Exploring Analog and Digital Signals: Understanding the Basics

1. Signals Prof. Choong Seon HONG

2. 3. 신호 (Signals) 3.1 아날로그와 디지털(Analog and Digital) 3.2 아날로그 신호(Analog signals) 3.3 디지털 신호(Digital signals) 3.4 Analog vs. Digital 3.5 Data Rate Limits 3.6 Transmission Impairment 3.7 More about Signals

3. Signals (cont’d) • Information can be voice, image, numeric data, characters, code, picture, and so on • To be transmitted, information must be into electromagnetic signals.

4. 3.1 Analog and Digital • Analog and Digital Data • An example of analog data : human voice • An example of digital data : data stored in the memory of a computer in the form of 0s and 1s

5. 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

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

7. 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

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

9. 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

10. 3.2 Analog signals ~ can be classified as 단순(simple) or 복합(complex) signal. • Simple Analog signals • the sine wave is the most fundamental form of a periodic analog signal.

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

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

13. 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)

14. 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.

15. Analog signals(cont’d)

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

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(단일 주기내에서 시간에 대한 상대적인 위치).

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

20. Analog signals(cont’d) • Example 2 : 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

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

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

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) • Time versus Frequency Domain • Time Domain : instantaneous amplitude with respect to time. • Frequency Domain : maximum amplitude with respect to frequency.

28. Analog signals(cont’d) • Time and Frequency domains

29. Analog signals(cont’d) • Time and Frequency domains for different signals

30. Analog signals(cont’d) • Complex 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. • When we change one or more characteristics of a single-frequency signal, it becomes a composite signal made of many frequencies.

31. Analog signals(cont’d) • According to Fourier analysis, any composite signal can be represented as a combination of simple sine waves with different frequencies, phases, and amplitudes • Square wave

32. Analog signals(cont’d) • Three harmonics • Adding first three harmonics

33. Analog signals(cont’d) • An demonstration on Fourier • http://www.earlevel.com/Digital%20Audio/harmonigraf.html

34. Analog signals(cont’d) • A signal with a DC component

35. Analog signals(cont’d) • Complex waveform

36. Analog signals(cont’d) • 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.

37. Analog Signals (cont’d) • Frequency Spectrum

38. Analog Signals • Composite Signal and Transmission Media

39. Analog Signals • 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.

40. Example 3 • If a period signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, What is the bandwidth? • Solution • Let fh be the highest frequency, fl be the lowest frequency, and B be the bandwidth. Then, • B = fh - fl = 900 - 100 = 800 Hz

41. Example 4 • A signal has a bandwidth of 20 KHz. The highest frequency is 60 KHz. What is the lowest frequency? • Solution • Let. fh : highest frequency fl : lowest frequency B : Bandwidth B = fh - fl  20 = 60 - fl = fl = 60 - 20 = 40 KHz

42. Example 5 • 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.

43. 3.3 Digital Signals • A digital signals

44. Digital Signals(cont’d) • Bit Interval and Bit Rate • Bit Interval ~ is the time required to send one single bit. • Bit Rate ~ is the number of bits sent in one second. • A digital signal has a bit rate of 2000 bps. What is the duration of each bit (bit interval)?  The bit interval is the inverse of the bit rate. Bit interval = 1/ 2000 s = 0.000500 s = 0.000500 x 106 ms = 500 ms

45. Digital Signals(cont’d) • Bit rate and bit interval

46. Digital versus Analog

47. Digital versus Analog • Bandwidth (for single harmonic) to send n bps through analog channel • B = n bps/2 • Adding third harmonic • B = n/2 + 3n/2 = 4n/2 Hz • Adding third and fifth harmonic • B = n/2 + 3n/2 + 5n/2 = 9n/2 • Bandwidth requirements : B >= n/2 or n <=2B

48. Digital versus Analog Bandwidth • The analog of a bandwidth of a medium is expressed in hertz; the digital bandwidth in bits per second

49. 3.4 Analog versus Digital • Low-pass versus Band-pass

50. Analog versus Digital • Digital transmission needs a low-pass channel. • Analog transmission can use a band-pass channel.