Topic 3 - Data and Signals 1 FIT1005 FIT – Monash University Data and Signals Reference: Chapter 3 -Stallings

Topic 3 - Data and Signals 1

FIT1005

FIT – Monash University

Data and Signals

Reference:Chapter 3 -Stallings


Transmission Media

• Data transmission occurs between a transmitter and receiver over some transmission medium

• Guided media, the waves are guided along a physical path – Twisted pair, Coaxial Cable, Fibre Optic

• Unguided media, also called wireless, provide a means of transmitting waves, but do not guide them – Radio, Microwave, Infrared

• In both cases, communication is in the form of electromagnetic waves


Twisted Pair

UTP Cat 5E – 4 pair


Coaxial Cable


Optical Fiber


Links

• The term direct link is used to refer to the transmission path between two devices in which signals propagate directly from a transmitter to receiver– There are no intermediate devices other than amplifiers or

repeaters used to increase signal strength– This term can apply to both guided and unguided media

If there are intermediate devices, it is an indirect link

• A guided transmission medium is point-to-point if it provides a direct link between two devices, if more than two devices share the medium it is multipoint


Links


Transmission Modes

• Simplex – Signals are transmitted in only one direction– One station is the transmitter and the other is the

receiver

• Half duplex– both stations may transmit, but only one at time

• Full-duplex– Both stations may transmit simultaneously– The medium is carrying signals in both directions at

the same time


Transmission Modes

• commercial radio

• CB radio• television • smoke signals• classroom discussion • family arguments• ocean tides • shortwave radio communications


Signals

• Data communications is concerned with electromagnetic signals used to transmit data

• An electromagnetic signal can be either analog or digital


Analog Data

• take on continuous values in some time interval

• For example:– Voice and video are continuously varying patterns of

sound intensity

– Most data collected by sensors, such as temperature and pressure, are continuous values


Digital Data

• Digital data take on discrete values, letters (A,B,C …) and integers (0,1,2 …)

• While textual data are most convenient for human beings

• Data processing and communication systems are designed using binary data (0,1)

• A number of codes (ASCII, Unicode) have been devised by which characters (A,B,C … 0,1,2 … ) are represented by a sequence of binary bits


Signals

• An Analog signal – is one in which the signal intensity varies in a smooth fashion over

time– There are no breaks or discontinuities in the signal

• A Digital signal – is one in which the signal intensity maintains a constant level for

some period of time and then changes to another constant level– It is discrete and discontinuous– The discrete signal might represent binary 1s and 0s


Signal Representation in Time Domain

• We can measure the amplitude, frequency, and phase of

a signal in relationship to time


Signal Representation in the Time Domain

Amplitude(volts)

Time

Amplitude(volts)

Time

Analog Signal

Digital Signal


Simple Signal Models

• Analog Signal Model – the sine wave, an example of a periodic continuous signal

• Digital Signal Model – the square wave, example of a periodic discrete signal

• These are periodic signals, in which the same signal pattern repeats over time


Simple Signal Models


The Sine Wave ModelCharacteristics

• Peak amplitude (A), the peak amplitude is the maximum value or strength of the signal over time

• frequency (f), the frequency is the rate (in cycles per sec or Hertz) at which the signal repeats

• period (T), which is the amount of time taken for one repetition

• phase (φ), phase is a measure of the relative position in time within a single period of a signal

• Wavelength (λ), the wavelength is the distance (in metres) occupied by a single cycle


The Sine Wave Model


Signal Representation in Frequency Domain

• An electromagnetic signal is made up of many frequencies

• We can identify each of the signal frequencies and measure its power (Amplitude)


Signal Representation in the Frequency Domain


Signalling versus Transmission

Signalling – is the physical propagation of an electromagnetic

signal along a suitable medium

Transmission– is the communication of data by the propagation and

processing of electromagnetic signals


Human Speech as an Analog Signal

• Human speech is an acoustic (science of sound) analog signal, with frequency components in the range of 20Hz - 20kHz

• This acoustic signal can easily be converted to an electromagnetic signal for transmission

• The amplitude of sound frequencies is measured in loudness while the amplitude of the converted electromagnetic frequency is measured in volts



• In the case of human speech, the data can be represented directly by an electromagnetic signal occupying the same spectrum (frequency range).

• However, there is a need to compromise between the fidelity of sound transmitted electrically and the cost of transmission

• The spectrum of speech is between 100Hz and 7kHz. A much narrower bandwidth will produce acceptable voice reproduction.



• The standard spectrum for a voice channel is 300-3400Hz, with bandwidth 3400 – 300 = 3100Hz.

• This is adequate for speech transmission• Minimises required transmission capacity• Allows the use of inexpensive telephone sets

• The telephone transmitter converts the incoming acoustic voice signal into an electromagnetic signal over the range 300-3400Hz

• This signal is transmitted through the telephone system (PSTN) to a receiver


Analog and Digital Signals

• Analog signals can be used to represent analog data• Digital signals can be used to represent digital data

• Digital data can also be represented by analog signals:– Use a modem (modulator/ demodulator)– The modem converts a series of binary voltage pulses

into an analog signal by encoding the digital data onto a carrier frequency

– At the other end of the line, another modem demodulates the signal to recover the original data


Analog and Digital Signals


Signal Attenuation

• Attenuation - the loss of signal strength (power)

• A signal will become weaker (attenuate) as the signal propagates (through the medium) over distance

• To achieve longer distances, the analog signal must be amplified and a digital signal must be regenerated.


Attenuation of Digital Signals


Signal Attenuation

Amplifiers

• Boost the energy in the analog signal

• Unfortunately, amplifiers boost noise components as well

– With amplifiers cascaded to achieve long distances, the signal becomes more and more distorted

– For analog data (voice), quite a bit of distortion can be tolerated before data becomes unintelligible

– For digital data, cascaded amplifiers will introduce errors


Signal Attenuation

Repeaters

• Regenerates the digital signal

• A repeater receives the digital signal, recovers the pattern of 1s and 0s and retransmit a new (noise is removed) signal, thereby overcoming attenuation


Digital versus Analog Transmission

• Which is the preferred method of transmission?

• The answer supplied by the telecommunications industry and its customers is digital

• Both long-haul telecommunications facilities and intra-building services have moved to digital transmission and, where possible digital signalling techniques


Digital TransmissionThe Way to GO

• Digital technology being more cost and size effective

– The advent of LSI and VLSI technology has caused a continuing drop in the cost and size of digital circuitry

• Higher data integrity

– With the use of repeaters rather than amplifiers, the effects of noise and other signal impairments are not cumulative

– Thus it is possible to transmit data longer distances over lower quality lines using digital means while maintaining the integrity of the data



• Better capacity utilisation

– It is economical to build transmission links of very high bandwidth

– A high degree of multiplexing is needed to utilise such capacity effectively

• This is more easily and cheaply achieved with digital (time division) rather than analog (frequency division) techniques

• Better security and privacy

– Encryption techniques readily applied to digital data



• Integration benefits

– By treating both analog and digital data digitally, all signals have the same form and can be treated similarly

– As a result, it is more economical and convenient to deal with voice, video, and digital data by integrating them


Transmission Impairments

• With any communications system, the signal that is received may differ from the signal that is transmitted due to various transmission impairments

• Analog signal, the impairments can degrade the quality of the signal,

• Digital signal, bit errors may be introduced



• Distortion – distorts the shape of the signal

• Noise – adds unwanted signals



• Attenuation

• Attenuation distortion

• Delay distortion

• Noise– Thermal noise– Intermodulation noise– Crosstalk– Impulse noise


Attenuation Issues

• A received signal must have sufficient strength so that the receiver can detect it

• The signal must maintain a level sufficiently higher than noise to be received without error

• Attenuation increases with an increase in frequency, leading to Attenuation Distortion


Signal Strength

• For a point-to-point link, the signal strength of the transmitter must be strong enough to be received intelligibly

– It should also be not so strong as to overload the circuitry of the transmitter or receiver, which could cause distortion

• More complex problem for multipoint lines where the distance from a transmitter to receiver is variable


Attenuation Distortion

• Has a greater impact on analog signals:– The amount of signal attenuation that occurs increases with an

increase in frequency

– As a result the received signal is distorted, reducing intelligibility

– To overcome this problem, techniques are available for equalising attenuation across a band of frequencies

– One such approach is to use amplifiers that amplify high frequencies more than lower frequencies


Delay Distortion

• Occurs because the velocity of signal propagation through a guided medium varies with frequency

• The received signal is distorted due to the varying delays experienced by its constituent frequencies

• Delay distortion is particularly critical for digital data– Some of the signal components of one bit position will

spill over into other bit positions, causing intersymbol interference


Noise

• For any data transmission event, the received signal will consist of the transmitted signal plus additional unwanted signals

– These unwanted signals are inserted somewhere between transmission and reception

– These signals are referred to as noise

– Noise is the major limiting factor in communication systems performance


Thermal Noise

• Is due to thermal agitation of electrons

• It is present in all electronic devices and transmission media

• It is a function of temperature

• It is uniformly distributed across the bandwidth used in communication systems and hence is referred to a white noise

• It cannot be eliminated and therefore places an upper bound on communication systems performance


Intermodulation Noise

• Occurs when signals of different frequencies share the same transmission medium

• Mixing of signals at frequencies f1 and f2 might produce energy at the frequency f1+f2, which could interfere with an intended signal at the frequency f1+f2


Crosstalk

• Crosstalk is an unwanted coupling between signal paths

• It can occur by electrical coupling between nearby twisted pairs or, coax cables lines carrying multiple signals

• Fibre Optic cables are not affected by crosstalk


Impulse Noise

• Variety of causes, including external electromagnetic disturbances, such as lightening, and faults and flaws in communications system can cause Impulse noise

• Impulse noise is noncontinuous, consisting of irregular pulses or noise spikes of short duration and of relatively high amplitude

• Impulse noise is generally only a minor annoyance for analog data

• It is the primary source of error in digital data communication


Channel Capacity

• Is maximum rate at which data can be transmitted over a given communication channel

• Need to consider:– Data rate, bits per second (bps), is the rate at which

data can be communicated

– The bandwidth of channel, cycles per second or Hertz

– Noise, average level over channel

– Error rate on channel


Channel Capacity

Nyquist (1924)

• In a noise free channel, the channel capacity, in bps, of the channel is twice the bandwidth of the channel

• On a telephone channel with a frequency range from 300Hz to 3400Hz, the bandwidth is

3400 – 300 = 3100Hz

• Hence, the channel capacity is 2 x 3100 = 6200 bps

• Using two level signaling


Channel Capacity • Multilevel signalling the Nyquist formulation becomes

C = 2B log2M

Where M is the number of discrete signal or voltagelevels

• For M=8, log28 = 3 ,C = 18600bps, for B = 3100Hz

• For a given B, C can be increased by increasing the number of different signal elements M

• Noise and other impairments will limit the practical value of M


Channel Capacity

• For a given level of noise a greater signal strength would improve the ability to receive data correctly

• This can be expressed as the signal-to-noise ratio

S/N eg 1000/1

• It can be convert to decibels via

SNRdb

10 log10

signal power

noise power


Channel Capacity

• Shannon (1949)

The channel capacity on a noisy channel, in bps is given by

C = Blog2(1+SNR)

C = capacity of the channel in bps

B = bandwidth of channel in Hz

• Shannon formula represents the theoretical maximum channel capacity that can be achieved

• Noise is thermal


The slides following this are for your interest only


Time Domain Concepts Contd.

• When a signal is travelling at a velocity v, the wavelength is related to the period as:

λ = vT or equivalently v = fλ

• Of particular relevance to this unit is the case where

v = c, the speed of light in free space, which is approximately 3 * 108 m / s


Frequency Domain Concepts Contd.

– The period of the total signal is equal to the period of the fundamental frequency

• It can be shown, using a discipline known as Fourier analysis, that any signal is made up of components at various frequencies in which each component is sinusoid

– That is, by adding together enough sinusoidal signals, each with the appropriate amplitude, frequency and phase, any electromagnetic signal can be constructed

• That is, there is a frequency domain function S(f) that specifies the peak amplitude of constituent frequencies





• The spectrum of a signal is the range of frequencies that it contains

– For the previous signal, which had components of frequencies f and 3f, has a spectrum extending from f to 3f

– The absolute bandwidth of a signal is the width of the spectrum

– In the above example the bandwidth is 2f

– Many signals (such as square waves) have infinite bandwidth, although most of the energy is contained in a relatively narrow band of frequencies

• This band is referred to as the effective bandwidth, or just bandwidth



• If a signal includes a component of zero frequency, that component is a direct current (dc) or constant component

• With no dc component, a signal has an average amplitude of zero, as can be seen in the time domain

• With dc component, it has a frequency term at f=0 and a nonzero average amplitude




Relationship Between Data Rate and

Bandwidth • Although a given waveform may contain frequencies

over a wide range, practically any transmission system can accommodate only a limited band of frequencies

– This in turn, limits the data rate that can be carried on transmission medium

• When we add additional odd multiples of base frequency f, the resulting waveform approaches that of a square wave more and more closely

– It can be shown that the frequency components of the square wave with amplitudes A and (-A) can be expressed as follows


Relationship Between Data Rate and Bandwidth

s t A4

Ï€ k odd ,k 1

sin 2 Ï€kft

k

• As can be seen, this waveform has an infinite number of frequency components and hence an

infinite bandwidth

• However, the peak amplitude of the kth frequency component kf is only 1/k

• So most of the energy in this waveform is in the first few frequency components


Relationship Between Data Rate and Bandwidth Contd.

• Suppose that we have A=1, k=1,3,5 and f=1MHz = 106Hz for an approximated square wave signal

– Then the bandwidth of the signal is (5*106) – 106 = 4MHz

– The period of the fundamental frequency is T= 1/106 = 1μs

– If we consider this waveform as a bit string of 1s and 0s, one bit occurs every 0.5 μs for a data rate of 2 * 106 = 2Mbps

– Thus, for a bandwidth of 4 MHz, a data rate of 2 Mbps is achieved with signal accuracy is limited to k <= 5



• In general, any digital waveform will have infinite bandwidth

• When this waveform is transmitted as a signal over any medium, the transmission system will limit the bandwidth that can be used

• Further, greater the bandwidth transmitted, the greater the cost

• Thus on the one hand, economic and practical reasons dictate that digital information be approximated by a signal of limited bandwidth


Relationship Between Data Rate and

Bandwidth • On the other hand, limiting the bandwidth creates

distortions, which makes the task of interpreting the signal more difficult

• As a general rule, for a data rate of a digital signal W bps, a very good representation can be achieved with a bandwidth of 2W Hz

– The higher the data rate of a signal, the greater is its required effective bandwidth



• We may think that bandwidth of a signal as being centred about some frequency referred to as the centre frequency

– Higher the centre frequency, the higher the potential bandwidth and therefore the higher the potential data rate

– For example, if a signal is centred at 2 MHz, its maximum bandwidth is 4 MHz


Analog and Digital Data Transmission

• The term analog and digital corresponds, roughly, to continuous and discrete

• These terms are used in data communications in at least three contexts

– Data, signalling and transmission

• Data are defined as entities that convey meaning

• Signals are electric or electromagnetic representations of data


Analog and Digital Data Transmission Contd.

• Today the most commonly used text code is the International Reference Alphabet (IRA)

– Each character in this code is represented by a unique 7.bit pattern; thus 128 different characters can be represented

– IRA-encoded characters are almost always stored and transmitted using 8 bits per character

– The eighth bit is a parity bit used for error detection


Analog and Digital Transmission Contd.

• The same technique may be used with an analog signal if it is assumed that the signal carries digital data

– At appropriately spaced points, the transmission system has repeaters rather than amplifiers

– The repeater recovers digital data from the analog signal and generates a new, clean analog signal

– As a result, noise is not cumulative


Transmission Impairments Contd.

• Attenuation is weakening of signal strength with distance that could happen over any transmission medium

– For guided media, attenuation is generally exponential and expressed as a constant number of decibels per unit distance

– For unguided media, attenuation is a more complex function of distance and make up of the atmosphere

• The problem of attenuation is overcome by using amplifiers and repeaters


Transmission Impairments Contd.

– Thermal noise cannot be eliminated and therefore places an upper bound on communications systems performance

– The amount of thermal noise to be found in a bandwidth of 1 Hz in any device or conductor is given by

N0 = kT (W/Hz)Where

N0 = noise power density in watts per 1 Hz of bandwidthk = Boltzmann’s constant = 1.38 * 10-23 J/KT = Temperature in kelvins


Channel Capacity Contd.

– Noise is the average level of noise over the communication path

– Error rate is the rate at which errors occur

• As all transmission channels of any practical interest are of limited bandwidth, we like to make as efficient use as possible of a given bandwidth

• For digital data, this means that we would like to get as high a data rate as possible at a particular limit of error for a given bandwidth


Channel Capacity Contd.• As a standard quality measure for digital communications system

performance the ratio of signal energy per bit to noise power density per Hz is used

– That is, Eb/N0

Where Eb = STb and N0= kT (from slide 48)

S = Signal power

Tb= the time required to send one bit

Further, the data rate R = 1/ Tb



• This gives

• In decibel notation, it gives

Eb

N0

S R

N0

S

kTR

Eb

N0 dB

SdBW

10 log R 10 log k 10 log T

SdBW

10 log R 228 .6 dBW 10 logT



• The Eb/N0 ratio is important as the bit error rate for digital data is a decreasing function of this ratio

• Given a value of the ratio needed to achieve a desired error rate, the parameters in the preceding formula may be selected

• As the bit rate R increases, the transmitted signal power, relative to noise, must increase to maintain the required Eb/N0



• Nyquist formula indicates that, all other things being equal, doubling the bandwidth doubles the data rate

• Now consider the relationship among data rate, noise and error rate

– If the data rate is increased , the bits become shorter, thereby affecting more bits by a given pattern of noise

– Thus at a given noise level, the higher the data rate, the higher the error rate

Documents

Topic 3 - Data and Signals 1 FIT1005 FIT – Monash University Data and Signals Reference: Chapter 3 -Stallings