process, input analog signal samples are compressed into logarithmic segments.
Each segment is then quantized and coded using uniform quantization. The
compression process is logarithmic. The compression increases as the sample
signals increase. In other words, the larger sample signals are compressed more
than the smaller sample signals. This causes the quantization noise to increase
as the sample signal increases. A logarithmic increase in quantization noise
throughout the dynamic range of an input sample signal keeps the SNR constant
throughout this dynamic range. The ITU-T standards for companding are called
A-law and u-law.
A-law and u-law are audio compression schemes (codecs) defined by
Consultative Committee for International Telephony And Telegraphy (CCITT) G.711
which compress 16-bit linear PCM data down to eight bits of logarithmic
data.
A-law Compander
Limiting the linear sample values to twelve magnitude bits, the A-law
compression is defined by this equation, where A is the compression parameter
(A=87.7 in Europe), and x is the normalized integer to be
compressed.
u-law Compander
Limiting the linear sample values to thirteen magnitude bits, the u-law
(u-law and Mu- law are used interchangeably in this document) compression is
defined by this equation, where m is the compression parameter (m =255 in the
U.S. and Japan) and x is the normalized integer to be
compressed.
A-law standard is primarily used by Europe and the rest of the world.
u-law is used by North America and Japan.
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Both are linear approximations of logarithmic input/output
relationship.
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Both are implemented using eight-bit code words (256 levels, one for
each quantization interval). Eight-bit code words allow for a bit rate of 64
kilobits per second (kbps). This is calculated by multiplying the sampling rate
(twice the input frequency) by the size of the code word (2 x 4 kHz x 8 bits =
64 kbps).
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Both break a dynamic range into a total of 16 segments:
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Eight positive and eight negative segments.
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Each segment is twice the length of the preceding one.
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Uniform quantization is used within each segment.
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Both use a similar approach to coding the eight-bit word:
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First (MSB) identifies polarity.
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Bits two, three, and four identify segment.
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Final four bits quantize the segment are the lower signal levels
than A-law.
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Different linear approximations lead to different lengths and
slopes.
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The numerical assignment of the bit positions in the eight-bit code
word to segments and the quantization levels within segments are
different.
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A-law provides a greater dynamic range than u-law.
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u-law provides better signal/distortion performance for low level
signals than A-law.
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A-law requires 13-bits for a uniform PCM equivalent. u-law requires
14-bits for a uniform PCM equivalent.
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An international connection needs to use A-law, u to A conversion is
the responsibility of the u-law country.
At the time of the PCM process, the differences between input sample
signals are minimal. Differential PCM (DPCM) is designed to calculate this
difference and then transmit this small difference signal instead of the entire
input sample signal. Since the difference between input samples is less than an
entire input sample, the number of bits required for transmission is reduced.
This allows for a reduction in the throughput required to transmit voice
signals. Using DPCM can reduce the bit rate of voice transmission down to 48
kbps.
How does DPCM calculate the difference between the current sample
signal and a previous sample? The first part of DPCM works exactly like PCM
(that is why it is called differential PCM). The input signal is sampled at a
constant sampling frequency (twice the input frequency). Then these samples are
modulated using the PAM process. At this point, the DPCM process takes over.
The sampled input signal is stored in what is called a predictor. The predictor
takes the stored sample signal and sends it through a differentiator. The
differentiator compares the previous sample signal with the current sample
signal and sends this difference to the quantizing and coding phase of PCM
(this phase can be uniform quantizing or companding with A-law or u-law). After
quantizing and coding, the difference signal is transmitted to its final
destination. At the receiving end of the network, everything is reversed. First
the difference signal is dequantized. Then this difference signal is added to a
sample signal stored in a predictor and sent to a low-pass filter that
reconstructs the original input signal.
DPCM is a good way to reduce the bit rate for voice transmission.
However, it causes some other problems that deal with voice quality. DPCM
quantizes and encodes the difference between a previous sample input signal and
a current sample input signal. DPCM quantizes the difference signal using
uniform quantization. Uniform quantization generates an SNR that is small for
small input sample signals and large for large input sample signals. Therefore,
the voice quality is better at higher signals. This scenario is very
inefficient, since most of the signals generated by the human voice are small.
Voice quality needs to focus on small signals. To solve this problem, adaptive
DPCM is developed.
Adaptive DPCM (ADPCM) is a waveform coding method defined in the ITU-T
G.726 specification.
ADPCM adapts the quantization levels of the difference signal that
generated at the time of the DPCM process. How does ADPCM adapt these
quantization levels? If the difference signal is low, ADPCM increases the size
of the quantization levels. If the difference signal is high, ADPCM decreases
the size of the quantization levels. So, ADPCM adapts the quantization level to
the size of the input difference signal. This generates an SNR that is uniform
throughout the dynamic range of the difference signal. Using ADPCM reduces the
bit rate of voice transmission down to 32 kbps, half the bit rate of A-law or
u-law PCM. ADPCM produces "toll quality" voice just like A-law or u-law PCM.
Coder must have feedback loop, using encoder output bits to recalibrate the
quantizer.
Applicable as ITU Standards G.726.
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Turn A-law or Mu-law PCM samples into a linear PCM sample.
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Calculate the predicted value of the next sample.
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Measure the difference between actual sample and predicted value.
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Code difference as four bits, send those bits.
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Feed back four bits to predictor.
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Feed back four bits to quantizer.
