British Computer Society (BCS)

1. British Computer Society (BCS) Computer Networks Digital Communications Data and Signals

2. Lesson Aim An understanding of digital data and analog data An understanding of digital transmission and analog transmission and various transmission impairments in communication systems An understanding of guided and unguided transmission media

3. Lesson Objective • To differentiate digital signals with analog one • Explain advantages of digital transmission over analog one • Understand the effects of transmission impairments in communication channel • Understand the techniques use to transmit data digitally • Understand the mechanism for modulating digital data into an analog signal and an analog to an analog signal • Explain the characteristics and applications of transmission medium

4. Digital Communications • Data and Signals • 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. Analog data take on continuous values. Digital data take on discrete values.

5. Digital Communications • Signals: • Information travels through a transmission system is in the form of electric or electromagnetic signals • Signaling is the physical propagation of the signal along a transmission media • Signals are represented in two ways: Analog and Digital • Analog signals: • Analog signals can have an infinite number of values in a range. As the wave moves from value A to value B, it passes through and includes an infinite number of values along its paths • Digital Signal: • Digital signals can have only a limited number of values. Although each value can be any number, it is often as simple as 1 and 0

6. Digital Communications Figure 1.1: Comparison of analog and digital signals

7. Digital Communications • Figure 1.1 above illustrate 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

8. Digital Communications • Periodic and Nonperiodic signals: • Both analog and digital signals can be periodic or non periodic • 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 nonperiodic signal changes without exhibiting a pattern or cycle that repeats over time • In data communications, we commonly use periodic analog signals and nonperiodic digital signals

9. Digital Communications • Periodic Analog Signals: • Sine Wave: • The sine wave is the most fundamental form of a periodic analog signal • A sine wave can be represented by three parameters: the peak amplitude, the frequency and the phase • 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

10. Digital Communications Figure 1.2: A Sine wave

11. Digital Communications Figure 1.3: Two signals with the same phase and frequency, but different amplitude

12. Digital Communications • Period and Frequency: • Period is the amount of time, in seconds, a signal needs to complete 1 cycle • Frequency is the number of periods in 1 seconds • Period and frequency are the inverse of each other, as the following formulas show: • Period is measured in seconds whereas frequency is measured in Hertz (Hz) f= 1/T and T= 1/f

13. Digital Communications Figure 1.4: Two signals with the same amplitude and phase, but different frequencies

14. Digital Communications Table 1.1 Units of period and frequency

15. Digital Communications Example 1.1: The power we use at home has a frequency of 60 Hz. The period of this sine wave can be determined as follows: Solution:

16. Digital Communications Example 1.2: The period of a signal is 100 ms. What is its frequency in kilohertz? Solution: First we change 100 ms to seconds, and then we calculate the frequency from the period (1 Hz = 10−3 kHz).

17. Digital Communications • Phase: • The term phase describes the position of the waveform relatives to time 0. • Phase is measured in degrees or radians • A phase shift of 3600 corresponds to a shift of a complete period • A phase shift of 1800 corresponds to a shift of one half of a period • A phase shift of 900 corresponds to a shift of one quarter of a period

18. Digital Communications Figure 1.5: Three sine waves with the same amplitude and frequency, but different phases

19. Digital Communications Example 1.3: A sine wave is offset 1/6 cycle with respect to time 0. What is its phase in degrees and radians? Solution: We know that 1 complete cycle is 360°. Therefore, 1/6 cycle is

20. Digital Communications • Wavelength: • Wavelength is another characteristic of a signal travelling through a transmission medium • Wavelength binds the frequency of a simple sine wave to the propagation speed of the medium • While the frequency of a signal is independent of the medium, the wavelength depends on both the frequency and the medium • If wavelength is represented by‘’ propagation speed by ‘c’ and frequency by ‘f’, we get wavelength = propagation speed* period = propagation speed/ frequency

21. Digital Communications Figure 1.6: Wavelength and period

22. Digital Communications • Time and Frequency Domain: • A sine wave is characterise by amplitude, frequency and phase • A sine wave can be represented by a time domain plot • The time domain plot shows changes in signal amplitude with respect to time • To show the relationship between amplitude and frequency, a frequency domain plot is used • A frequency domain plot is concerned with only the peak value and the frequency. Change of amplitude during one period are not considered.

23. Digital Communications Figure 1.7 The time-domain and frequency-domain plots of a sine wave

24. Note Digital Communications A complete sine wave in the time domain can be represented by one single spike in the frequency domain.

25. Digital Communications Example 1.4: The frequency domain is more compact and useful when we are dealing with more than one sine wave. For example, Figure 1.8 shows three sine waves, each with different amplitude and frequency. All can be represented by three spikes in the frequency domain.

26. Digital Communications Figure 1.8 The time domain and frequency domain of three sine waves

27. Digital Communications • Composite Signals: • A composite signal is a combination of simple sine waves with different frequencies, amplitude, and phases • A composite signal can be periodic or non periodic • If the composite signal is periodic, the decomposition gives a series of signals with discrete frequencies • If the composite signal is non periodic, the decomposition gives a combination of sine waves with continuous frequencies

28. Digital Communications Example 1.5: Figure 1.9 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

29. Digital Communications Figure 1.9 A composite periodic signal

30. Digital Communications • Figure 1.10 shows the result of decomposing the above signal in both the time and frequency domain • The amplitude of the sine wave with frequency f is almost the same as the peak amplitude of the composite signal. This is also called the fundamental frequency or 1st harmonic • The amplitude of the sine wave with frequency 3f is one third of that of the first. This is called the third harmonic • The amplitude of the sine wave with frequency 9f is one ninth of the first. This is called the ninth harmonic • Note that the frequency decomposition of the signal is discrete; it has frequencies of f, 3f, and 9f . The frequency domain of a periodic composite signal is always made of discrete spikes

31. Digital Communications Figure 1.10 Decomposition of a composite periodic signal in the time and frequency domains

32. Digital Communications Example 1.6: Figure 1.11 shows a non periodic 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.

33. Digital Communications Figure 1.11 The time and frequency domains of a nonperiodic signal

34. Digital Communications • In a time domain representation of this composite signal, there are an infinite number of simple sine frequencies • Although the number of frequencies in a human voice is infinite, the range is limited. A normal human being can create a continuous range of frequencies between 0 and 4 KHz • Note that the frequency decomposition of the signal yields a continuous curve. There are an infinite number of frequencies between 0.0 and 4000.0 (real values). To find the amplitude related to frequency f, we draw a vertical line at f to intersect the envelope curve. The height of the vertical line is the amplitude of the corresponding frequency

35. Digital Communications • Bandwidth: • The bandwidth of a composite signal is the difference between the highest and the lowest frequencies contained in that signal • Figure 1.12 below shows the concept of bandwidth. • The figure depicts two composite signals, one periodic and the other non periodic • The bandwidth of the periodic signal contains all integer frequencies between 1000 and 5000 (1000,1001, 1002,….) • The bandwidth of the non periodic signals has the same range, but the frequencies are continuous

36. Digital Communications Figure 1.12: The bandwidth of periodic and nonperiodic composite signals

37. Digital Communications • Digital Signals: • An information can be represent by a digital signal • A digital information ‘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 • Figure 1.13 shows two signals, one with two levels and the other with four • In general, if a signal has ‘L’ levels, each level needs log2 L bits

38. Digital Communications Figure 1.13 Two digital signals: one with two signal levels and the other with four signal levels

39. Digital Communications Example 1.7 A digital signal has eight levels. How many bits are needed per level? We calculate the number of bits from the formula Each signal level is represented by 3 bits

40. Digital Communications • Bit Rate: • Bit rate is the number of bits sent in one second • It is expressed in bits per second (bps) • Bit Length: • The bit length is the distance one bit occupies on the transmission medium Bit length = propagation speed * bit duration

41. Digital Communications Example 1.8: Assume we need to download text documents at the rate of 100 pages per minute. What is the required bit rate of the channel? Solution A page is an average of 24 lines with 80 characters in each line. If we assume that one character requires 8 bits, the bit rate is

42. Digital Communications • Digital Signal as a Composite Analog Signal: • Base on Fourier analysis, a digital signal is a composite analog signal • If the digital signal is periodic, which is rare in data communications, the decomposed signal has a frequency domain representation with an infinite bandwidth and discrete frequencies • If the digital signal is non periodic, the decomposed signal still has an infinite bandwidth, but the frequencies are continuous • Figure 1.14 shows a periodic and a nonperiodic digital signal and their bandwidths

43. Digital Communications Figure 1.14 The time and frequency domains of periodic and non periodic digital signals

44. Digital Communications • Transmission of Digital signal: • To transmit a digital signal from point ‘A’ to point ‘B’, one of two different approaches can be used • Baseband Transmission • Broadband Transmission

45. Digital Communications • Baseband Transmission: • Baseband transmission means sending a digital signal over a channel without changing the digital signal to an analog signal. • Fig 1.15 shows the baseband transmission • Baseband transmission is carried out on a low pass channel, a channel with a bandwidth that starts from zero. This is the case if we have a dedicated medium with a bandwidth constituting only one channel. • For example, the entire bandwidth of a cable connecting two computers is one single channel • Figure 1.16 shows two low pass channel: one with a narrow bandwidth and the other with a wide bandwidth • As a low pass channel with infinite bandwidth is ideal, but cannot achieve such a channel in real life. However, we can get close to it

46. Digital Communications Figure 1.15 Baseband transmission

47. Digital Communications Figure 1.16 Bandwidths of two low-pass channels

48. Digital Communications • Broadband Transmission: • Broadband transmission means changing the digital signal to an analog signal for transmission. • Broad band transmission use a band pass channel, a channel with a bandwidth that does not start from zero • Figure 1.17 shows a band pass channel • Figure 1.18 shows the modulation of a digital signal • In the figure , a digital signal is converted to a composite analog signal. This composite analog signal is transmit through band pass channel . At the receiver the received analog signal is converted to digital and the result is a replica of what has been sent

49. Digital Communications Figure 1.17 Bandwidth of a band pass channel

50. Digital Communications Figure 1.18 Modulation of a digital signal for transmission on a bandpass channel