Lecture Focus:

1. Data and Signals CSCS 311 Lecture Focus: Data Communications and Networking Lecture 13

2. Data and Signals Background • One of the major functions of the physical layer is to move data in the form of electromagnetic signals across a transmission medium. • Generally, the data usable to a person or application are not in a form that can be transmitted over a network. • For example, a photograph must first be changed to a form that transmission media can accept. • Transmission media work by conducting energy along a physical path. To be transmitted, data must be transformed to electromagnetic signals.

3. Data and Signals To be transmitted, data must be transformed to electromagnetic signals. • Viewed as a function of time, an electromagnetic signal can be either continuous or discrete. • A continuous signal is one in which the signal intensity varies in a smooth fashion over time. • There are no breaks or discontinuities in the signal. • A discrete signal is one in which the signal intensity maintains a constant level for some period of time and then changes to another constant level.

4. Data and Signals • Figure below shows examples of both kinds of signals. • The continuous signal might represent speech, and the discrete signal might represent binary 1s and 0s.

5. Data and Signals ANALOG AND DIGITAL Both data and the signals that represent them can be either analog or digital in form. ANALOG AND DIGITAL DATA • 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. • For example, an analog clock that has hour, minute, and second hands gives information in a continuous form; the movements of the hands are continuous. • On the other hand, a digital clock that reports the hours and the minutes will change suddenly from 8:05 to 8:06.

6. Data and Signals ANALOG AND DIGITAL Both data and the signals that represent them can be either analog or digital in form. ANALOG AND DIGITAL DATA • Analog data, such as the sounds made by a human voice, take on continuous values. • When someone speaks, an analog wave is created in the air. This can be captured by a microphone and converted to an analog signal or sampled and converted to a digital signal. • Digital data take on discrete values. For example, data are stored in computer memory in the form of 0s and 1s. • They can be converted to a digital signal or modulated into an analog signal for transmission across a medium.

7. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL DATA • Data can be analog or digital. • Analog data are continuous and take continuous values. • Digital data have discrete states and take discrete values.

8. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL SIGNALS • Like the data they represent, signals can be either analog or digital. • An analog signal has 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. • A digital signal can have only a limited number of defined values. • Although each value can be any number, it is often as simple as 1 and 0.

9. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL SIGNALS Analog signals can have an infinite number of values in a range. Digital signals can have only a limited number of values.

10. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL SIGNALS • The simplest way to show signals is by plotting them on a pair of perpendicular axes. • The vertical axis represents the value or strength of a signal. • The horizontal axis represents time.

11. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL SIGNALS • Figure below illustrates an analog signal and a digital signal: • The curve representing the analog signal passes through an infinite number of points. • The vertical lines of the digital signal, however, demonstrate the sudden jump that the signal makes from value to value.

12. Data and Signals ANALOG AND DIGITAL ANALOG AND DIGITAL SIGNALS Comparison of analog and digital signals

13. Data and Signals PERIODIC AND NONPERIODIC SIGNALS • Both analog and digital signals can take one of two forms: • Periodic • Non-periodic ( orAperiodic ). • A periodic signal completes a pattern within a measurable time frame, called a period, and repeats that pattern over subsequent identical periods. • The completion of one full pattern is called a cycle. • A non-periodic signal changes without exhibiting a pattern or cycle that repeats over time. The simplest sort of signal is a periodic signal, in which the same signal pattern repeats over time.

14. Data and Signals PERIODIC AND NONPERIODIC SIGNALS • Both analog and digital signals can be periodic or non-periodic. • In data communications, we commonly use: • Periodic analog signals (because they need less bandwidth), and • Non-periodic digital signals (because they can represent variation in data).

15. PERIODIC AND NONPERIODIC SIGNALS • Example of a periodic analog signal (sine wave)

16. PERIODIC AND NONPERIODIC SIGNALS • Example of a periodic digital signal (square wave)

17. PERIODIC AND NONPERIODIC SIGNALS Mathematically, a signal s(t) is defined to be periodic if and only if s(t + T) = s(t) - < t < + where the constant T is the period of the signal.(T is the smallest value that satisfies the equation.) Otherwise, a signal is aperiodic.

18. Data and Signals PERIODIC ANALOG SIGNALS • Periodic analog signals can be classified as: • Simple • 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.

19. PERIODIC ANALOG SIGNALS Sine Wave • The sine wave is the most fundamental form of a periodic continuous analog signal. • When we visualize it as a simple oscillating curve, its change over the course of a cycle is smooth and consistent, a continuous, rolling flow.

20. Data and Signals PERIODIC ANALOG SIGNALS Sine Wave • Figure below shows a sine wave. • Each cycle consists of a single arc above the time axis followed by a single arc below it.

21. PERIODIC ANALOG SIGNALS Sine Wave • A general sine wave can be represented by three parameters: • The amplitude • The frequency • The phase • These three parameters fully describe a sine wave. • The general sine wave can be written: s(t) = A sin(2ft + )

22. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude • The peak amplitude of a signal is the absolute value of its highest intensity, proportional to the energy it carries. • For electric signals, peak amplitude is normally measured in volts or watts.

23. Data and Signals PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude • Figure below shows a signal and its peak amplitude.

24. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude Period and Frequency • Period refers to the amount of time, in seconds, a signal needs to complete 1 cycle. • Frequency refers to the number of periods in 1s. • Frequency = cycles per second • Period and frequency are just one characteristic defined in two ways. Frequency and period are inverses of each other. • Period is formally expressed in seconds. • Frequency is formally expressed in Hertz (Hz), which is cycle per second.

25. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude • Period and Frequency

26. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude • Period and Frequency

27. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude Two signals with the same phase and frequency, but different amplitudes

28. PERIODIC ANALOG SIGNALS Sine Wave Peak Amplitude Two signals with the same amplitude and phase, but different frequencies

29. PERIODIC ANALOG SIGNALS Sine Wave

30. PERIODIC ANALOG SIGNALS Sine Wave

31. PERIODIC ANALOG SIGNALS Sine Wave

32. PERIODIC ANALOG SIGNALS Sine Wave Units of periods and frequencies

33. PERIODIC ANALOG SIGNALS Sine Wave Frequency Frequency is the rate of change with respect to time. Change in a short span of time means high frequency. Change over a long span of time means low frequency. If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.

34. PERIODIC ANALOG SIGNALS Sine Wave Phase The term phase describes the position of the waveform relative to time 0. If we think of the wave as something that can be shifted backward or forward along the time axis, phase describes the amount of that shift. It indicates the status of the first cycle. Phase is measured in degrees or radians [360° is 2 rad; 1° is 2 /360 rad, and 1 rad is 360/(2 )]. A phase shift of 360° corresponds to a shift of a complete period; a phase shift of 180° corresponds to a shift of one-half of a period; and a phase shift of 90° corresponds to a shift of one-quarter of a period.

35. PERIODIC ANALOG SIGNALS Sine Wave Phase Three sine waves with the same amplitude and frequency, but different phases • A sine wave with a phase of 0° starts at time 0 with a zero amplitude. The amplitude is increasing. • A sine wave with a phase of 90° starts at time 0 with a peak amplitude. The amplitude is decreasing. • A sine wave with a phase of 180° starts at time 0 with a zero amplitude. Theamplitude is decreasing.

36. PERIODIC ANALOG SIGNALS Sine Wave Phase Three sine waves with the same amplitude and frequency, but different phases • A sine wave with a phase of 0° is not shifted. • A sine wave with a phase of 90° is shifted to the left by 1/4 cycle. However, note that the signal does not really exist before time 0. • A sine wave with a phase of 180° is shifted to the left by ½ cycle. However, note that the signal does not really exist before time 0.

37. PERIODIC ANALOG SIGNALS Sine Wave Figure below shows the effect of varying each of the three parameters. In part (a) of the figure, the frequency is 1 Hz; thus, the period is T = 1 second. Part (b) has the same frequency and phase but an amplitude of 1/2. In part (c), we have f = 2, which is equivalent to T = 1/2. Finally, part (d) shows the effect of a phase shift of / 4 radians, which is 45 degrees (2 radians = 3600 = 1 period).

38. PERIODIC ANALOG SIGNALS Sine Wave

39. PERIODIC ANALOG SIGNALS Sine Wave Wavelength Wavelength binds the period or the frequency of a simple sine wave to the propagation speed of the medium. The frequency of a signal is independent of the medium. The wavelength depends on both the frequency and the medium. In data communications, we often use wavelength to describe the transmission of light in an optical fiber.

40. PERIODIC ANALOG SIGNALS Sine Wave Wavelength The wavelength is the distance a simple signal can travel in one period. Direction of propagation

41. PERIODIC ANALOG SIGNALS Sine Wave Wavelength Wavelength can be calculated if one is given the propagation speed (the speed of light) and the period of the signal. If we represent wavelength by , propagation speed by c (speed of light), and frequency by f, we get Wavelength = Propagation Speed / Frequency = Propagation Speed x Time period The wavelength is normally measured in micrometers (microns) instead of meters.

42. PERIODIC ANALOG SIGNALS Sine Wave Wavelength Wavelength = Propagation Speed / Frequency = Propagation Speed x Time period Example: The wavelength of red light (frequency =4 x 1014) in air is: In a coaxial or fiber-optic cable, the wavelength is shorter (0.5 µm) because the propagation speed in the cable is decreased.

43. Time and Frequency Domains • A sine wave is comprehensively defined by its amplitude, frequency, and phase. • We can show a sine wave by two ways: • Time Domain • Frequency Domain

44. Time and Frequency Domains The time-domain plot shows changes in signal amplitude with respect to time (it is an amplitude-versus-time plot). Phase is not explicitly shown on a time-domain plot.

45. Time and Frequency Domains Frequency-domain shows the relationship between amplitude and frequency. A frequency-domain plot is concerned with only the peak value and the frequency. Changes of amplitude during one period are not shown.

46. Time and Frequency Domains Frequency domain is easy to plot and conveys the information that one can find in a time domain plot. The advantage of the frequency domain is that we can immediately see the values of the frequency and peak amplitude. A complete sine wave is represented by one spike. The position of the spike shows the frequency; its height shows the peak amplitude. The frequency domain is more compact and useful when we are dealing with more than one sine wave. An analog signal is best represented in the frequency domain.

47. Time and Frequency Domains Figure below shows three sine waves, each with different amplitude and frequency. All can be represented by three spikes in the frequency domain.

48. Time and Frequency Domains Time Domain Frequency Domain

49. Time and Frequency Domains Frequency Domain Time Domain

50. Time and Frequency Domains Composite Signals Simple sine waves have many applications in daily life. We can send a single sine wave to carry electric energy from one place to another. For example, the power company sends a single sine wave with a frequency of 60 Hz to distribute electric energy to houses and businesses. As another example, we can use a single sine wave to send an alarm to a security center when a burglar opens a door or window in the house. In the first case, the sine wave is carrying energy; in the second, the sine wave is a signal of danger.