T305: Digital Communications

T305: DIGITAL COMMUNICATIONS

Arab Open University-Lebanon Tutorial 1 1

T305: Digital Communications

Block I – Introducing networks


2Arab Open University-Lebanon

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General Information about the CourseDigital communication, in the guise of telephony, the Internet or digital broadcast entertainment, is affecting our lives to an ever-greater extent.In this course you will discover what digital communication is, how it works, why it is the way it is, and how it might develop in the future.In a nutshell, T305 is about:

communication of sound, images and data: from telephony and, computer networks.

The T305 course is a Level 3 Technology course worth 16 credit hours.



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Course BreakdownThe T305 course is taught over 2 semesters at AOU. The Semester-Wise Breakdown of the Course is given below:

Part 1 (Semester 1): The following blocks are covered in this part:

Block 1Block 3Block 3

Part 2 (Semester 2): The following blocks are covered in this part:

Block 4Block 5Block 6



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Course Assessment

Exams: Exams for this course consist of the following:

Mid-Term Exam: This will be conducted at the end of Part 1 (Blocks 1, 2 & 3).Final Exam: This will be conducted at the end of Part 2 (Blocks 4, 5 & 6).



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Signal Processing (Sinwaves, Fourier, bandwidth, Digitization): Sinwave:

A periodically repeating curve whose shape when plotted as a graph is as shown below.

A sinewave showing variation with time t



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Amplitude

Sinewave superimposed on fixed value of y given by c

The blue sinewave has larger amplitude than the black



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Cycle, frequency and periodThe frequency of a sinewave is simply the number of cycles per second, a cycle being the basic shape of the waveform that repeats indefinitely.

The black sinewave has a higher frequency than the blue

T = 1/f, where T is the periodic time and f is the frequency.



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PhasePhase, or, more correctly, phase shift, denotes how far a sinewave is shifted along the horizontal axis (time) relative to another sinewave taken as a reference.The blue sinewave is said to be delayed or lagging relative to the black one.

The blue sinewave is shifted 1/4 cycle (90 degree) to the right of the reference sinewave.



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Sinewave equation

The general equation for a time-varying sinewave is y = a sin(2πft + φ) where

y represents displacement at time t a represents the amplitudef is the frequency and φ is the phaseThe term (2πft + φ) represents an angle that is growing as time passes. This angle is measured in radians rather than degrees.Angular frequency in radians per second: ω

= 2 π f



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Sinewave equation

Reference sinewave

Sinewave with an amplitude of 5 volts

Period T= 0.01s

F = 100 Hz

F= 1/T

Pay attention to phase difference between the two sinewaves at t=0.

y = 5 sin(200πt – π/2) volts

y = 5 sin(200πt) volts



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Fourier's Theorem

Any periodic signal can be thought of as a sum of a number of sinewaves of different amplitudes, frequencies and phases.(it is recommended to read chapter 5 in the reference book)

Fourier synthesisAdding sinewaves together creates non-sinusoidal waveforms. This process is known as Fourier synthesis.

Fourier analysis is the process of analysing periodic non-sinusoidal waveforms in order to determine their component sinewaves.



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y = 2 sin 2000πt + sin 4000πt+ 0.5 sin 6000πt

(a) sinewave, frequency 1 kHz

(b) sinewave of frequency 2 kHz

(c) sinewave of frequency 3 kHz

Sum of sinewaves (a), (b) and (c).

time domain representations,



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Fourier frequency spectrumFor periodic signals, the frequency spectrum is always a line spectrum. The amplitude line spectrum corresponding to the periodic, non-sinusoidal waveform composed of sinewaves (a), (b) and (c) is shown below.

Amplitude spectrum of the periodic, non-sinusoidal waveform (frequency domain representation)



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Fourier spectral characteristics: periodic waves

Because an amplitude spectrum does not give any phase information, it is the same for both sinewaves and cosine waves

Example waveform (cosine wave)



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Non-sinusoidal periodic waveforms have more than one component, and more than one spectral line.

Example square wave



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The equation for a square wave like this is most conveniently expressed as a series of cosines. For a square wave of amplitude a and frequency f, it is:

Line spectrum of square wave with fundamental frequency of 1000 Hz and amplitude π/4

Any waveform that has sudden discontinuities, such as perfectly sharp corners or instantaneous changes of value, has an infinite spectrum.



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The sharper the features of the waveform, the higher the frequency components needed to represent it.

This figure shows the result of adding only the first five components of a square wave and ignoring all the higher-frequency components



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Power spectrum

A graph showing the average power associated with each of the sinusoidal Fourier components of a non-sinusoidal waveform.

Power spectra can be either line spectra (periodic signals) or continuous spectra (non-periodic signals).

A continuous power spectrum is known as a power density spectrum.



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Line power spectrumPeriodic waveforms, which have discrete amplitude spectra, also have discrete power spectra. A typical discrete power spectrum (line spectrum) might look something like the graph below.

Line power spectrum

The height of each line represents the average power associated with the component sinewave at the corresponding frequency (f1, f2, f3 or f4 in this case).



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Power density spectrumNon-periodic waveforms, The vertical axis, rather than representing average power (as it would in a line power spectrum), represents average power density. The reason is the continuous nature of the distribution.

Power density spectrum or continuous power spectrum



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Power density spectrum

The average power associated with frequencies in the range f1 to f2



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Power density spectrum for white noiseSo-called ‘white noise ’, for instance, has a constant power spectral density for all frequencies as shown below.

Power density spectrum of white noise



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BandwidthAnalogue bandwidthThe span of frequencies in the spectrum is an indication of the bandwidth of the signal. For instance, the spectrum of the signal shown below,, has bandwidth f1 – f2. That is, the bandwidth is the frequency difference between the upper and lower cut-off frequencies.

Idealized frequency spectrum of an analogue signal with cut-off frequencies f1 and f2



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Analogue bandwidthA spectrum like that shown above is impossible to achieve in practice because a continuous frequency spectrum cannot have such sharply defined cut-off frequencies.

Typical spectrum of an analogue signal with cut-off frequenciesf1 and f2

If the bandwidth of a channel is less than the bandwidth of a signal passing through it, the signal will be distorted to some extent by having some of its frequency spectrum attenuated or truncated.



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Digital bandwidth

The maximum bit rate of a digital communication system is the ‘bandwidth’. The number of symbols transmitted per unit time over a digital transmission link is known as the signalling rate, measured in baud. One baud is one symbol per second. For a binary system, the signalling rate in baud is identical to the bit rate in bits per second.

It can be shown that the maximum theoretical signalling rate S baud over a channel of bandwidth B Hz is given by the expressionS = 2 × B



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Regeneration of digital signals

One of the advantages of a digital signal is that, provided it has not been degraded too much during transmission, the effects of noise and distortion can effectively be removed and the digital signal perfectly reconstituted. This process is called regeneration. This process is not possible with analogue signals.

Signal attenuation/amplification - noise



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Sound digitization

The process of digital representation of sound in terms of binary codesIn order to digitize sound, sampling is used. This consists of breaking the sound into equal-duration segments.



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Sound: sampling rateThe lower-frequency waveform that fits these samples is shown below; it is clearly not an accurate representation of the original sinewave. This waveform is called an alias.

Waveform S1 with sampling points

Waveform S1 and its alias S2 constructed from the sampled points



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Modulation

The modification of some property of the waveform of a signal (the carrier), in response to the information contained in another signal (the message). When, as is usually the case, the carrier wave is sinusoidal, the properties modified are amplitude, frequency or phase (or a combination of these).Modulation is carried out in order to make the message signal more suitable for transmission, processing or storage.



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Amplitude modulationIn this technique it is the amplitude which is modulated in response to the original signal.

The amplitude of the carrier is varied in proportion to the magnitude of the original signal (a), so that the transmitted signal has an outline or ‘envelope’ reflecting the sawtooth shape of the original.



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Digital signals and modulation



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Digital signals and modulation

(c) a frequency-modulated binary signal; (d) an amplitude-modulated binary signal



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phase modulation

(e) a phase-modulated binary signal



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Multiplexing

The process of combining a number of signals so that they can share a single transmission channel.



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Frequency-division multiplexing (FDM)

Using frequency-division multiplexing (FDM), two or more signals can be transmitted over the same transmission channel by using different parts of the available frequency band for each signal.

Frequency-division multiplexing of three signals using carriers at frequencies f1,f2 and f3

The commonest example of FDM is in analogue radio and television broadcasting, where each broadcasting service or station is allocated a specific frequency band.



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Time-division multiplexing (TDM)

In time-division multiplexing (TDM), samples of the individual signals are transmitted in turn, with each signal being allocated a regular, repeating, time slot.



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Time-division multiplexing (TDM)

The type of time-division multiplexing described here is known as synchronous TDM. Asynchronous TDM allows data to be sent as it becomes ready, without having to wait for pre-determined slots. In an asynchronous system, the data must include information to identify its source, and the communication channel usually has some way of detecting and remedying ‘collisions’, when two or more sources try to send data at the same time.



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Representing a frequency spectrumAs an example of the way frequencies in a spectrum may be represented, consider the analogue radio broadcast spectrum. By international agreement, the frequencies available for analogue broadcasting in the medium wave band for use by European radio stations are as follows:531 kHz 540 kHz 549 kHz ...1611 kHz

Tabular spectrum of medium-wave broadcast frequencies

Radio station Frequency/kHz

Radio A 531

Radio B 540

Radio C 549

etc. etc.

Radio Z 1611



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Representing a frequency spectrum

The figure shows the same information as a graphical display. Either the table or the figure could be described as a frequency spectrum.

Graphic spectrum of medium-wave broadcast frequencies



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Error Detection

Error detection (and error correction) are practicable in situations where digital signals are used.



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Parity check codes in error detection and correctionIn an even-parity system the extra bit is added in such a way as to ensure that there is an even number of 1s in any correct code. Thus, any received pattern with an odd number of 1s in it must be in error. Alternatively, odd parity can be used, in which case code words with an odd number of 1s are correct and those with an even number are in error.



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Error correction

A simple technique of error correction uses the Hamming code.



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Hamming code

The Hamming code uses redundant bits in such a way that when an error occurs the redundant bits indicate where it has occurred. Suppose that the denary integers 0 to 9 need to be coded for transmission. For example, each of the digits 0 to 9 might represent a reading from a measuring instrument. Suppose 4-bit binary coding is used. The four bits of the coding system are labeled A, B, C and D.



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Hamming code

The trick is to add three redundant bits, called X, Y and Z, to each 4-bit pattern ABCD in such a way that if an error occurs in any one of the resulting seven bits the receiver can calculate where the error must have been. The receiver can therefore correct the error without any more help from the transmitter.To see how the 7-bit code is constructed, suppose that the message to be sent is the number 2 (0010 in binary). Then A is 0, B is 0, C is 1 and D is 0. The four bits ABCD are taken in groups of three, BCD, ACD and ABD and an even parity check bit is calculated for each group. Let X represent the parity check bit for BCD, Y the parity check bit for ACD and Z the parity check bit for ABD. For the example, the group BCD is 010 so the even parity bit X will be 1, because that makes the number of 1s even. Group ACD is 010, so Y will be 1; and group ABD is 000, so Z will be 0.



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Hamming codeBits X, Y and Z are now attached to the original code ABCD to form a seven-bit code word ABCDXYZ. In the example, the word is 0010110 and this is the code word transmitted.The job of the receiver, when this seven-bit code arrives, is to carry out even-parity checks on the groups BCDX, ACDY and ABDZ. That is, the receiver checks whether each of the groups BCDX, ACDY and ABDZ has an even number of 1s. If none of the groups fail this parity check, then no error has occurred in transmission and the redundant bits can be ignored. If a single error occurs somewhere in the seven bits, and if all three parity checks fail, the source of the error must be bit D, since only bit D appears in all three parity-check groups. Of course, the method fails if more than one error occurs.By adding more redundancy the signal can be protected from more than one error per code pattern. A good code is one that can correct for many errors for a minimum increase of bandwidth and for a given rate of message transmission.



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8-bit ASCII code

Some 7-bit ASCII codes and their 8-bit even-parity equivalents



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UnicodeUnicode assigns a unique, standard character string for every character in use in the world’s major written languages. It also has character strings for punctuation marks, diacriticals (such as the tilde ~ used over some characters in, for example, Spanish), mathematical symbols, and so on. Unicode uses 16 bits, enabling over 65 000 characters to be coded. It also allows for an extension mechanism to enable an additional 1 million characters to be coded.



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Preparation for Next Tutorial:

Students have to do the following activities before coming to the next face-to-face tutorial:

1. Read the Course Guide.2. Read Block 1 Companion.3. Read TMA 0.4. Read the Study Calendar.5. Overview the Contents of Block 1Systems and

Processes: Part 1.

T305: Digital Communications

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