Data Transmission

1. Terminology Transmitter Receiver Medium —Guided medium e.g. twisted pair, optical fiber —Unguided medium e.g. air, water, vacuum

Frequency, Spectrum and Bandwidth Time domain concepts —Analog signal Varies in a smooth way over time —Digital signal Maintains a constant level then changes to another constant level —Periodic signal Pattern repeated over time —Aperiodic signal Pattern not repeated over time

Analogue & Digital Signals

Periodic Signals

Sine Wave Peak Amplitude (A) —maximum strength of signal —volts Frequency (f) —Rate of change of signal —Hertz (Hz) or cycles per second —Period = time for one repetition (T) —T = 1/f Phase ( φ ) —Relative position in time

Varying Sine Waves s(t) = A sin(2 π ft + φ )

Wavelength Distance occupied by one cycle Distance between two points of corresponding phase in two consecutive cycles λ=wavelength Assuming signal velocity v — λ = vT — λf = v — c =2,98*10 8 m/s (approximately 3*10 8 m/s) speed of light in free space

Frequency Domain Concepts Signal usually made up of many frequencies Components are sine waves Can be shown (Fourier analysis) that any signal is made up of component sine waves Can plot frequency domain functions

Addition of Frequency Components (T=1/f) (1/3) sin(2π(3f)t) sin(2πft) (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)]

Spectrum & Bandwidth Spectrum —range of frequencies contained in signal Bandwidth (BW) —Narrow band of frequencies containing most of the signal energy —Absolute bandwidth: Width of the spectrum —Effective bandwidth (or bandwidth): energy of signal contained in a narrow band of frequencies (usually expressed as the –3 dB points) DC Component —Component of zero frequency

Frequency Domain Representations Fundamental frequency (f) Signal spectrum Absolute bandwidth= 3f-1f=2f This signal has an infinite bandwidth. Its effective bandwidth is limited in a relatively narrow band of frequencies where the most energy of the signal is contained (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] s(t)=1, -X/2<t<X/2

Signal with DC Component Frequency Domain Time Domain Bandwidth s(t) = 1 + (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)]

Square wave Square wave signal consists of an infinite number of odd harmonics (4/π) Σ [sin(2πkft)]/k for odd k (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t) +(1/7)sin(2π(7f)t)]]

Data Rate and Bandwidth (1) Any transmission system has a limited band of frequencies This limits the data rate that can be carried

Data Rate and Bandwidth (2) Suppose a digital transmission system is capable of transmitting signals with a BW of 4MHz. Let us attempt to transmit a square wave signal (i.e. a sequence of alternating 0s and 1s. What is the achievable data rate?

Data Rate and Bandwidth (3) Case 1: Assume that the square wave is approximated to this signal. BW=f upper – f lower = 5f – f =4f If f=1MHz, then the BW=4MHz. Since T=1/f then signal period is 1/1MHz=1μs Since one bit occurs every 0.5T then Data rate=1/0.5T=2Mbps So, for this particular example, for a BW of 4MHz, the Data Rate achieved is 2Mbps (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)]

Data Rate and Bandwidth (4) Case 2: Assume that the square wave is approximated to this signal. BW=f upper – f lower = 5f – f =4f If f=2MHz, then the BW=8MHz. Since T=1/f then signal period is 1/2MHz=0.5μs Since one bit occurs every 0.5T then Data rate=1/0.5T=4Mbps So, for this particular example, for a BW of 8MHz, the Data Rate achieved is 4Mbps (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)]

Data Rate and Bandwidth (5) Case 3: Assume that the square wave is approximated to this signal. BW=f upper – f lower = 3f – f =2f If f=2MHz, then the BW=4MHz. Since T=1/f then signal period is 1/2MHz=0.5μs Since one bit occurs every 0.5T then Data rate=1/0.5T=4Mbps So, for this particular example, for a BW of 4MHz, the Data Rate achieved is 4Mbps (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)]

Data Rate and Bandwidth (6) Conclusions —In general, any digital waveform has infinite BW —If a digital waveform is transmitted over any medium, the transmission system will limit the BW that can be transmitted —For any given medium, the greater the BW transmitted, the greater the cost —Limiting the BW creates distortions, which makes the task of interpreting the received signal more difficult —The more limited the BW, the greater the distortion, and the greater the potential for error by the receiver

2. Analog and Digital Data Transmission Data —Entities that convey information Signals —Electric or electromagnetic representations of data —Signaling is the physical propagation of the signal along a suitable medium Transmission —Communication of data by propagation and processing of signals

Analog and Digital Data Analog —Continuous values within some interval —e.g. sound, video Digital —Discrete values —e.g. text, integers

Acoustic Spectrum (Analog) (log scale)

Analog and Digital Signals Means by which data are propagated Analog —Continuously variable —Various media wire, fiber optic, space —Speech bandwidth 100Hz to 7kHz —Telephone bandwidth 300Hz to 3400Hz —Video bandwidth 4MHz Digital —Use two DC components (binary 0 and 1)

Advantages & Disadvantages of Digital Cheaper Less susceptible to noise Greater attenuation —Pulses become rounded and smaller —Leads to loss of information

Attenuation of Digital Signals

Components of Speech Frequency range (of hearing) 20Hz-20kHz —Speech 100Hz-7kHz Easily converted into electromagnetic signal for transmission Sound frequencies with varying volume converted into electromagnetic frequencies with varying voltage Limit frequency range for voice channel — Hz

Conversion of Voice Input into Analogue Signal

Advantages of Digital Transmission Digital technology —Low cost large-scale and very-large scale integration technology Data integrity —Longer distances over lower quality lines Capacity utilization —High bandwidth links economical —High degree of multiplexing easier with digital techniques Security & Privacy —Encryption Integration —Can treat analog and digital data similarly —Economies of scale and convenience can be achieved by integrating voice, video and digital data

3. Transmission Impairments Signal received may differ from signal transmitted For Analog signals - degradation of signal quality For Digital signals - bit errors may occur Most significant transmission impairments are —Attenuation and attenuation distortion —Delay distortion —Noise

Attenuation Signal strength reduces with distance over any transmission medium Depends on medium Received signal strength: —must be enough to be detected —must be sufficiently higher than noise to be received without error Attenuation is an increasing function of frequency, i.e. the higher the frequency, the more the attenuation attenuation

Delay Distortion (DD) Only in guided media It occurs because the propagation velocity of a signal through a guided medium varies with frequency Received signal is distorted due to varying delays experienced at its constituent frequencies DD is particularly critical for digital signals —some of the signal components of one bit may spill over into other bit positions, causing intersymbol interference, which limits the maximum data rate over a transmission channel

Noise (1) Additional signals inserted between transmitter and receiver Noise is the major limiting factor in communication system performance Noise can be divided into 4 main categories —Thermal —Intermodulation —Crosstalk —Impulse noise

Noise (2) Thermal —Due to thermal agitation of electrons in all electronic devices —Uniformly distributed across the bandwidth —Also referred to a white noise Intermodulation —Signals that are the sum and difference of original frequencies sharing the same transmission medium —Example: mixing of signals at f1 and f2 may produce energy at f1±f2, which could interfere with an intended signal at (f1+f2) or (f1-f2) Crosstalk —Unwanted coupling between signal paths —Antennas or wires may pick up other unwanted signals, eg. phone line Impulse —Non continuous, consisting of irregular pulses or noise spikes of short duration but of high amplitude —e.g. External electromagnetic interference, such as lightning

4. Channel Capacity As we have seen so far, there is a variety of impairments that distort or corrupt a signal. To what extent do these impairments limit the maximum achievable data rate? Channel Capacity is the maximum rate at which data can be transmitted over a communication channel. Data rate —In bits per second (bps) —Rate at which data can be communicated Bandwidth —In cycles per second, or Hertz —Constrained by transmitter and medium

Nyquist Bandwidth Assume a noise-free channel If rate of signal transmission is 2B, then a signal with frequencies no greater than B is sufficient to carry signal rate or, given bandwidth B, highest signal rate is 2B Given a binary signal, the maximum data rate supported by a channel of bandwidth B Hz is 2B bps Maximum data rate, C, can be increased by using M signal levels Nyquist formula: C= 2 B log 2 M in bps However, receiver must be able to distinguish one of M possible signal elements. Noise and other transmission impairments limit the practical value of M.

Shannon Capacity Formula Nyquist’s formula indicates that doubling BW, doubles the data rate in a noise-free channel. In practice, noise is always present. So, let us consider the relationship between data rate, noise and error rate. Faster data rate shortens each bit duration so a burst of noise affects more bits —So, at a given noise level, the higher the data rate, the higher the error rate Signal-to-Noise ratio (SNR or S/N) expressed in decibels SNR dB = 10 log 10 (Signal power/Noise power) Max channel Capacity is C=B log 2 (1+SNR) in bps This formula is for error-free capacity and assumes white noise. In practice, data rate is lower than C.