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Chapter 4 Signals

Chapter 4 Signals. Analog and digital Aperiodic and periodic signals Analog signals.  The McGraw-Hill Companies, Inc., 1998. WCB/McGraw-Hill. Fundamentals. Goals Explain ways in which voice, data and images can be represented by electro-magnetic signals

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Chapter 4 Signals

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  1. Chapter 4Signals • Analog and digital • Aperiodic and periodic signals • Analog signals The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  2. Fundamentals • Goals • Explain ways in which voice, data and images can be represented by electro-magnetic signals • Discuss transmission impairments that affect the quality and transfer rate of information. • Describe the various transmission media, their applications and transmission characteristics.

  3. Figure 4-1 Transformation of Information to Signals The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  4. Terminology • Guided or unguided • Direct link • Point to Point • simplex, half duplex or full duplex

  5. Describing Signals • Amplitude (A) • Peak value - volts • Frequency (f) • Repetition rate - cycles per second - Hertz (HZ) • Period (T) • Time for one repetition/cycle T = 1/f • Wavelength () • Distance traveled in a single cycle  = T • Phase () • Relationship between this signal and a reference signal.

  6. Figure 4-11 Time and Frequency Domain The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  7. Examples Figure 4-12 The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  8. Electromagnetic Signals • Analog: Signal varies in a continuous fashion over time • Digital: Discrete signal maintains a constant level for some period of time • Periodic Signal: Repeats over time s( t + T ) = s(t) • Sine Wave: Basic Analog periodic signal • Square Wave: Basic Digital periodic signal

  9. Figure 4-2 Analog and Digital Clocks The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  10. Figure 4-3 Analog and Digital Signals The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  11. Periodic Signals Figure 4-4 The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  12. Figure 4-5 Aperiodic Signals The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  13. Sine Waves • All Analog signals can built by adding sine waves. • Fourier analysis • any signal is made up of components at various frequencies - each is a sine wave. • Building an Analog Squarewave

  14. Figure 4-6 Sine Wave

  15. Phases Figure 4-7

  16. Figure 4-10 Phase Change

  17. Signal with DC Component Figure 4-13 The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  18. Figure 4-14 Complex Waveform The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  19. Relationship betweenData Rate and Bandwidth • Any transmission medium will be able to accommodate only a limited band of frequencies. • most of the energy is contained in a narrow band of frequencies. • Determine what a ‘good enough’ signal requires • ex: Build a squarewave with f1 + f2 + f3 …. • In general any digital signal requires infinite bandwidth - it must be approximated. • Minimum sampling rate - 2* frequency to be recovered • A given bandwidth can support various data rates depending on the requirements of the receiver.

  20. Frequency Domain Concepts • Spectrum: • Range of frequencies that a signal contains. • Bandwidth: • Absolute Bandwidth is width of spectrum • Effective Bandwidth - most of the energy is contained in a narrow band of frequencies. • DC Component • Component of 0 frequency • with no DC component average amplitude is 0

  21. Figure 4-15 Bandwidth The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  22. Figure 4-16 Digital Signal The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  23. Figure 4-17 Amplitude, Period, and Phase for a Digital Signal The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  24. Figure 4-18 Bit Rate and Bit Interval The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  25. Figure 4-19 Harmonics of a Digital Signal The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  26. Figure 4-20 Exact and Significant Spectrums The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  27. Figure 4-21 Bit Rates and Significant Spectrums The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  28. Figure 4-22 Corruption Due to Insufficient Bandwidth The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  29. Figure 4-23 Bandwidth and Data Rate The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  30. Figure 4-24 Example The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  31. Figure 4-25 Example The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  32. Figure 4-26 Example The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  33. Figure 4-9 Frequency Change The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  34. Analog Signals - Voice • Spectrum: • Human voice 20 Hz to 20,000 Hz • Telco 300 Hz to 3400 Hz • Bandwidth: • Absolute Bandwidth is width of spectrum • Effective Bandwidth - most of the energy is contained in a narrow band of frequencies. • Encoding: • Modulation - Telephone handset converts voice produced sound wave into an electronic signal and adds it to the carrier (base) frequency.

  35. Figure 4-8 Amplitude Change The McGraw-Hill Companies, Inc., 1998 WCB/McGraw-Hill

  36. Analog Signals - Video • Bandwidth: • 6 Mhz for standard color television • Encoding: • Scanlines Paint the Picture • 483 horizontal lines at 30 scans per second • interlace vs non-interlace • Horizontal Retrace time • Vertical Retrace time

  37. DATA • ASCII: • Digital encoding of characters • 7 or 8 bit standard • going to double byte for non - roman based languages • Control and Data intermixed

  38. Transmission Impairments • Attenuation • Signal must have significant strength • Repeaters - digital data • Amplifiers - analog data • Attenuation distortion • Attenuation varies as a function of frequency • use load coils • non-linear amplifiers - amplify high freq more than low

  39. Transmission Impairments • Delay Distortion • Propagation varies by frequency • highest near the center frequency • various frequency components arriving at different times • Critical for Digital - • bits arriving in overlapping time slots • Intersymbol interference • non-linear amplifiers - amplify high freq more than low

  40. NOISE • Thermal Noise • Intermodulation Noise • Crosstalk • Impulse Noise

  41. Noise • Thermal noise • White noise cannot be eliminated • N0 = kT • k= Boltzmann’s constant = 1.3803 x 10 -23 J/oK • T=temp, degrees Kelvin • N = kTW

  42. Noise • Intermodulation noise • when signals of different frequencies share the same medium f1, f2 • energy at f1 + f2 or f1 - f2 …. • Produced when there is some nonlinearity in system

  43. Noise • Crosstalk noise • unwanted coupling between signals…. • Typically same magnitude as thermal noise • Twisted pair.. • Microwave..

  44. Noise • Impulse noise • noise spikes of short duration and high magnitude…. • lightning, flaws in communications system • primary source of error in digital data.

  45. Channel Capacity • Data rate • rate in bits per second at which data can be communicated • Bandwidth • bandwidth of transmitted signal constrained by the transmitter and nature of transmission medium (Hz) • Noise • Average level of noise over communication path • Error Rate • rate at which errors occur

  46. Channel Capacity • Nyquist • if the rate of signal transmission is 2W then a signal with frequencies no greater than W is sufficient to carry the data rate. • Given a bandwidth of W the highest signal rate that can be supported is 2W • C = 2W log2 M • M = number of discrete signal or voltage levels • All other things being equal, doubling the bandwidth doubles the data rate

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