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Chapter 4

Chapter 4. Data Transmission. Learning Objectives. Various ways in which audio, data, image, and video can be represented by electromagnetic signals Characteristics of Analog & Digital waveform Various transmission impairments that affect the quality and transfer rate of information

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Chapter 4

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  1. Chapter 4 Data Transmission

  2. Learning Objectives • Various ways in which audio, data, image, and video can be represented by electromagnetic signals • Characteristics of Analog & Digital waveform • Various transmission impairments that affect the quality and transfer rate of information • Concept of channel capacity & the factors that affect it

  3. Electromagnetic Signals • Electromagnet energy travels in waves that radiate outward from its source • In a computer network, the source is generically called a transmitter • The electromagnetic energy that is created by the transmitter is carried over transmission media in the form of electromagnetic waves • Fundamental characteristics • Signal is expressed mathematically as is a function of time • Signal can also be expressed as a function of frequency • It is the presence of multiple frequencies that enable us to distinguish one person’s voice from another or one musical instrument from another. • The frequency view of a signal is most important for understanding data transmission due to signal impairments (e.g. noise).

  4. Information Transfer • Information is transmitted by means of Electrical Signals ( or Electromagnetic, EM) Example: Voice Transmission via Telephone Voice >>> Air Vibration >>> Microphone (Receiver) >>> Electric Signal >>> Transmission Medium (Wire) >>> Speaker (Receiver)

  5. Analog and Digital Waveforms

  6. Examples of Periodic Signals

  7. Periodic Signal Characteristics • Peak Amplitude (A) • Maximum height of the wave above or below a given reference point • Represents the strength of the signal over time • Typically measured in volts • Frequency (f) • Number of times the signal makes a complete cycle within a given time frame • Typically expressed in cycles per second or hertz (Hz) • Period (T) • The time interval for one cycle (sec) • Phase () • A measure of the position of the waveform relative to a given moment of time within the period of a signal (Degree)

  8. Sinusoidal Waveform V (Volt) Vm:= Amplitude (Volt) T :=Period, Sec (1 Cycle) f := Frequency (1/T)(Hz)  :=2f=2 /T (2  = 360)  =:= Phase Angle (Relative Position) Vm T t (sec)  A sine wave can be represented by 3 parameters Amplitude (Vm), Frequency(f), and Phase angle()

  9. 3

  10. Classification of Signals 1.Time Domain 2. Frequency Domain 1.1. Analog 1.2. Digital Signal Classification

  11. Time Domain: Analog / Digital • Function of time • Analog (Signal varies smoothly over time, is continuous, i.e. no break or discontinuities) • Digital (constant level over some period of time, followed by a change to another level)

  12. Frequency Domain • Concept: • A periodical signal is made up of many frequencies. • Example: • S(t) = (4/).[sin(2 ft) + (1/3)sin(2 (3f)t)] • f := Fundamental frequency • Wavelength: Distance occupied by a single cycle •  = ν.T ; ( := Wavelength, ν:=velocity of signal; T:= period) • c := speed of light = 3x108 m/s • Or:  = ν/f • Bandwidth := 3f –f (where 3f is max frequency & f in min or fundamental) • Spectrum: range of frequencies that signal contains: from f to 3f (f-3f)

  13. Time Domain vs Frequency Domain • Function of frequency (more important) • Spectrum • range of frequencies contained in a signal. For a signal containing frequencies f and 3f spectrum is f to 3f • Bandwidth • The difference between the limiting frequencies of a continuous frequency band. Or, width of the spectrum of frequencies that can be transmitted • In the above case it is 3f-f = 2f • if spectrum=300 to 3400Hz, bandwidth=3100Hz • Greater bandwidth leads to greater costs • Limited bandwidth leads to distortion

  14. Figure 4.4Addition of Frequency Components(T = 1/f) (a) sin (2 ft) Fundamental Frequency (b) (1/3)sin (2 (3f)t ) 1stHarmonic Frequency

  15. Figure 4.5Frequency Componentsof Square Wave(T = 1/f) 3nd Harmonic Frequency Fundamental Frequency 4nd Harmonic Frequency 2nd Harmonic Frequency

  16. Amplitude spectrum of square wave

  17. Frequency Perspective Concepts

  18. Case I: Relation between data rate and Bandwidth f=106 Hz(Cycle/Sec) T = 1/f = 1/106 = 1 s Using 1st, 2nd & 3rd Harmonics (ief, 3f, 5f) v(t) = (4/)[sin(2(106)t) + (1/3)sin(2 (3x 106)t) + (1/5)sin(2 (5x106)t)] Bandwidth = 5f - f = (5x106) - (106 ) = 4 x 106 Hz=4MHz V (Volt) T=1 s 1 1 0 Bit Duration: (1 bit)  (0.5 s) or (1/2)*(10-6) sec i.e. (2,000,000 bits)  (1sec) Thus for a bandwidth of 4MHza Data rate of 2Mbs is achieved. t = 0.5 s t = 0.5 s 1 bit 1 bit t (Sec)

  19. Case II f = 2,000,000 (Cycle/Sec) 2x106 Hz  2MHz T = 1/f = 1/(2x106)= 0.5 s Using 1st, 2nd & 3rd Harmonics (ief, 3f, 5f) v(t) = (4/)[sin(2(2x106)t) + (1/3)sin(2 (3x 2x106)t) + (1/5)sin(2 (5x2x106)t)] Bandwidth = 5f - f = 5(2x106) - (2x106 )= 8x106 Hz=8MHz V(Volt) T=0.5 s 1 1 Bit Duration: (1 bit)  (0.25 s)  (1/4)*(10-6) sec i.e. (4,000,000 bits)  (1sec)  (4,000,000bps)=4Mbps Thus for a bandwidth of 8MHz a Data rate of 4Mbs is achieved. By doubling the bandwidth the data rate is doubled (everything else stayed the same).. 0 t = 0.25 s t = 0.25 s or 1 bit 1 bit t (Sec)

  20. Case III f = 2,000,000 (Cycle/Sec) 2x106 Hz  2MHz T = 1/f = 1/(2x106)= 0.5 s Using 1st Harmonics (ief, 3f) v(t) = (4/)[sin(2(2x106)t) + (1/3)sin(2 (3x 2x106)t) ] Bandwidth=3f- f = 3(2x106) - (2x106 )= 4x106 Hz=4MHz V(Volt) T=0.5 s 1 1 Bit Duration: (1 bit)  (0.25 s) (1/4)*(10-6) sec i.e. (4,000,000 bits)  (1sec)  (4,000,000bps)=4Mbps Thus for a bandwidth of 4MHza Data rate of 4Mbps is achieved. 0 t = 0.25 s t = 0.25 s or 1 bit 1 bit t (Sec)

  21. Comparing Cases I, II, III • Any digital wave will have infinite bandwidth. • In transmitting, the transmission system will limit the Bandwidth. • The higher the bandwidth The higher the Cost • For Economic & Practicality, Digital information are approximated by limited bandwidth • Limiting the bandwidth, Creates distortion • Thus a given bandwidth can support various data rates depending on the ability of receiver.

  22. Why Study Analog in a Data Comm Class? • Much of our data begins in analog form; must understand it in order to properly convert it • Telephone system is primarily analog rather than digital (designed to carry voice signals) • Low-cost, ubiquitous transmission medium • If we can convert digital information (1s and 0s) to analog form (audible tone), it can be transmitted inexpensively

  23. Analog data Voice Images Digital data Text Digitized voice or images Data vs Signals

  24. Voice/Audio Analog Signals • Easily converted from sound (air vibration, measured in loudness/db) to electromagnetic frequencies, measured in voltage • Human voice has frequency components ranging from 20Hz to 20kHz • For practical purposes, the telephone system has a narrower bandwidth than human voice, from 300 to 3400Hz

  25. The Voice Band

  26. Pixelization and Binary Representation • Used in digital fax, bitmapped graphics Binary code:00000000 00111100 01110110 01111110 01111000 01111110 00111100 00000000

  27. Digital Signals

  28. Transmission Media • the physical path between transmitter and receiver (“channel”) • design factors affecting data rate • bandwidth • physical environment • number of receivers • impairments

  29. Impairments and Channel Capacity • Impairments exist in all forms of data transmission • Analog signal impairments result in random modifications that impair signal quality • Digital signal impairments result in bit errors (1s and 0s transposed)

  30. Regenerative Repeaters

  31. Impairments of Guided Media Most significant impairments for the guided media such as twisted pair, coaxial cable, and optical fiber are: • Attenuation and attenuation distortion • Delay Distortion • Noise

  32. Transmission Impairments: Guided Media 1.Attenuation,2. Delay Distortion,3. Noise • 1. Attenuation: loss of signal strength over distance 1.1. A signal must have sufficient strength to be detected by the receiver 1.2. Signals must maintain a level higher than noise 1.2.1. The above two problems can be improved by Amplifiers, but may cause distortion. Digital signals use Regenerative Repeaters, digital errors persists for the remainder of the path. 1.3. Attenuation is greater at higherfrequencies causing distortion (Attenuation Distortion: different losses at different frequencies) 1.3.1. Mainly in analog can be overcome by equalizing attenuation such as using loading coils in telephone lines 1.3.2. Digital signals may have a number of frequencies but within a narrow band, therefore they have less problems with attenuation distortion.

  33. Transmission Impairments: Guided Media • 2. Delay Distortion • different speeds for different frequencies, higher near the centre frequency. • Major problem is Digital signals. Some signal energy in one bit position will spill over into other bit positions. This puts a limitation on the data rate. • 3. Noise • distortions of signal caused by interference. Unwanted electromagnetic energy • Thermal, Intermodulation, Crosstalk, Impulse noise

  34. Transmission Impairments-Guided Media • Noise • Is the major limiting factor in communication system performance • Can be divided into four categories: • Thermal noise (often referred to as white noise) • Uniformly distribute, cannot be eliminated • Intermodulation noise • Different frequencies collide and create harmonics • Crosstalk • Overlap of signals • Impulse noise • Irregular Spikes, less predictable

  35. Effect of Noise on Digital Signal

  36. Transmission Impairments:Unguided (Wireless) Media • Free-Space Loss • Signals disperse with distance (speed of electromagnetic wave: c=3x108m/s) • Atmospheric Absorption • Water vapor (22 GHz Worse, f < 15Ghz less) and oxygen contribute (60GHz worse, f <30GHz less) to signal loss. • Remedy for high precipitation areas, lower f and lower path length

  37. Transmission Impairments:Unguided (Wireless) Media • Multipath • Obstacles reflect signal creating multiple copies • Refraction (bend) • Changes in the speed of propagation due to changes in the atmospheric properties, may result in signal not reaching receiving antenna • Noise • White noise due to thermal agitation of electrons in conductor, results in white noise in devices and media. It is particularly important for satellite communication because the weakness of this type of signals.

  38. Channel Capacity • Definition: The rate at which data can be transmitted over a given communication path, or channel, under given conditions is referred to as Chanel Capacity CC. • Four interrelated concepts: • Data rate • Bandwidth • Noise • Error rate

  39. Four interrelated concepts: • Data rate (bps communication rate) • Bandwidth (Hz constrained by transmitter & transmission medium) • Noise • Error rate (reception of 1 when 0 was transmitted or vise versa) Objective (putting 4 concepts together): To make efficient use of a given bandwidth means as high a data rate as possible at a particular limit of error rate for a give bandwidth.

  40. Relationship between data rate, noise, and error rate • The presence of noise can corrupt one or more bits. If the data rate is increased, the bits become shorter so that more bits are affected by a given pattern of noise. • Therefore at a given noise level, the higher the data rate, the higher the error rate

  41. Shannon Equation C = B log2 (1 + SNR) B = Bandwidth of the channel (in Hertz) C= Channel capacity (in bits per second) SNR = Signal-to-noise ratio

  42. Shannon Equation:Max channel capacity • Signal to noise ratio is the ratio of the power in a signal to the power contained in the noise that is present at a particular point in a signal • C = B log2 (1 + SNR) • B = Bandwidth (Hz) • C= Channel capacity (bps) • SNR = Signal-to-noise ratio (power ratio) C/B is bps/Hz efficiency of a digital transmission

  43. Wavelength The distance occupied by a single cycle. Or The distance between two points of corresponding phase of two consecutive cycles.  = .T Special case :  = c =3x108 m/s (c:= speed of light)

  44. Summary • Signals for conveying information • Electromagnetic signals • Analog signals • Digital signals • Chapter 4: Data Transmission • Transmission impairments and channel capacity • Guided media • Unguided media • Channel capacity

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