Understanding Signals - Analog vs Digital, Frequency, Bandwidth

1. Part II. Physical Layer and Media Chapter 3. Data and Signals COMP 3270 Computer Networks Computing Science Thompson Rivers University

2. Learning Objectives • Interpret three characteristics of a sine wave. • Explain the basic idea of encoding/decoding. • Define the time domain plot and the frequency domain plot. • Interpret the concept of bandwidth. • Interpret a composite signal. • Relate the bandwidth of a signal and the bandwidth of a transmission medium when data is transmitted. • List the types of noise. • Use decibel to calculate the attenuation of a signal. • Use Nyquist bit rate and Shannon capacity formulas to determine the appropriate bit rate and signal level when a channel is given. • Interpret the concept of bandwidth-delay product.

3. Position of the Physical Layer

4. Main responsibility/role: node-to-node delivery of bits

5. Note: To be transmitted, data (i.e., bits) must be transformed to electric or electromagnetic signals.

6. 1. Analog and Digital • Analog and Digital Data • Analog and Digital Signals • Periodic and Aperiodic Signals

7. Analog and Digital Data

8. Analog and Digital Signals Signals can be analog or digital. Analog signals can have an infinite number of values (energy strength) in a range; digital signals can have only a limited number of values.

9. AC electric signals, Electromagnetic signals DC electric signals

10. In data communication, we commonly use periodic analog signals and aperiodic digital signals.

11. 2. Periodic Analog Signals • Sine Wave • Phase • Examples of Sine Waves • Time and Frequency Domains • Composite Signals • Bandwidth

12. Sine Wave A most fundamental form of a periodic analog signal Three characteristics: PeakAmplitude Frequency Phase

13. Amplitude: energy level of a signal

14. 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. The number of sine waves in a second

15. Frequency and period are inverses of each other.

16. Period and frequency f = 1/T, T = 1/f

18. Units of periods and frequencies

19. Example Express a period of 100 ms in microseconds, and express the corresponding frequency in kilohertz. Solution From the previous table we find the equivalent of 1 ms. We make the following substitutions: 100 ms = 100  10-3 s = 100  10-3 10s = 105s Now we use the inverse relationship to find the frequency, changing hertz to kilohertz 100 ms = 100  10-3 s = 10-1 s f = 1/10-1 Hz = 10  10-3 KHz = 10-2 KHz

20. If a signal does not change at all, its frequency is zero. If a signal changes instantaneously, its frequency is infinite.

21. Phase Phase describes the position of the waveform relative to time zero.

22. Relationships between different phases

23. Example 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 2 /360 rad = 1.046 rad

24. Wavelength

25. Sine wave examples s(t) = A sin (2πft + φ)

28. Time and Frequency Domain Plots An analog signal is best represented in the frequency domain plot.

31. Composite Signals 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. ☺ What characteristics? ☺ Basic idea of encoding/decoding? The change of a characteristic

32. When we change one or more characteristics of a single-frequency signal, it becomes a composite signal made of many frequencies. Any non-single-frequency sine wave is a composite signal.

33. According to Fourier analysis, any composite signal (even digital signal)can be represented as a combination of simple sine waves with different frequencies, phases, and amplitudes.

34. Example: Square wave (electric signal with two different voltage levels)

35. The sine waves in the Fourier transform of the previous square wave The first three sine waves in the Fourier transform of the previous square wave

37. Adding first three harmonics Not the exact original square wave! It is still possible to decode the information.

38. The time and frequency domains of a nonperiodic signal

39. Signal corruption A transmission medium can pass only some frequencies, not all of them. ☺ What does this mean?

40. Intermediate summary • Two types of signals • Analog and digital signal • Three characteristics of analog signals • Peak amplitude, frequency, phase • The basic idea of encoding/decoding • Composite signals • A transmission medium can pass only some frequencies, not all of them.

41. Bandwidth The bandwidth is a property of a medium: It is the difference between the highest and the lowest frequencies that the medium can satisfactorily pass. Frequencies of at least one half of the peak amplitude.

42. The bandwidth is also a property of a composite signal: It is the difference between the highest and the lowest frequencies.

43. We use the term bandwidth to refer to • the property of a medium, or • the width of a single spectrum.

44. Composite signal from the source Composite signal at the destination

45. Example If a periodic signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, what is the bandwidth? Draw the spectrum, assuming all components have a maximum amplitude of 10 V. Solution B = fhfl = 900  100 = 800 Hz The spectrum has only five spikes, at 100, 300, 500, 700, and 900 (see Figure 13.4 )

47. Example A 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 integral frequencies of the same amplitude. Solution B = fh fl 20 = 60 fl fl = 60 20 = 40 Hz

49. Example A signal has a spectrum with frequencies between 1000 and 2000 Hz (bandwidth of 1000 Hz). A medium can pass frequencies from 3000 to 4000 Hz (a bandwidth of 1000 Hz). Can this signal faithfully pass through this medium? Solution The answer is definitely no. Although the signal can have the same bandwidth (1000 Hz), the range does not overlap. The medium can only pass the frequencies between 3000 and 4000 Hz; the signal is totally lost.

50. Bandwidth of a signal Bandwidth of transmission media