Bdatach4

C H A P T E R 4

Multichannel Data Communication

4.1 INTRODUCTION

Although digital communications offer many advantages over analog, one may have to deal withmany analog components and systems in a total communication system design. Figure 4.1 showshow a complete communication system looks from signal perspective.

Figure 4.1Complete communica-tion system

Central Office

PersonalComputer

ComputerPersonal

TimeDivision

Multiplexers

MultiplexersDivision

Time

Central Office

Modem

Modem

Local LoopAnalog

AnalogLocal Loop

T1CarrierTrunk

Binary Signal Modulated Analog Signal Digital Signal

Modulated Analog SignalBinary Signal Digital Signal

80 Data Communication

A good understanding of the differences between these digital and analog signals and how tobring the two together is the key to connectivity. The communications channels provide the linkfor data communications.

You will note in Figure 4.1 that the link between the PC to the central office or telephoneexchange is by modulated analog signal created by the modem. The communication betweenexchange or central office to another trunk exchange or central office is by digital signal usingtime division multiplexers (codecs). The final communication between the trunk exchange and thePC is again by using modulated analog signal. Modem at the other end converts this analog signalto digital signal to be detected by the PC.

Figure 4.2 (a)Analog signal showing asine wave,represen-tative of apure tone

The difference between the two basic forms of electronic communication, namely, analog anddigital is a little like the difference between water streaming from a hose and bullets firing from aa machine gun. An analog signal is a continuous electro magnetic wave, whose pattern varies torepresent the message being transmitted. A digital signal, by contrast is a series of discrete elec-tronic burst and the bursts indicate the message.

Figure 4.2 (a) shows analog signal. The key characteristics of an analog signal includestrength, or amplitude (vertical distance between a wave trough and crest) and frequency (thenumber of times per second the wave cycle repeats).

Figure 4.2 (b)Typical sound signalin Analogform

Figure 4.2(b) shows a typical analog signal, the many variations in amplitude and frequencyconvey the gradations of loudness and pitch in speech or music. Similar signals are used to trans-mit television pictures, but at much higher frequencies. Telephone equipment allows the voice aband width of 4,000 hertz, which includes a guard band at top and bottom to prevent interference.T.V. Signals a band width of four million hertz (4 MHZ).

Electronic Analogs for Sound

One Cycle

0 hertz

3,400 hertz

250 hertz

4,000 hertz

Multichannel Data Communication 81

Figure 4.2(c) shows the binary digital form of electronic signal. Computer messages are com-posed of bytes, or groups of binary digits (group of eight bits) conveys the presence or absence ofvoltage in an electronic signal. For the byte shown in Figure 4.2(c) the voltage goes successivelyoff, on, off, off, off, off, off, on.

Figure 4.2 (c)Electronic pulses forBinary Digits

Figure 4.2 (d)Two digital signals withdifferent bitsper secondrate

Figure 4.2(d) shows two digital signals, each made up of 0s (zero volts, white space) and 1s(five-volt pulses), are depicted as transmitted at different rates over a 1/50- second interval. Thetop signal carries 300 bits per second (bps) the bottom one 2,400 bps.

4.2 CIRCUITS, CHANNELS AND CONCEPT OF MULTICHANNELLING

If every message had to move single file through every link in the global telecommunications net-work, like bicyclists on a narrow path communications would be hopelessly slow and costly.But, if at some point the bicyclist can be loaded onto buses and sent down a multi-lane highway,traffic is enormously speeded. That, in effect, is what happens when many signals from telephones

Byte

0 1 0 0 0 0 0 1Bit

Off On OffOff OffOff Off On

0 Volts

5 Volts

5 Volts

0 Volts


or computers reach a local exchange or central office on their way across a big city. This "multi-plexing" allows multiple streams of electronic messages to be transmitted over the same connec-tion in the time otherwise required for one message.

4.2.1 Frequency Division Multiplexing (FDM)

Frequency Division Multiplexing abbreviated as FDM is a method of sharing a transmissionchannel by dividing the band width into several parallel paths, defined and separated by guardbands of different frequencies. All signals are carried simultaneously.

Multiplexing is effected in two major ways namely, frequency division multiplexing (FDM)and time-division multiplexing (TDM). The older of the two, FDM, is used with analog transmis-sion.

The analog signal is impressed on another analog signal of different frequency a carrieraltering the carrier’s shape so that it bears the pattern of the message. The carrier frequency gen-erally remains constant. Only its amplitude varies, at the rate corresponding to that of the messagesignal. Since each carrier has a different frequency, carriers can be stacked on top the other andsent together over a cable or microwave radio link capable of carrying a broad range of frequen-cies. The carriers are then separated at the other end. The greater the medium’s band width, themore carriers it can transmit, and more messages it can handle simultaneously.

Figure 4.3 Frequency Division Multiplexing of voice channels

Figure 4.3 shows the FDM of voice channels. The telephone exchange takes each voice chan-nel and modulates the signal to a higher frequency as shown.

300 3300

1000 2000 3000 4000

Frequency (Hz)

Am

plitu

de (

Vol

ts)

Voice Bandwidth

Voice Channel

3300

1000 2000 3000

Frequency (Hz)

Voice Bandwidth

Am

plitu

de (

Vol

ts)

300

4000

Voice Channel

Voice Bandwidth

1000

Frequency (Hz)

300

Am

plitu

de (

Vol

ts)

30002000 4000

3300

Voice Channel

2000

Frequency (Hz)

Voice Bandwidth

300

1000

Am

plitu

de (

Vol

ts)

40003000

3300

Voice Channel

40,000 50,000 60,000 70,000 80,000

Frequency (Hz)

Frequency DivisionChannel Bandwidth

OriginalSpeech

A BSpeechOriginal Original

SpeechC

A

B

C

CarrierFrequency

A


Figure 4.4(a)Frequency DivisionMultiplexingwith guardband

Each voice signal starts out in the 300 to 3,300 Hz range. The exchanges modulates the signalto a new frequency range with a clear space called a guard band between each signal. (See Figure4.3) The first signal might have a range of 60,000 to 63,000. The second signal then starts at64,000 and ends at 67,000, thus providing a 1,000 Hz guard band between the two signals. Thethird signal starts at 68,000.

The FDM technique of multiplexing requires guard bands to keep signals from contaminatingeach other. If the signals are modulated to new frequency ranges and does not provide sufficientseparation, then the extraneous signals would create noise called cross talk. Thus FDM and ade-quate guard band allow several telephone connections to take place through the same trunk. [SeeFigure 4.4 (a)]

74

1 2 36

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74

1 2 36

85 9

0*

#

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1 2 36

85 9

0*

#

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#

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0*

#

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1 2 36

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0*

#

Central OfficeA B

Central Office

Trunk

Frequency DivisionMultiplex Trunk

Signal

MultiplexedSignalOriginal

Analog

Guard Band

Guard Band


Figure 4.4(b)Mixer

Figure 4.5(a)Group struc- ture for ana-log telephonemodulation

Mixersin[2 fs]π

(Source Signal)

πsin[2 fc](Carrier Signal)

Low PassFilter

sin[2 (fc - fs)]π

πsin[2 (fc + fs)]

sin[2 fc]π

πsin[2 (fc - fs)]

sin[2 fs]π

74

1 2 36

85 9

0*

#1

FrequencyDivision

Multiplexor

74

1 2 36

85 9

0*

#2

74

1 2 36

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0*

#3

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1 2 36

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0*

#4

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0*

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1 2 36

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0*

#

12

11

Central Office

12 VoiceChannels

48,0

00 H

z B

andw

idth

MultiplexTrunk

GroupChannel


4.2.2 FDM GROUPS

All voice-grade channels have a bandwidth of 0 to 4 kHz. In order to be transmitted as part of abroadband signal, the voice channel is mixed with a carrier frequency. A Mixer is a nonlinear cir-cuit that produces the original signal and the sum and difference frequencies of two input waveforms. When a balanced modulator is used as the mixer’s output, all frequencies above thedifference frequency are filtered out, so that the mixer/filter circuit only produces the differencefrequency. [See Figure 4.4 (b)]

Figure 4.5(a) shows the basic building block of groups of channels used on the analog tele-phone lines. These Channel Group use FDM to convey 12 voice channels through one trunk witha 48,000 Hz bandwidth. Each voice channel can convey voice signals or data communicationssignals.

Figure 4.5(b)A twelve- channelgroup

Mixer

LPFChannel 1

0 - 4 kHz

f = 108 kHzC

104 - 108 kHz

f = 104 kHz

0 - 4 kHz

Channel 2

C

LPF100 - 104 kHz

f = 100 kHz

0 - 4 kHz

Channel 3

C

96 - 100 kHzLPF

f = 64 kHz

0 - 4 kHz

C

Channel 12 LPF60 - 64 kHz

Channels4 - 11

1

2

3

12

Group60 - 108 kHz

LPF : Low Pass Filter


Figure 4.5(c)FDM multi- plexerGroups as perAT & T

The telephone communication system has a set of standards that specify the frequency alloca-tions for a broadband FDM system. The standard begins with twelve voice channels, each mixedwith carrier signals that are 4 kHz apart. These carrier signals a single Group channel by linearlysumming the outputs of several mixers as shown in Figure 4.5 (b).

Jumbogroup Multiplex

(10,800 Voice Channels)

(600 Voice Channels)

Mastergroup

(12 Voice Channels)

Channelgroup

1 2 3

1 2

1 2 3 4 5 6 7 8 9 10

Jumbogroup


Mastergroup multiplex


321 54

1 2 3 4 5 6 7 8 9 10 11 12Voice Channel


Each mixes a voice channel (0 to 4 kHz) with a carrier signal. The carrier signals are 4 kHzapart, placing each channel adjacent to the next group ranges from 60 kHz to 108 kHz. This 48kHz bandwidth is verified by multiplying 12 channels times 4 kHz per channel, resulting a 48 kHz.Notice that the 60-to-108 kHz bandwidth is well above the telephone system’s 300 Hz to 3 kHzbandwidth. This group channel is meant to be sent by mediums other than voice grade telephonelines. It could be sent on a fiber optic cable that has a larger bandwidth or using a radio microwaveor a satellite transmission. Since both these methods have very large bandwidths compared with48 kHz. As such, larger groupings are created in similar manner to take full advantage of theselarge bandwidth.

4.2.3 Frequency Division Multiplex Subgroups

By repeating the process of creating groups, larger groupings are developed according to thetransmission frequencies increase. Five Groups (sixty channels) are assembled to form a Super-group, which fills a bandwidth between 312 and 552 kHz. The actual bandwidth(552 312 = 240 kHz) equals the five groups (5 × 48), which in turn is equivalent to the sixtychannels (60 × 4 kHz) that make up the five groups. The next level formed from ten supergroups isthe Mastergroup. An additional carrier pilot at 2,840 kHz is inserted at the mastergroup level foramplitude regulation at that level. [See Figure 4.5 (c)]

A Jumbo group is composed of six mastergroups, each master group encompasses ten super-groups, one supergroup contains five groups, each with twelve channels. A Jumbo Mux combinesthree Jumbo groups into a signal channel. By performing a little multiplication, it is determinedthat 3 × 6 × 10 × 5 × 12 = 10,800 channels are carried by a Jumbo mux system.

4.3 TIME DIVISION MULTIPLEXING

FDM suffers from the problem that channels are permanently assigned. Although TDM is moreefficient than FDM, in that it does not require guard bands and it operates directly in digital formbut both are left behind by the advantages of Statistical Time Division Multiplexing (STATDM)which takes advantage of the statistical of data transfer in several sophisticated ways. This permitsthe efficiency of channel use to increase by ten-fold and in some cases even more.

Figure 4.6(a)Conventionalmultipoint communica-tion

Consider the sending of three messages of varying lengths as shown in Figure 4.6 (a). Themain drawback is that message C must wait until messages A and B are sent before it can betransmitted.

SendingStation Station

ReceivingC B A

Time

Header


Figure 4.6(b)Packetedforms of TDM trans-mission

In Figure 4.6(b), the three messages are to be sent to three different places. The three stationsshould receive the messages just at the same time. To solve such a problem, all the three messagesneeds to be reformed into smaller parts called packets. These packets are of equal length, as seenin Figure 4.6 (c).

Figure 4.6(c)Conventionaltransmission

The packets forming messages A, B and C are interleaved and assigned time slots as seen inthe lower diagram of this figure. A header (shaded area), containing the address and packet num-ber information, precedes each packet. The interleaved packet are transmitted and received by thereceiving station. The appropriate packets (determined by destination address in the header) areextracted by each station as they are received and reassembled (by packet number, included in theheader) into their original message form. This is the full operation of Time Division Multiplexing.

The two basic forms of TDM are:(a) Synchronous Time Division Multiplexing (STDM)(b) Asynchronous Time Division Multiplexing (ASTDM) or Statistical TDM (STATDM)

Primary 1Secondary

C B A

Time

A

2SecondaryB

3SecondaryC

C4

8B

3

B7

C2

C4

C1

B6

C

B5

8

A2

B7

C3

B6

C2

B5

B4

B4

B3

B3

C1

B2

A1

B1

B2

B

B1

2A

1A

(a) Packet Forms

(b) TDM Time Slot Frame

Time

Headers


4.3.1 Synchronous Time Division Multiplexing (STDM)

Synchronous TDM assigns time slots of equal length to all packets regardless whether or not any-thing is to be sent by each station with an assigned time slot. For example, if message A has notincluded, then its allotted time would still be allocated. It would still be allotted time but time slotsfor message A would not contain information.

STDM systems are comparatively easy to implement once the software allocates the time slots.

4.3.2 Statistical Time Division Multiplexing (STATDM)

STATDM does not make a fixed assignment of time slots so that any port which is idle does notreceive a (full) slot. In order to identify which slot corresponds to which data stream, it is neces-sary to append address and control symbols to each slot that is used. This "overhead" is usuallysmall and is more than compensated for by the increased efficiency derived from not having totake up channel space with idle bits.

These systems are more complex but allow for a means of reassigning time slots that are not inuse. STATDM networks assign time slots only when they are to be used and delete them whenthey are idle. The total time used for a STATDM frame varies with the amount of traffic currentlybeing handled. STATDM systems are most suitable for these high-density, high-traffic applica-tions. The continuous messages are assigned time slots and interleaved as each channel on thesend side becomes active and requires communications with another channel. If a channel does nothave any traffic, its time slots are deleted and reassigned to an active channel. In this way theinterconnecting media achieves a higher state of efficiency that with STDM systems.

Figure 4.6(d) illustrates the comparison of FDM, TDM and Statistical TDM with fixed frameand variable frame methods. In the variable-frame method, the size of the slots and the frame arenot fixed but depend on the data itself. Statistical TDM are also built either for asynchronous dataor synchronous data or both.

TDM and STATDM require a modem in order to interface with the voice line, but this may bebuilt in. All modern STATDMs have at least one and usually many microprocessors with pro-grammed and programmable functions of great diversity available that are varied and above thebasic multiplexer functions. They are thus named as "Smart" or "Intelligent MUXs."

Data Compression

Data compression is a technique by which the efficiency of transmission can be increased in therange of about 50%. You will find, that in any sequence of data representing a natural language,such as English, some letters and symbols occur much more frequently than others. For example, aSPACE occurs about 17% of the time, the lowercase letters e, t, a, i, and r collectively occur about30% of the time, whereas uppercase letters J, Z and W occur less than 0.1% of the time. Therefore,why assign the same number of bits (7 plus 1 parity in ASCII) to all including the rarely usedcontrol characters? The better way is to assign a few bits to the most frequently occurring symbolsand the larger number pf notes (if necessary)


Figure 4.6(d)Differenttypes of data multiplexing

to those rare ones. That way, the average length will be small. In order to be able to uniquelydecipher a string of these variable-length codewords without separators, the prefix of any code-word that represents a character, itself, cannot be a (shorter) codeword representing another char-acter. Techniques for accomplishing this assignment, in an optimum way which reduces the

1 2 3 4 5 N

Empty

N 1 2 3 4 N 1 2

(a) Frequency division multiplexing; all frequency channels are permanently

Empty

(b) Time - division multiplexing; all time slots are permanently assigned

(c) Statistical time - division multiplexing (fixed frame); time slots are only

A B C N A

(d) Statistical time - division multiplexing (variable frame); the variable

A B C D E E A

Guard Bands Frequency

assigned to corresponding input ports.

TDM Frame

Time

to corresponding input ports.

Addressing and Control Overhead

assigned to active ports.

time slots are only assigned to active ports.


average number of bits/character to the minimum possible, have been well known. The codes arecalled Huffman codes. The use of variable-length bit representation of characters requires specialhandling of encoding and decoding and STATDM becomes a variable frame type.

4.3.3 Multichannel TDM

Many channels of communication on a single line are managed by a Broadband system. In thismethod, each channel occupies a portion of that bandwidth. This would require the bandwidth ofthe system to be larger so as to contain all the channels. Multichannel use of a TDM system relieson sharing transmission time periods rather than a system’s bandwidth. (See Figure 4.7)

Figure 4.7MultichannelTDM System

4.3.4 Sampling using TDM

When we sample two or more signals at different times, then we use the technique of samplingusing TDM. The samples are all sent and extracted at the receiver according to their time relation-ship. In brief, the samples of one signal will be assigned to specific time slots, while samples fromother signals occupy different time slots. Figure 4.8 shows the sampling of two signals at one time.

Let us assume that the signals A and B have the same frequency and are sampled at the sameNyquist rate. Signal A is sampled at time t0. Samples are take at an interval of 1/Sr time periods.The first sample for signal B is taken at a time of t0 + 1/2Sr or halfway between the first two sam-ples for signal A. Each succeeding sample for signal B occurs 1/Sr time period from the last sam-ple. This places the samples for signal B in between the samples for signal A. All the samples aresent sequentially. The receiver extracts the sample pulses starting at t0 and occurring each 1/Sr

following t0. From this the receiver recreates signal A. The receiver also extracts the samplesstarting at t0 + 1/2Sr and each succeeding sample 1/Sr away. From these samples, signal B isreconstructed.

4.3.5 Quantization

Quantization is the process of approximating sample levels into their closest fixed value. The val-ues are preselected and since they are fixed, they are easy to encode. The new waveform called thequantized waveform has either quantum changes in amplitude or no change in amplitude.

Given a signal, fs, with peak voltage point of Vh and Vl, the size (S) of a quantum step isdetermined by the following relationship:

MUX DEMUX

Channel A

Channel B

Channel C

Channel A

Channel B

Channel C

TDM Message

Time

Send Receive


Figure 4.8Sampling twosignals at one time (TDM)

S = (Vh - Vl)/n

Here, n is the number of steps between Vh and Vl. Figure 4.9 shows the relationship between fsand a quantized example. The quantized levels are those fixed levels that are the nearest to fs at thepoint the sample is taken.

The process of sampling and quantizing a signal is a form of pulse amplitude modulation(PAM) where the samples produce pulses of varying amplitudes. When these amplitudes arerestricted to discrete quantized values and assigned specific binary codes which are to be trans-mitted, then a technique called pulse coded modulation is being used.

4.4 PULSE CODE MODULATION (PCM)

Pulse Code Modulation abbreviated as PCM is a digitizing process in which an analog or continu-ous, signal is represented in digital or discrete form. Some of the newer trunking systems, spe-cially within metropolitan areas, have changed to a digital time-division multiplexing (T-carrier)system which uses pulse-code modulation (PCM)

Combined Pulse Train

1/Sr

t0

1/Sr1/2Sr

Signal A

Signal B


Figure 4.9Quantizedsignal

to digitize each voice signal to 64 Kbps. The multiplexing hierarchy is organized (in USA) to col-lect 24-and 64-Kbps channels into a 1.544 Mbps T-1 carrier, then four T-1 carrier into a 6.312Mbps T-2 carrier, with seven T-2 carriers collected into a 44.736 Mbps T-3 carrier. Then six T-3carriers are collected into a 274.176 Mbps T-4 carrier. The T-3 and T-4 carrier levels containing672 and 4032 independent 64 Kbps channels, respectively are currently used on microwaves sys-tems, coaxial cables and fiber-optical cable systems in many networks designed primarily forvoice communications. Similar systems are in use in Europe, Japan and other places but both thesystems are not fully compatible.

4.4.1 Converting Voice to Ones and Zeros

The varying sounds of human speech must first be transformed into discrete pulses to be sent bydigital means. The device for making this transformation is called a codec, a name derived from itsfunction of coding an analog signal into digital form at the sending end and then decoding it backto analog form at the receiving end. These are mainly used at exchanges for routing calls overmain trunk lines. A codec accomplishes its tasks in three stages.

Stage 1

In the first stage, codec does the sampling of the amplitude of the analog signal at very shortintervals. See Figure 4.10(a). The voltage of the signal is measured at discrete intervals.

Stage 2

This is the stage of quantizing or assigning decimal values to the amplitude samples. The result isknown as pulse amplitude modulation (PAM). The value of each voltage sample is

S/2

S

Step Size

Time of a Step

Vl

Vh

fs

Quantum Jump


Figure 4.10(a)Digitizing thevoice

Figure 4.10(b)Digitizing thevoice channel using 8 bitbinaryencoding

Sampling Quantizing

t1

1t t2 3t

t4 5t t6

V = 01001110 = 010110112Vt = 01001010tV 3

= 10011110tV 4

t1V

0

2tV

+Vmax

t∆ =1/8000 sec

1

0

Digital Representation of tV 1

8-Bit Binary Encoding of the Speech sample using

Pulse Code Modulation (PCM)

Vmin

Digital Speech Waveform

Analog Speech Waveform


quantized, or assigned a specific measurement (bars of varying height in Figure 4.10(a), which isthen converted to a digital number expressed in the 1s and 0s of binary code. The digital numberscan then be transmitted.

Stage 3

In this stage, known as pulse code modulation (PCM) , the voltage values are converted, or coded,into binary numbers for digital transmission. Encapsulated in eight-bit bytes, amplitude sampleszip through a communications link as a stream of digital bursts. Figure 4.10 (b) shows the digitalencoding of speech signal.

After the receiving end, the original analog-to-digital conversion is reversed. Voltage valuesare read and the sampled voltages recreated, producing a signal that exactly duplicates the quan-tized one as shown in Figure 4.10(b). A simpler filter converts the samples into a continuous waveand finally, the telephone receiver converts the recreated signal into sound waves. Because therecreated signal depends only on numbers, not on gradations in transmitted voltages, it producessound virtually identical to the original, even over extremely long distances.

PCM Transmitter (Block Diagram)

A typical PCM transmitting system consists of a low-pass filter and amplifying circuit followed bya quantizing and encoding unit. These last two functional blocks are combined into a single analogto digital converter (ADC). The most commonly used analog to digital converter for this purposeis a successive approximations converter. [See Figure 4.10 (c)]

PCM Decoder

A PCM decoder reverses the process of converting the digital to analog equivalent signal. Thedigital data are fed serially into the decoder. Each one of the data bits is reshaped to remove dis-tortions caused by the transfer along the interconnecting medium used. After shaping, the data bitsare fed into a digital to analog converter to produce the quantized samples they

Figure 4.10(c)PCM Trans-mitter Block Diagram Low

PassFilter

Sampler Quantizer EncoderADC

sin(2 fs)(Input Signal)

π

Binary Codes


Figure 4.10(d)PCM Decoder

represent. These samples are held and filtered to recreate the original signal, fs. The differencesbetween the original signal and the recreated one result from quantization error and any possiblebit errors that might occur in the transmission.

4.4.2 Sampling Rate

In order to make sure that speech remains intelligible, a great many samples must be taken. Thesampling rate as per Nyquist Theorem, must be twice that of the highest significant frequency tobe transmitted. Thus for a voice signal, with an upper frequency limit of 4,000 hertz over thephone system, the codec must take 8,000 samples per second. The speech lost between samples,known as the Nyquist interval, is unnoticeable when the signal is decoded at the receiving end.

The sampling rate and the number of quantizing levels determine the bit rate of the digitalcommunications channel. To convey 128 discrete volume levels requires seven binary data bits.The Pulse Code Modulation (PCM) component must generate all seven data bits each time thePulse Amplitude Modulation (PAM) component performs a sample of the analog signal. To oper-ate the system, you need to sample at a rate of 8,000 samples per second and generate seven databits each time. This produces 7 × 8,000 = 56,000 bps.

Figure 4.10(e)Recovering the analogsignal

Besides, the 56 Kbps of digitized voice, these systems provide an additional 8 Kbps for thesystem control. The total bit rate is 64 Kbps. For economies of scale for long-distance communi-cations require vendors to combine several 64-Kbps channels into one channel of larger capacity.

Binary Decoderand Hold

Restorer DACand Filter

Sample

CodeBinary

(Replicated)fs

Coded Values Reconverted Signal

10 10110010 10101001 10101010


By sampling a signal of limited bandwidth at twice its highest frequency, which for speech istaken as 4000 Hz (8000 times per second), it is possible to reproduce the speech signal perfectly.However, the process of assigning a discrete binary number to each sample introduces an errorknown as the quantization error. This unavoidable error is the difference between the actual valueof the analog sample and the nearest value encoded by one of the binary numbers. The averagequantization error is a measure of the trade-off between using a scale with more bits per sample(which yields smaller steps) versus using a coarser scale that requires fewer bits. The standardscale used in USA is an 8-bit nonlinear scale known as µ-law 255. The required bit rate or digitalbandwidth for a PCM encoded speech signal using µ-law 255 is then

8 bits × 8000 samples/second = 64,000 bits/second.PCM encoding according to µ-255 is standard throughout the USA. European countries use a dif-ferent encoding algorithm known as A-law.

4.4.3 Natural Sampling

As seen in Figure 4.11, samples are created by generating a short pulse at the specific time. Theamplitude of the pulse is determined equal to the amplitude of the signal at the time of the sample.The width of the pulse is designated tp and the time period pulses (1/Sr) is Tr. The shapes of thepulses themselves come in two forms. One is called Natural Sampling, in which the peak of thepulse follows the signal’s actual shape. The second pulse form is Flattop shape in which the peakamplitude is held flat by the sample and the hold circuit. (See Figure 4.11 part (d). For the flattopsampling, the reconstructed signal (So) for a given signal f(s) is represented by the relationship:

where tp is the time period for the sampling pulse and Tr is the reciprocal of sampling rate (Sr).Since tp/Tr is the duty cycle of the sampling signal, the relationship of So to sin(2πfs) is a directfactor of that duty cycle.

Example 1

A 3.6 cosf signal is naturally sampled at the rate of 56 kHz using 1.25 microsecond samplingpulses. What is the value of the reconstructed output signal?

Substituting the values in the equation 4.1 we havetp = 1.25 × 10-6, Tr = 1/56 × 103

Therefore So = (1.25 × 10-6 × 3.6 cosf)/(1/56 × 103)Calculating we get So = 0.252 cosf

4.4.4 Sample and Hold

In order to reproduce the waveform accurately, we use the method of Sample and Hold. A samplepulse’s amplitude is detected and that value retained until the occurrence of the next sample pulse.(See Figure 4.12). For this method to be effective, the hold time between samples (TH) is rela-tively small compared with he time period of the original signal.

So =tpTr

sin(2πfs) (4.1)


Figure 4.11Sampling types

The most common method used for sample and hold circuits is to employ a capacitance at theoutput of the buffer amplifier. The capacitor is charged to the sample pulse value. When theamplitude falls to zero between pulses, the capacitor remains charged to the pulse value. The next

t

V(t)

(a) Input Signal Sin(2 fs)

(b) Sampling Pulses at Rate Sr. (Pulse Exaggerated for Clarity)

V(t)

t

(c) Natural Sampling

V(t)

t

V(t)

(d) Flattop Sampling

t

π

Tr tp

Tr = 1/Sr

So

Leadingedge edge

TrailingMidway

Recovered Signal So = (tp/Tr) x sin(2 fs)π


Figure 4.12Sampling and Hold wave-form

sample pulse causes the capacitor to charge or discharge to that value. Again the value is held untilthe next pulse arrives. Figure 4.13 shows the circuit diagram for sample and hold waveform cre-ation for accurate reproduction of the waveform.

Figure 4.13Sampling and Hold Circuit

4.4.5 Coding a Quantized Signal

The range of voltages for signal fs as illustrated in Figure 4.14 is divided into discrete quantizedsteps (S). The signal is sampled at each step, with the resulting amplitude of the samples codedinto binary values. The binary equivalents are actually associated with analog values midwaybetween step amplitudes to minimize errors. These binary codes are shown at the bottom of thefigure. The original waveform is transmitted as a serial stream of binary bits representing thequantized levels of each of the samples. At the receiving station the binary bits are decoded intothe quantized samples and the original signal is reproduced from the resulting samples.

V(t)

timeSample Hold

sin(2 fs)π

V in

V out

Chold

Sample Time


Figure 4.14Codification of a Signal

4.4.6 Companding

One method of increasing the volume of traffic on a given line is to reduce the number of digitalbits that represent a signal to be transmitted without corrupting the signal that is replicated at thereceiving end. It is desirable to compress the digital codes at the transmitter and then expand themback to their original from at the receiver. The acronym for this procedure is Companding (com-pression/expension).

Companding can be done in analog or digital form. In analog companding the signal to bedigitized is companded first and then sampled and digitized. Digital companding reduces the digi-tal code created after the signal has been digitized. Companding is also used to increase thesignal-to-noise ratio of the coded signal.

4.5 CODECS

A CODer/DECoder (CODEC) is a device designed to convert analog signals, such as voice com-munications, into PCM compressed samples to be sent onto digital carriers and to reverse the pro-cess, replicating the original analog signal, at the receiver. The term CODEC signify the pulsecoding/decoding function of the device. These functions are sampling, quantizing, analog todigital and digital to analog conversion, filtering, and companding. All these functions are avail-able on a single CODEC IC chip such as INTEL’s IC 2910. This chip allows the selection of eitherthe American method of digitizing called µ-255 coding or the A-law applicable in Europe andJapan for companding function.

Figure 4.15 illustrates the block diagram of a Codec transmitter. The analog signal is fed intoan operational amplifier, whose gain is set by external resistor components shown as R1 and R2.The gain (Av) for the op amp is given by:

001

3

010

2

011

1

100

0

101

1

110

2

V

3Code

010 011 100 101 110 110 110 100 100 100 100 011 011 100 100Binary Code


Figure 4.15Codec Trans-mitter BlockDiagram

The output of the op amp is fed through an antialiasing filter to a sample and hold circuit. Thepassband filter following the antialiasing filter is designed to yield a flat response from 300 Hz to3 kHz. An additional high-pass filter rejects power line frequencies (50Hz and 60 Hz).

Samples are held for encoding and µ-255 law or A law compression in an internal sample andhold circuit. One additional unit, an auto-zero circuit is used to correct for any DC offsets thatwere created by the process to this point. The compressed PCM serialized data are sent outthrough the Dx transmit data line.

Figure 4.16 illustrates the receiver side of the CODEC. The serial data stream on the datareceive pin (DR) is shifted into the input register and output in parallel to the digital to analogconverter. The resulting analog signal is held in a second internal sample and hold circuit until thenext coded sample is shifted into the input register. The coded samples are then shaped and filteredbefore being sent out through a power amplifier. The filter is a passband filter with a sharp roll-offat 4,000 Hz. It has a flat response between 300 Hz and 3 kHz.

The maximum voltage level from the power amplifier is 1.5 Vrms. The actual output (Vo)between the PWRO outputs is a function of the gain (Ao) of the op amp circuit and can be setanywhere from the maximum of 1.5 Vrms to a minimum of 0.375 Vrms. The output level is set bythe voltage level applied to gain set pin GSr. Maximum output is achieved by connecting GSr toPWRO-, while minimum voltage is achieved by connecting GSr to PWRO+. Voltage levelsbetween these extremes can be accomplished with a potentiometer connected from PWRO+ toPWRO- whose wiper is connected to GSr as illustrated in Figure 4.17.

The gain of the power amplifier is given by:

Filter

R1

2R

andSample

HoldComparator

Successive

A/DApproximation

RegisterOutput

Dx

TSx /DCLKx

ASEL

GNDD

FSx/TSxl

Logic

Reference

Control

CLKSEL

CLKx

VFX1

VFX1

GSx

GNDATransmit Control Logic

(from General Control Logic-Receiver)

ControlLogic

Av =1 + R2

R1(4.2)

Ao =R1 + R2R1 + 4R2

(4.3)


Figure 4.16Codec ReceiverBlock Dia-gram

Figure 4.17Gain setting resistors forpower ampli-fier

or

A CODEC can operate using either the µ-255 law or A law for companding. The selection ismade by using the ASEL ( A Law Select) input. (See Figure 4.16).

Hold

Sampleand Buffer Filter

Reference

Digital to AnalogConverter and Receive

Control LogicRegisterInput

DR

DCLKR

CLKx

FSR/TSR1

LogicControlGeneral

Transmit Control Logic

R1

R2

PWRO

PWROΣ

SetGain

Logic

PDN

CLKO

R 2

R 1

PWRO

PWRO

GSr RLVo

(1.5 Vrms maximum)

R1R2

=4Ao − 11 − Ao

(4.4)


REVIEW QUESTIONS WITH ANSWERS

State True or False.

1. A Phase Shift Keying receiver must incorporate carrier recovery.2. A phase shift keying signal is less susceptible to noise than amplitude shift keying signal.3. Frequency shift keying scheme requires less bandwidth than PSK.4. Quantization noise in a PCM system increase when the number of levels of quantization is

increased.5. In DPSK, the information in the two consecutive bits is used.

Answers

1. True 2. True 3. False 4. False 5. True

Select the correct answer.

1. Digitization refers to

(a) Sampling (b) Quantization

(c) Either sampling or quantization (d) Sampling and quantization

2. If r is the bit data rate in a digital wave form then the bit period of T is equal to

(a) 1/r (b) r

(c) 1/2 × r (d) log2r

3. In long distance data transmission system, the most preferable mode of communica-tion is:

(a) Serial transmission (b) Parallel transmission

(c) Either serial or parallel transmis- (d) None of the abovesion

4. QAM is

(a) PSK combined with AM (b) FSK combined with AM

(c) ASK combined with AM (d) QPSK combined with AM

5. The following modulation requires the lowest bandwidth:

(a) PSK (b) FSK

(c) DPSK (d) ASK

Answers

1. (d) 2. (a) 3. (a) 4. (a) 5. (a)


TEST PAPER

Time: 3 Hrs. Marks: 100

Note: Answer all questions.1. (a) What do you understand by the term aliasing error? What is done to limit

this error?(b) What additional equipment do you need to transmit computer data over a

telephone line? With the help of a diagram, draw its functional blocks andtheir interconnection?

2. (a) What are the types of multiplexing used in telephone trunk circuits totransmit a large number of voice channels by the same transmitter?Explain with the help of a diagram, any one such a scheme.

(b) A communication system uses an 8-bit converter at exactly the Nyquistrate for signals with 30 kHz bandwidth. Calculate the bit-rate at the out-put.

3. (a) What is differential phase shift keying? How is it achieved? Explain theadvantage of a differential phase-shift keying modulation over ordinaryPSK.

(b) Taking a suitable stream of binary digital data, indicate the phases of abinary DPSK wave form, illustrating the DPSK modulation scheme.

4. (a) A system is designed to sample analog signals, convert them to digitalform with a 3-bit converter, and transmit them, What bit rate is required ifthe analog signal contains frequencies between 300 Hz to 3400 Hz?

(b) A system can support a data rate of 100 kbps. How many users can itmultiplex if each user is a 3 kHz bandwidth signal, sampled at the Nyquistrate, and using 7 bit digitization coding?

(c) With the help of a diagram, explain how an analog signal is converted to adigital signal?

5. Describe in your own words, the nature of attenuation of an optical signal througha glass fiber and how does it vary with the wavelength of the optical signal. Statethe principal causes of attenuation in a fiber.

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