Data Transmission

1. Data Transmission

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

3. 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

4. Analogue & Digital Signals

5. PeriodicSignals

6. 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

7. Varying Sine Wavess(t) = A sin(2πft +φ)

8. 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*108 m/s (approximately 3*108 m/s) speed of light in free space

9. 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

10. Addition of FrequencyComponents(T=1/f) sin(2πft) (1/3) sin(2π(3f)t) (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)]

11. 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

12. FrequencyDomainRepresentations Signal spectrum Absolute bandwidth= 3f-1f=2f Fundamental frequency (f) (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] 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 s(t)=1, -X/2<t<X/2

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

14. Square wave Square wave signal consists of an infinite number of odd harmonics (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)]] (4/π)Σ[sin(2πkft)]/kfor odd k

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

16. 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?

17. Data Rate and Bandwidth (3) Case 1: Assume that the square wave is approximated to this signal. (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] BW=fupper – flower = 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

18. Data Rate and Bandwidth (4) Case 2: Assume that the square wave is approximated to this signal. (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)+(1/5)sin(2π(5f)t)] BW=fupper – flower = 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

19. Data Rate and Bandwidth (5) Case 3: Assume that the square wave is approximated to this signal. (4/π) [sin(2πft)+(1/3)sin(2π(3f)t)] BW=fupper – flower = 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

20. 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

21. 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

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

23. Acoustic Spectrum (Analog) (log scale)

24. 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)

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

26. Attenuation of Digital Signals

27. 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 • 300-3400Hz

28. Conversion of Voice Input into Analogue Signal

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

38. 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 log2M 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.

39. 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 • SNRdB=10 log10 (Signal power/Noise power) • Max channel Capacity is C=B log2(1+SNR) in bps • This formula is for error-free capacity and assumes white noise. In practice, data rate is lower than C.