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<html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Digital Telephony</title><link rel="stylesheet" href="styles.css" type="text/css" /><meta name="generator" content="DocBook XSL Stylesheets V1.69.1" /><link rel="start" href="index.html" title="Asterisk™: The Future of Telephony" /><link rel="up" href="asterisk-CHP-7.html" title="Chapter 7. Understanding Telephony" /><link rel="prev" href="asterisk-CHP-7-SECT-1.html" title="Analog Telephony" /><link rel="next" href="asterisk-CHP-7-SECT-3.html" title="The Digital Circuit-Switched Telephone Network" /></head><body><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">Digital Telephony</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="asterisk-CHP-7-SECT-1.html">Prev</a> </td><th width="60%" align="center">Chapter 7. Understanding Telephony</th><td width="20%" align="right"> <a accesskey="n" href="asterisk-CHP-7-SECT-3.html">Next</a></td></tr></table><hr /></div><div class="sect1" lang="en" xml:lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a id="asterisk-CHP-7-SECT-2"></a>Digital Telephony</h2></div></div></div><p>Analog telephony <a id="ch07_digital" class="indexterm"></a>is almost dead.</p><p>In the PSTN, the famous Last Mile is the final remaining piece of
the telephone network still using technology pioneered well over a hundred
years ago.<sup>[<a id="asterisk-CHP-7-FN-5" href="#ftn.asterisk-CHP-7-FN-5">90</a>]</sup></p><p>One of the primary challenges when transmitting analog signals is
that all sorts of things can interfere with those signals, causing low
volume, static, <a id="I_indexterm7_tt1028" class="indexterm"></a><a id="I_indexterm7_tt1029" class="indexterm"></a>and all manner of other undesired effects. Instead of trying
to preserve an analog waveform over distances that may span thousands of
miles, why not simply measure the characteristics of the original sound
and send that information to the far end? The original waveform wouldn’t
get there, but all the information needed to reconstruct it would.</p><p>This is the principle of all digital audio (including telephony):
sample the characteristics of the source waveform, store the measured
information, and send that data to the far end. Then, at the far end, use
the transmitted information to generate a completely new audio signal that
has the same characteristics as the original. The reproduction is so good
that the human ear can’t tell the difference.</p><p>The principle advantage of digital audio is that the sampled data
can be mathematically checked for errors all along the route to its
destination, ensuring that a perfect duplicate of the original arrives at
the far end. Distance no longer affects quality, and interference can be
detected and eliminated.</p><div class="sect2" lang="en" xml:lang="en"><div class="titlepage"><div><div><h3 class="title"><a id="asterisk-CHP-7-SECT-2.1"></a>Pulse-Code Modulation</h3></div></div></div><p>There are<a id="ch07_pulsecode" class="indexterm"></a><a id="I_indexterm7_tt1030" class="indexterm"></a> several ways to digitally encode audio, but the most
common method (and the one used in telephony systems) is known as
Pulse-Code Modulation (PCM). To illustrate how this works, let’s go
through a few examples.</p><div class="sect3" lang="en" xml:lang="en"><div class="titlepage"><div><div><h4 class="title"><a id="asterisk-CHP-7-SECT-2.1.1"></a>Digitally encoding an analog waveform</h4></div></div></div><p>The principle of PCM is that <a id="I_indexterm7_tt1031" class="indexterm"></a><a id="I_indexterm7_tt1032" class="indexterm"></a>the amplitude<sup>[<a id="id4136462" href="#ftn.id4136462">91</a>]</sup>of the analog waveform is sampled at specific intervals
so that it can later be re-created. The amount of detail that is
captured is dependent both on the bit resolution of each sample and on
how frequently the samples are taken. A higher bit resolution and a
higher sampling rate will provide greater accuracy, but more bandwidth
will be required to transmit this more detailed information.</p><p>To get a better idea of how PCM works, consider the waveform
displayed in <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-2" title="Figure 7.2. A simple sinusoidal (sine) wave">Figure 7.2, “A simple sinusoidal (sine) wave”</a>.</p><p>To digitally encode the wave, it must be sampled on a regular
basis, and the amplitude of the wave at each moment in time must be
measured. The process of slicing up a waveform into moments in time
and measuring the energy at each moment is <a id="I_indexterm7_tt1033" class="indexterm"></a><a id="I_indexterm7_tt1034" class="indexterm"></a>called <span class="emphasis"><em>quantization</em></span>, or
<span class="emphasis"><em>sampling</em></span>.</p><p>The samples will need to be taken frequently enough and will
need to capture enough information to ensure that the far end can
re-create a sufficiently similar waveform. To achieve a more accurate
sample, more bits will be required. To explain this concept, we will
start with a very low resolution, using four bits to represent our
amplitude. This will make it easier to visualize both the quantization
process itself and the effect that resolution has on quality.</p><p><a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-3" title="Figure 7.3. Sampling our sine wave using four bits">Figure 7.3, “Sampling our sine wave using four bits”</a> shows the information
that will be captured when we sample our<a id="I_indexterm7_tt1035" class="indexterm"></a> sine wave at four-bit resolution.</p><div class="figure"><a id="asterisk-CHP-7-FIG-2"></a><p class="title"><b>Figure 7.2. A simple sinusoidal (sine) wave</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1036"></a><img src="figs/web/ast2_0702.png" alt="A simple sinusoidal (sine) wave" /></div></div><div class="figure"><a id="asterisk-CHP-7-FIG-3"></a><p class="title"><b>Figure 7.3. Sampling our sine wave using four bits</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1037"></a><img src="figs/web/ast2_0703.png" alt="Sampling our sine wave using four bits" /></div></div><p>At each time interval, we measure the amplitude of the wave and
record the corresponding intensity—in other words, we sample it. You
will notice that the four-bit resolution limits our accuracy. The
first sample has to be rounded to <code class="literal">0011</code>, and the next quantization yields a
sample of <code class="literal">0101</code>. Then comes <code class="literal">0100</code>, followed by <code class="literal">1001</code>, <code class="literal">1011</code>, and so forth. In total, we have 14
samples (in reality, several thousand samples must be taken per
second).</p><p>If we string together all the values, we can send them to the
other side as:</p><a id="I_programlisting7_tt1038"></a><pre class="programlisting">0011 0101 0100 1001 1011 1011 1010 0001 0101 0101 0000 1100 1100 1010</pre><p>On the wire, this code might look something like <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-4" title="Figure 7.4. PCM encoded waveform">Figure 7.4, “PCM encoded waveform”</a>.</p><div class="figure"><a id="asterisk-CHP-7-FIG-4"></a><p class="title"><b>Figure 7.4. PCM encoded waveform</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1039"></a><img src="figs/web/ast2_0704.png" alt="PCM encoded waveform" /></div></div><p>When the far end’s digital-to-analog (D/A) converter<a id="I_indexterm7_tt1040" class="indexterm"></a> receives this signal, it can use the information to
plot the samples, as shown in <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-5" title="Figure 7.5. Plotted PCM signal">Figure 7.5, “Plotted PCM signal”</a>.</p><div class="figure"><a id="asterisk-CHP-7-FIG-5"></a><p class="title"><b>Figure 7.5. Plotted PCM signal</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1041"></a><img src="figs/web/ast2_0705.png" alt="Plotted PCM signal" /></div></div><p>From this information, the waveform can be reconstructed (see
<a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-6" title="Figure 7.6. Delineated signal">Figure 7.6, “Delineated signal”</a>).</p><div class="figure"><a id="asterisk-CHP-7-FIG-6"></a><p class="title"><b>Figure 7.6. Delineated signal</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1042"></a><img src="figs/web/ast2_0706.png" alt="Delineated signal" /></div></div><p>As you can see if you compare <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-2" title="Figure 7.2. A simple sinusoidal (sine) wave">Figure 7.2, “A simple sinusoidal (sine) wave”</a> with <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-6" title="Figure 7.6. Delineated signal">Figure 7.6, “Delineated signal”</a>, this reconstruction of the waveform
is not very accurate. This was done intentionally, to demonstrate an
important point: the quality of the digitally encoded waveform is
affected by the resolution and rate at which it is sampled. At too low
a sampling rate, and with too low a sample resolution, the audio
quality will not be acceptable.</p></div><div class="sect3" lang="en" xml:lang="en"><div class="titlepage"><div><div><h4 class="title"><a id="asterisk-CHP-7-SECT-2.1.2"></a>Increasing the sampling resolution and rate</h4></div></div></div><p>Let’s take another look at our original waveform, this time
using five bits to define our quantization intervals (<a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-7" title="Figure 7.7. The same waveform, on a higher-resolution overlay">Figure 7.7, “The same waveform, on a higher-resolution overlay”</a>).</p><div class="figure"><a id="asterisk-CHP-7-FIG-7"></a><p class="title"><b>Figure 7.7. The same waveform, on a higher-resolution overlay</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1043"></a><img src="figs/web/ast2_0707.png" alt="The same waveform, on a higher-resolution overlay" /></div></div><div class="tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title"><a id="asterisk-CHP-7-NOTE-39"></a>Tip</h3><p>In reality, there is no such thing as five-bit PCM. In the
telephone network, PCM samples are encoded using eight
bits.<sup>[<a id="asterisk-CHP-7-FN-6" href="#ftn.asterisk-CHP-7-FN-6">92</a>]</sup></p></div><p>We’ll also double our sampling frequency. The points plotted
this time are shown in <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-8" title="Figure 7.8. The same waveform at double the resolution">Figure 7.8, “The same waveform at double the resolution”</a>.</p><div class="figure"><a id="asterisk-CHP-7-FIG-8"></a><p class="title"><b>Figure 7.8. The same waveform at double the resolution</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1044"></a><img src="figs/web/ast2_0708.png" alt="The same waveform at double the resolution" /></div></div><p>We now have twice the number of samples, at twice the
resolution. Here they are:</p><p><a id="I_programlisting7_tt1045"></a></p><pre class="programlisting">00111 01000 01001 01001 01000 00101 10110 11000 11001 11001 11000 10111
10100 10001 00010 00111 01001 01010 01001 00111 00000 11000 11010 11010
11001 11000 10110 10001</pre><p>When received at the other end, that
information can now be plotted as shown in <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-9" title="Figure 7.9. Five-bit plotted PCM signal">Figure 7.9, “Five-bit plotted PCM signal”</a>.</p><div class="figure"><a id="asterisk-CHP-7-FIG-9"></a><p class="title"><b>Figure 7.9. Five-bit plotted PCM signal</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1046"></a><img src="figs/web/ast2_0709.png" alt="Five-bit plotted PCM signal" /></div></div><p>From this information, the waveform shown in <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-10" title="Figure 7.10. Waveform delineated from five-bit PCM">Figure 7.10, “Waveform delineated from five-bit PCM”</a> can then be generated.</p><p>As you can see, the resultant waveform is a far more accurate
representation of the original. However, you can also see that there
is still room for improvement.</p><div class="tip" style="margin-left: 0.5in; margin-right: 0.5in;"><h3 class="title"><a id="asterisk-CHP-7-NOTE-40"></a>Tip</h3><p>Note that 40 bits were required to encode the waveform at
4-bit resolution, while 156 bits were needed to send the same
waveform using 5-bit resolution (and also doubling the sampling
rate). The point is, there is a tradeoff: the higher the quality of
audio you wish to encode, the more bits required to do it, and the
more bits you wish to send (in real time, naturally), the more
bandwidth you will need to consume.</p></div><div class="figure"><a id="asterisk-CHP-7-FIG-10"></a><p class="title"><b>Figure 7.10. Waveform delineated from five-bit PCM</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1047"></a><img src="figs/web/ast2_0710.png" alt="Waveform delineated from five-bit PCM" /></div></div></div><div class="sect3" lang="en" xml:lang="en"><div class="titlepage"><div><div><h4 class="title"><a id="asterisk-CHP-7-SECT-2.1.3"></a>Nyquist’s Theorem</h4></div></div></div><p>So how much sampling is enough? <a id="I_indexterm7_tt1048" class="indexterm"></a>That very same question was considered in the 1920s by
an electrical engineer (and AT&T/Bell employee) named Harry
Nyquist. Nyquist’s Theorem states: “When sampling a signal,
the<a id="I_indexterm7_tt1049" class="indexterm"></a> <span class="emphasis"><em>sampling frequency</em></span> must be greater
than twice the bandwidth of the input signal in order to be able to
reconstruct the original perfectly from the sampled version.”<sup>[<a id="asterisk-CHP-7-FN-7" href="#ftn.asterisk-CHP-7-FN-7">93</a>]</sup></p><p>In essence, what this means is that to accurately encode an
analog signal you have to sample it twice as often as the total
bandwidth you wish to reproduce. Since the 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.</p></div><div class="sect3" lang="en" xml:lang="en"><div class="titlepage"><div><div><h4 class="title"><a id="asterisk-CHP-7-SECT-2.1.4"></a>Logarithmic companding</h4></div></div></div><p>So, we’ve gone over the basics<a id="I_indexterm7_tt1050" class="indexterm"></a><a id="I_indexterm7_tt1051" class="indexterm"></a> 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 sample rate needed to accurately 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.</p><p><span class="emphasis"><em>Companding</em></span> 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.</p><p>Two companding methods are commonly <a id="I_indexterm7_tt1052" class="indexterm"></a>employed: μlaw<sup>[<a id="asterisk-CHP-7-FN-8" href="#ftn.asterisk-CHP-7-FN-8">94</a>]</sup> 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.</p><p>Companding divides the waveform <a id="I_indexterm7_tt1053" class="indexterm"></a>into <span class="emphasis"><em>cords</em></span>, each of which has
several <span class="emphasis"><em>steps</em></span>. Quantization 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 companding 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 eight-bit, not
five-bit, resolution).</p><p><a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-11" title="Figure 7.11. Five-bit companding">Figure 7.11, “Five-bit companding”</a> illustrates five-bit
companding. As you can see, amplitudes near the zero-crossing point
will be sampled far more accurately than higher amplitudes (either
positive 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.</p><div class="figure"><a id="asterisk-CHP-7-FIG-11"></a><p class="title"><b>Figure 7.11. Five-bit companding</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1054"></a><img src="figs/web/ast2_0711.png" alt="Five-bit companding" /></div></div><p>A quantized sample might look like <a href="asterisk-CHP-7-SECT-2.html#asterisk-CHP-7-FIG-12" title="Figure 7.12. Quantized and companded at 5-bit resolution">Figure 7.12, “Quantized and companded at 5-bit resolution”</a>. It yields the following bit
stream:</p><div class="figure"><a id="asterisk-CHP-7-FIG-12"></a><p class="title"><b>Figure 7.12. Quantized and companded at 5-bit resolution</b></p><div class="mediaobject"><a id="I_mediaobject7_tt1055"></a><img src="figs/web/ast2_0712.png" alt="Quantized and companded at 5-bit resolution" /></div></div><a id="I_programlisting7_tt1056"></a><pre class="programlisting">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</pre></div><div class="sect3" lang="en" xml:lang="en"><div class="titlepage"><div><div><h4 class="title"><a id="asterisk-CHP-7-SECT-2.1.5"></a>Aliasing</h4></div></div></div><p>If you’ve ever watched the wheels<a id="I_indexterm7_tt1057" class="indexterm"></a> on a wagon turn backward in an old Western movie,
you’ve seen the effects of aliasing. The frame rate of the movie
cannot keep up with the rotational frequency of the spokes, and a
false rotation is perceived.</p><p>In a digital audio system (which the modern PSTN arguably is),
aliasing always occurs if frequencies that are greater than one-half
the sampling rate are presented to the<a id="I_indexterm7_tt1058" class="indexterm"></a> analog-to-digital (A/D) converter. In PSTN, that
includes any audio frequencies above 4,000 Hz (half the sampling rate
of 8,000 Hz). This problem is easily corrected by passing the audio
through a low-pass filter<sup>[<a id="asterisk-CHP-7-FN-9" href="#ftn.asterisk-CHP-7-FN-9">95</a>]</sup> before presenting it to the A/D converter.<a id="I_indexterm7_tt1059" class="indexterm"></a><a id="I_indexterm7_tt1060" class="indexterm"></a><sup>[<a id="id4137541" href="#ftn.id4137541">96</a>]</sup></p></div></div><div class="footnotes"><br /><hr width="100" align="left" /><div class="footnote"><p><sup>[<a id="ftn.asterisk-CHP-7-FN-5" href="#asterisk-CHP-7-FN-5">90</a>] </sup>“The Last Mile” is a term that was originally used to describe
the only portion of the PSTN that had not been converted to fiber
optics: the connection between the central office and the customer.
The Last Mile is more than that, however, as it also has significance
as a valuable asset of the traditional phone companies; they own a
connection into your home. The Last Mile is becoming more and more
difficult to describe in technical terms, as there are now so many
ways to connect the network to the customer. As a thing of strategic
value to telecom, cable, and other utilities, its importance is
obvious.</p></div><div class="footnote"><p><sup>[<a id="ftn.id4136462" href="#id4136462">91</a>] </sup>Amplitude is essentially the power or strength of the
signal. If you have ever held a skipping rope or garden hose and
given it a whip, you have seen the resultant wave. The taller the
wave, the greater the amplitude.</p></div><div class="footnote"><p><sup>[<a id="ftn.asterisk-CHP-7-FN-6" href="#asterisk-CHP-7-FN-6">92</a>] </sup>Other digital audio methods may employ 16 bits or
more.</p></div><div class="footnote"><p><sup>[<a id="ftn.asterisk-CHP-7-FN-7" href="#asterisk-CHP-7-FN-7">93</a>] </sup>Nyquist published two papers, “Certain Factors Affecting
Telegraph Speed” (1924) and “Certain Topics in Telegraph
Transmission Theory” (1928), in which he postulated what became
known as Nyquist’s Theorem. Proven in 1949 by Claude Shannon
(“Communication in the Presence of Noise”), it is also referred to
as the Nyquist-Shannon sampling theorem.</p></div><div class="footnote"><p><sup>[<a id="ftn.asterisk-CHP-7-FN-8" href="#asterisk-CHP-7-FN-8">94</a>] </sup>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.</p></div><div class="footnote"><p><sup>[<a id="ftn.asterisk-CHP-7-FN-9" href="#asterisk-CHP-7-FN-9">95</a>] </sup>A low-pass filter, as its name implies, allows through only
frequencies that are lower than its cut-off frequency. Other types
of filters are high-pass filters (which remove low frequencies)
and band-pass filters (which filter out both high and low
frequencies).</p></div><div class="footnote"><p><sup>[<a id="ftn.id4137541" href="#id4137541">96</a>] </sup>If you ever have to do audio recordings for a system, you
might want to take advantage of the band-pass filter that is built
into most telephone sets. Doing a recording using even high-end
recording equipment can pick up all kinds of background noise that
you don’t even hear until you downsample, at which point the
background noise produces aliasing (which can sound like all kinds
of weird things). Conversely, the phone records in the correct
format already, so the noise never enters the audio stream. Having
said all that, no matter what you use to do recordings, avoid
environments that have a lot of background noise. Typical offices
can be a lot noisier than you’d think, as HVAC equipment can
produce noise that we don’t even realize is there.</p></div></div></div><div class="navfooter"><hr /><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="asterisk-CHP-7-SECT-1.html">Prev</a> </td><td width="20%" align="center"><a accesskey="u" href="asterisk-CHP-7.html">Up</a></td><td width="40%" align="right"> <a accesskey="n" href="asterisk-CHP-7-SECT-3.html">Next</a></td></tr><tr><td width="40%" align="left" valign="top">Analog Telephony </td><td width="20%" align="center"><a accesskey="h" href="index.html">Home</a></td><td width="40%" align="right" valign="top"> The Digital Circuit-Switched Telephone Network</td></tr></table></div><div xmlns="" id="svn-footer"><hr /><p>You are reading <em>Asterisk: The Future of Telephony</em> (2nd Edition for Asterisk 1.4), by Jim van Meggelen, Jared Smith, and Leif Madsen.<br />
This work is licensed under the <a href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Attribution-Noncommercial-No Derivative Works License v3.0</a>.<br />
To submit comments, corrections, or other contributions to the text, please visit <a href="http://oreilly.com/catalog/9780596510480/">http://www.oreilly.com/</a>.</p></div></body></html>
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