The document discusses analog and digital telephone systems and multiplexing techniques. It provides details on: 1) How analog telephone systems work using local loops and trunk lines to connect central offices. 2) The use of frequency division multiplexing and time division multiplexing to combine multiple signals over telephone lines. 3) How digital telephone systems convert analog signals to digital using pulse amplitude modulation, pulse code modulation, and codecs at central offices. 4) The process of quantization and coding used in pulse code modulation to represent analog signals with digital codes.

1. THE TELEPHONE SYTEM AND
MULTIPLEX SYSTEMS
ANALOG TELEPHONE SYSTEMS
F When two computers owned by the same company or
organization and located close to each other need to
communicate, it is often easiest to just run a cable
between them. This is how local area networks work.
F However, when the distances are large, or there are
many computers, or the cables would have to pass
through a public road or other public right of way, the
costs of running private cables are usually prohibitive.
F Consequently, the network designers must rely upon
the existing telecommunication facilities such as the
Public Switched Telephone Network (PSTN).
F The PSTN was designed many years ago with a
completely different goal in mind: transmitting human
voice in a more or less recognizable form. Their
suitability for computer-to-computer communication is
often marginal at best.
The Telephone System and Multiplex Systems 1

2. F The typical error of using telephone lines for computer
communication is about one error per 100,000 bits
sent. The error rate for a direct cable connection
(LAN) is about one error per 10,000,000,000,000 bits
sent.
F However, the situation is changing rapidly with the
introduction of fiber optics and digital technology.
F Analog telephone systems provide either two or four
wires that connect the telephone handset and a local
telephone company central office (also called
switching office or end office).
TELEPHONE
CENTRAL
OFFICE
TELEPHONE TELEPHONE
TELEPHONE
The Telephone System and Multiplex Systems 2

3. The Telephone System and Multiplex Systems 3

4. F The lines connecting the subscriber’s telephone and
the central office are know as local loop lines. Local
loops consist of twisted pairs nowadays, although in
the early days of telephony, uninsulated wires spaced
25 cm apart on telephone poles were common.
F Central offices are connected to each other via toll
offices through high-bandwidth lines called trunk
lines. Trunk connections are often implemented using
coax cables, fiber optics, or microwave transmission.
TELEPHONE TELEPHONE
TOLL
OFFICE
CENTRAL CENTRAL
OFFICE OFFICE
TRUNK LINES
TELEPHONE TELEPHONE
TELEPHONE TELEPHONE
The Telephone System and Multiplex Systems 4

5. F With the advent of digital technology, long-distance
trunk lines within the telephone system are rapidly
being converted to digital. The old system used analog
transmission over copper wires; the new one uses
digital transmission over optical fibers.
F Telephone lines that go through a central office switch
can make two types of connections with other
telephones:
1. Connecting two telephones within the same
central office. In this scenario, the switching
mechanism within the central office sets up
a direct connection between two local loops.
This connection remains intact for the
duration of the call.
2. Connecting two telephones belonging to
different central offices.
In either case, the call requests the closure of electrical
switches to make the connection (circuit-switched
connection).
F Telephone calls between central offices are more
complex than local-loop calls.
F The calls go through trunk lines and these lines
aggregate several telephone calls through wire or fiber
cable.
The Telephone System and Multiplex Systems 5

6. MULTIPLEXING
F Telephone companies have developed elaborate
schemes in combining several conversations over a
single physical trunk line.
F Multiplexing is the process of combining several
signals and transmitting them through the same
channel simultaneously.
F Types of Multiplexing Techniques
1. Frequency Division Multiplexing (FDM)
2. Time Division Multiplexing (TDM)
F Frequency division multiplexing relies on the general
rule that signals with different frequencies, if
transmitted simultaneously, can be easily separated at
the receiver.
If signals have the same frequency, FDM translates
each signal to a new frequency range.
The Telephone System and Multiplex Systems 6

7. 0 4 KHz 60 KHz 64 KHz
0 4 KHz 65 KHz 69 KHz
0 4 KHz 70 KHz 74 KHz
AFTER MULTIPLEXING:
60 KHz
64 KHz
65 KHz
69 KHz
70 KHz
74 KHz
The Telephone System and Multiplex Systems 7

8. The FDM technique of multiplexing requires guard
bands (spaces between adjacent signals) to keep
signals from contaminating each other.
A radio-frequency modem (or RF modem) is just one
of the several devices that can do frequency
translation.
FDM and adequate guard bands allow several
telephone connections to take place through the same
trunk.
The trunk should have a high
bandwidth.
The multiplexed signals should be demultiplexed to
bring the signals back to their original frequencies.
The Telephone System and Multiplex Systems 8

9. DIGITAL TELEPHONE SYSTEMS
F While long-distance trunk lines are now largely digital
in the more advanced countries, the local loops are still
analog and are likely to remain so for at least a decade
or two, due to the enormous cost of converting them.
F To switch from analog-based equipment to digital-
based communications networks requires an analog-to-
digital conversion.
Central
Office
Telephone
Analog Local Loop Digital Trunk
F A codec (coder/decoder) is a device that translates
analog voice signals into digital signals.
The Telephone System and Multiplex Systems 9

10. F Steps in analog-to-digital conversion:
1. Pulse-Amplitude Modulation (PAM). The first
step in analog-to-digital conversion is to convert
the analog signal into discrete signals that have
amplitudes that simulate the original signal
(pulses). This technique is commonly called as
signal sampling.
2. Pulse Code Modulation (PCM). PCM converts
the stream of continuously varying PAM signals
into a stream of binary digital signals
PCM requires two steps:
A. Quantization. This reduces the PAM
signal to a limited number of discrete
amplitudes.
B. Coding. This converts each PAM pulse
into a binary word.
The Telephone System and Multiplex Systems 10

11. F Pulse-Amplitude Modulation
A PAM signal consists of a sequence of pulses in
which the amplitude of each pulse is proportional to
the amplitude of the analog information signal at the
corresponding point where the sample was taken.
analog
information
signal
x(t)
fs
P
sampling
pulse
0
train
p(t)
sampled-data
signal
xs(t)
Ts
The Telephone System and Multiplex Systems 11

12. F A sampling pulse train, p(t), guides the sampling
process.
F In order for the sampling to take place, x(t) should be
observed during short intervals of time of width τs
seconds (which is the aperture time), which
corresponds to a pulse. So at the presence of a pulse,
the system takes a sample.
F The system takes a sample after every Ts seconds,
where Ts is the sampling period (the time between the
beginning of one sample to the beginning of the next
sample). From this, the sampling rate f s = 1 / Ts
samples per second.
F Therefore, the amplitudes of the pulses in the pulse
train are modulated by the information signal. In other
words, this train of pulses acts as the carrier instead of
the usual analog sine wave.
F The amplitude of the pulses of the sampled-data signal
xs(t) corresponds to the amplitude of the modulating
signal x(t) at the point where it was sampled
F The frequency of the sampling pulse train (the number
of samples per second) should be at least 2 x the
highest frequency of the analog signal. This is known
as Shannon’s Sampling Theorem.
The Telephone System and Multiplex Systems 12

13. F Pulse-Code Modulation
For the discussions, assume that the number of bits to
be used is n = 4 bits. This choice results in m = 24 =
16 digital or PCM words.
Natural Binary Decimal Unipolar Bipolar
Number Value Normalized Normalized
Decimal Value Decimal Value
0000 0 0/16 = 0.0000 -8/8 = -1.000
0001 1 1/16 = 0.0625 -7/8 = -0.875
0010 2 2/16 = 0.1250 -6/8 = -0.750
0011 3 3/16 = 0.1875 -5/8 = -0.625
0100 4 4/16 = 0.2500 -4/8 = -0.500
0101 5 5/16 = 0.3125 -3/8 = -0.375
0110 6 6/16 = 0.3750 -2/8 = -0.250
0111 7 7/16 = 0.4375 -1/8 = -0.125
1000 8 8/16 = 0.5000 0/8 = 0.000
1001 9 9/16 = 0.5625 1/8 = 0.125
1010 10 10/16 = 0.6250 2/8 = 0.250
1011 11 11/16 = 0.6875 3/8 = 0.375
1100 12 12/16 = 0.7500 4/8 = 0.500
1101 13 13/16 = 0.8125 5/8 = 0.625
1110 14 14/16 = 0.8750 6/8 = 0.750
1111 15 15/16 = 0.9375 7/8 = 0.875
The Telephone System and Multiplex Systems 13

14. Because of the different possible voltage levels and
the widely different decimal values of the binary
number system as the number of bits is changed, it is
frequently desirable to normalize the levels of both the
analog signal and the digital words so that the
maximum magnitudes of both forms have (or at least)
approached unity.
Normalized Input = Actual Input Analog Voltage
Analog Voltage FSV of A/D Converter
where FSV = Full-Scale Voltage
Actual Output = Normalized Value of x FSV of
Analog Voltage Digital Word DAC
Two Most Common Forms Employed in A/D
Conversion
1. Unipolar
2. Bipolar
The Telephone System and Multiplex Systems 14

15. Unipolar Encoding
The unipolar representation is most appropriate
when the analog signal x(t) is always of one
polarity (including zero). If the signal is negative,
it can be inverted before sampling.
The normalized range, x, is therefore:
0≤x<1
Let xu be the unipolar quantized decimal
representation of x following the A/D conversion.
The maximum value of xu is therefore:
xu(max) = 1 - 2-n
Let ∆xu be the normalized step size, which
represents in a decimal value the difference
between successive levels.
∆xu = 2-n
The Telephone System and Multiplex Systems 15

16. Bipolar Encoding
The bipolar representation is most appropriate
when the analog signal x(t) has both polarities.
The normalized range, x, is therefore:
-1 ≤ x < 1
Let xb be the bipolar quantized decimal
representation of x following the A/D conversion.
The maximum value of xb is therefore:
xb(max) = 1 - 2-n + 1
Let ∆xb be the normalized step size, which
represents in a decimal value the difference
between successive levels.
∆xb = 2-n + 1
The Telephone System and Multiplex Systems 16

17. Quantization may be done in two ways:
1. Rounding. The sampled value of the analog
signal is assigned to the nearest quantized
level.
2. Truncation. The sampled value is adjusted
to the next lowest quantized level.
Example:
A certain 5-bit A/D converter with a FSV of 8V is
to be employed in a binary PCM system. The
input analog signal is adjusted to cover the range
from zero to slightly under 8V, and the converter
is connected for unipolar encoding.
1. What is the normalized step size?
2. What is the actual step size in volts?
3. What is the normalized maximum quantized
analog level?
4. What digital word would the value 0.51 V
correspond to?
5. What voltage would the digital word 00101
correspond to?
The Telephone System and Multiplex Systems 17

18. Solution:
1. Normalized Step Size
∆xu = 2-n
= 2-5
= 0.03125
2. Actual Step Size
Actual Step Size = ∆xu x FSV
= 0.03125 x 8
= 0.25 v
3. Normalized Maximum Quantized Analog
Level
xu(max) = 1 - 2-n
= 1 - 2-5
= 0.96875
The Telephone System and Multiplex Systems 18

19. Natural Binary Decimal Unipolar Normalized Actual Value
Number Value Decimal Value in volts
00000 0 0/32 = 0.0000 0v
00001 1 1/32 = 0.03125 0.25 v
00010 2 2/32 = 0.0625 0.5 v
00011 3 3/32 = 0.09375 0.75 v
00100 4 4/32 = 0.125 1.0 v
00101 5 5/32 = 0.15625 1.25 v
00110 6 6/32 = 0.1875 1.5 v
00111 7 7/32 = 0.21875 1.75 v
. . . .
. . . .
. . . .
11011 27 27/32 = 0.84375 6.75 v
11100 28 28/32 = 0.875 7.0 v
11101 29 29/32 = 0.90625 7.25 v
11110 30 30/32 = 0.9375 7.50 v
11111 31 31/32 = 0.96875 7.75 v
4. What digital word would the value 0.51 V
correspond to?
00010
5. What voltage would the digital word 00110
correspond to?
1.5 v
The Telephone System and Multiplex Systems 19

20. Rounding or truncation always results in quantization
error since the rounded or truncated value can never
be recovered at the receiver side.
For unipolar representation:
Normalized Resolution = ± ½ ∆xu = ± 2-(n+1)
Actual Resolution = ± 2-(n+1) x FSV
% Resolution = ± 2-(n+1) x 100%
For bipolar representation:
Normalized Resolution = ± ½ ∆xb = ± 2-n
Actual Resolution = ± 2-n x FSV
% Resolution = ± 2-n x 100%
To minimize quantization errors, the system should use
more bits.
The Telephone System and Multiplex Systems 20

21. Example:
A certain 5-bit A/D converter with a FSV of 8V is
to be employed in a binary PCM system. The
input analog signal is adjusted to cover the range
from zero to slightly under 8V, and the converter
is connected for unipolar encoding.
1. What is the normalized resolution?
2. What is the actual resolution in volts?
Solution:
Normalized Resolution = ± ½ ∆xu = ± 2-(n+1)
= ± 2-(5+1)
= ± 0.015625
Actual Resolution = ± 2-(n+1) x FSV
= ± 0.015625 x 8
= ± 0.125 v
The Telephone System and Multiplex Systems 21

22. F Time division multiplexing is used to combine several
digital voice signals into one channel. This technique
interleaves more than one individual digital signal into
another channel by giving each original signal time
slots in the multiplexed channel.
1 ADC DAC 1
Telephone Telephone
TIME DIVISION MULTIPLEXER
TIME DIVISION MULTIPLEXER
2 ADC DAC 2
Telephone Telephone
n ADC DAC n
Telephone Telephone
MULTIPLEXED DATA:
byte 2 byte 2 byte 2 byte 1 byte 1 byte 1
from from from from from from
... channel ... channel channel channel ... channel channel
n 2 1 n 2 1
The Telephone System and Multiplex Systems 22

23. F Case Study: T1 Channel Banks
AT&T combines 24 digitized voice signals into one
high-capacity channel called the T1 Carrier.
TIME DIVISION MULTIPLEXER
1
Telephone
CODEC T1 Channel
2
Telephone 1.544 Mbps
24
Telephone
Central Office
data rate
per phone = 8000 samples/sec x 8
bits/sample
(output of
each codec)
= 64,000 bps
total data
rate of T1 = 64,000 bps x 24 = 1.536
Mbps
The Telephone System and Multiplex Systems 23

24. channel
The Telephone System and Multiplex Systems 24