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Chapter 3 Data and Signals

Chapter 3 Data and Signals. Data and Signals. Information can be voice, image, numeric data, characters, code, picture, and so on To be transmitted, information must be into electromagnetic signals. 3.1 ANALOG AND DIGITAL.

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Chapter 3 Data and Signals

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  1. Chapter 3 Data and Signals

  2. Data and Signals • Information can be voice, image, numeric data, characters, code, picture, and so on • To be transmitted, information must be into electromagnetic signals.

  3. 3.1 ANALOG AND DIGITAL Data can be analog or digital. The term analog data refers to information that is continuous; digital data refers to information that has discrete states. Analog data take on continuous values. Digital data take on discrete values. Topics discussed in this section: Analog and Digital DataAnalog and Digital SignalsPeriodic and Nonperiodic Signals

  4. Analog and Digital Signals • Analog signal • Having infinitely many levels of intensity over a period of time • As the wave moves from value A to value B, it passes through and includes an infinite number of values along its path. • Digital signal • Can have only a limited number of defined values

  5. Analog and Digital Signals (cont’d) • Comparison of analog and digital signals

  6. Aperiodic and periodic signals • Periodic signals(주기신호) ~ consists of a continuously repeated pattern. • The periodic of a signal(T) is expressed in seconds. • A cycle : the completion of one full pattern

  7. Aperiodic and periodic signals (cont’d) • Example of periodic signals

  8. Aperiodic and periodic signals (cont’d) • Aperiodic signals(비주기 신호) ~ changes constantly without exhibiting a pattern or cycle that repeat over time. ~ signal has no repetitive pattern. • In data communication, we commonly use periodic analog signals and aperiodic digital signals

  9. 3.2 PERIODIC ANALOG SIGNALS Periodic analog signals can be classified as simple or composite. A simple periodic analog signal, a sine wave, cannot be decomposed into simpler signals. A composite periodic analog signal is composed of multiple sine waves. • the sine wave is the most fundamental form of a periodic analog signal. Topics discussed in this section: Sine WaveWavelengthTime and Frequency DomainComposite Signals Bandwidth

  10. Analog signals(cont’d) • Sine Wave (정현파)

  11. Analog signals(cont’d) • Sine wave can be fully described by three characteristics • amplitude(진폭) • period(주기), frequency(주파수) • phase(위상)

  12. Analog signals(cont’d) • Amplitude(진폭) ~ refer to the height of the signal. 특정 순간의 신호 값; voltage(전압), amperes(전류), watts(전력) • Period(주기), Frequency(주파수) • Period ~ refers to the amount of time, in seconds, a signal needs to complete one cycle. • Frequency ~ refers to number of periods a signal makes over the course of one second.(주기의 역수(1/t), 초당 주기의 반복 횟수)

  13. Analog signals(cont’d) Frequency=1/Period, Period=1/Frequency f = 1 / T , T = 1 / f • Unit of Frequency ~ is expressed in Hertz(Hz). • Unit of Period ~ is expressed in seconds.

  14. Analog signals (cont’d) Figure 3.3Two signals with the same phase and frequency, but different amplitudes

  15. Analog signals (cont’d) Figure 3.4Two signals with the same amplitude and phase, but different frequencies

  16. Analog signals(cont’d) Table 3.1 Units of period and frequency

  17. Analog signals(cont’d) • More about Frequency • Frequency is rate of change with respect to time • Change in a short span of time means high frequency. • Change in a long span of time means low frequency. • Two Extremes • If a signal does not change at all, its frequency is zero. • If a signal changes instantaneously, its frequency is infinity.

  18. Analog signals(cont’d) • Phase(위상) ~ describes the position of the waveform relative to time zero(시간 0에 대한 파형의 상대적인 위치)

  19. Analog signals(cont’d) • Relationship between different phases

  20. Analog signals (cont’d) • Example 3.6 : A sine wave is offset one-sixth of a cycle with respect to time zero. What is its phase in degrees and radians? • Solution • We know that one complete cycle is 360 degrees. • Therefore, 1/6 cycle is • (1/6) 360 = 60 degrees = 60 x (2p/360) rad = 1.046 rad 2pi radians equal to 360 degrees, thus 1 radian = 180/pi

  21. Analog signals(cont’d) • Sine wave examples ft

  22. Analog signals(cont’d) • Sine wave examples ft

  23. Analog Signals(cont’d) • Sine wave examples ft

  24. Analog signals(cont’d) • Amplitude change

  25. Analog signals(cont’d) • Frequency change

  26. Analog signals(cont’d) • Phase change

  27. Analog signals(cont’d) • Wavelength = Lamda = c/f (propagation speed/frequency)

  28. Analog signals(cont’d) • Time versus Frequency Domain • Time Domain : instantaneous amplitude with respect to time. • Frequency Domain : maximum amplitude with respect to frequency.

  29. Analog signals(cont’d) • Time versus Frequency Domain • Time Domain : instantaneous amplitude with respect to time. • Frequency Domain : maximum amplitude with respect to frequency.

  30. Analog signals(cont’d) • Time and Frequency domains Peak value Peak value

  31. Analog signals(cont’d) Figure 3.8The time domain and frequency domain of three sine waves

  32. Composite Signal • Composite Signal • A single-frequency sine wave is not useful in data communications; we need to change one or more of its characteristics to make it useful. • When we change one or more characteristics of a single-frequency signal, it becomes a composite signal made of many frequencies.

  33. Composite Signal (cont’d) • According to Fourier analysis, any composite signal is a combination of simple sine waves with different frequencies, amplitudes, and phases. Fourier analysis is discussed in Appendix C. • If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies; if the composite signal is nonperiodic, the decomposition gives a combination of sine waves with continuous frequencies.

  34. Composite Signal (cont’d) Example 3.8 Figure 3.9 shows a periodic composite signal with frequency f. This type of signal is not typical of those found in data communications. We can consider it to be three alarm systems, each with a different frequency. The analysis of this signal can give us a good understanding of how to decompose signals.

  35. Composite Signal (cont’d) Figure 3.9A composite periodic signal

  36. Composite Signal (cont’d) Figure 3.10Decomposition of a composite periodic signal in the time and frequency domains

  37. Composite Signal (cont’d) Example 3.9 Figure 3.11 shows a nonperiodic composite signal. It can be the signal created by a microphone or a telephone set when a word or two is pronounced. In this case, the composite signal cannot be periodic, because that implies that we are repeating the same word or words with exactly the same tone.

  38. Composite Signal (cont’d) Figure 3.11The time and frequency domains of a nonperiodic signal

  39. Composite Signal (cont’d) • An demonstration on Fourier • http://www.earlevel.com/Digital%20Audio/harmonigraf.html

  40. Bandwidth • Frequency Spectrum and Bandwidth • The frequency spectrum of a signal is the combination of all sine wave signals that make signal. • The bandwidth of a signal is the width of the frequency spectrum • The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal.

  41. Bandwidth (cont’d) • Frequency Spectrum

  42. Bandwidth (cont’d) Figure 3.12The bandwidth of periodic and nonperiodic composite signals

  43. Bandwidth (cont’d) Example 3.10 If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is its bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V.

  44. Bandwidth (cont’d) Figure 3.13The bandwidth for Example 3.10

  45. Bandwidth (cont’d) Example 3.11 A periodic signal has a bandwidth of 20 Hz. The highest frequency is 60 Hz. What is the lowest frequency? Draw the spectrum if the signal contains all frequencies of the same amplitude.

  46. Bandwidth (cont’d) Figure 3.14 The bandwidth for Example 3.11

  47. Bandwidth (cont’d) Example 3.12 A nonperiodic composite signal has a bandwidth of 200 kHz, with a middle frequency of 140 kHz and peak amplitude of 20 V. The two extreme frequencies have an amplitude of 0. Draw the frequency domain of the signal.

  48. Bandwidth (cont’d) Figure 3.15The bandwidth for Example 3.12

  49. 3.3 DIGITAL SIGNALS In addition to being represented by an analog signal, information can also be represented by a digital signal. For example, a 1 can be encoded as a positive voltage and a 0 as zero voltage. A digital signal can have more than two levels. In this case, we can send more than 1 bit for each level. Topics discussed in this section: Bit RateBit LengthDigital Signal as a Composite Analog Signal Application Layer

  50. Digital Signals Figure 3.16Two digital signals: one with two signal levels and the other with four signal levels

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