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 An example of analog data : human voice
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
~ 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)
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 = 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

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 = = 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 = = 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 = s = x 106 ms = 500 ms

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

46. Digital versus Analog

47. Digital versus Analog B = n bps/2 Adding third harmonic
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
Bit
Rate
Harmonic 1
Harmonics
1, 3
1, 3, 5
1, 3, 5, 7
1 Kbps
500 Hz
2 KHz
4.5 KHz
8 KHz
10 Kbps
5 KHz
20 KHz
45 KHz
80 KHz
100 Kbps
50 KHz
200 KHz
450 KHz
800 KHz

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.

51. 3.5 Data Rate Limits Data rate depends on three factors
The Bandwidth available
The levels of signals we can use
The quality of the channel (the level of the noise)
Noiseless channel : Nyquist Bit Rate
BitRate = 2 x Bandwidth x log2 L
L : number of signal levels
Example 7
Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal with two signal levels. The maximum bit rate can be calculated as
Bit Rate = 2  3000  log2 2 = 6000 bps

52. C = B log2 (1 + SNR) = B log2 (1 + 0) = B log2 (1) = B  0 = 0
Data Rate Limits
Noisy channel: Shannon Capacity
Capacity = Bandwidth x log2 (1 + SNR)
Example 9
Consider an extremely noisy channel in which the value of the signal-to-noise ratio is almost zero. In other words, the noise is so strong that the signal is faint. For this channel the capacity is calculated as 
C = B log2 (1 + SNR) = B log2 (1 + 0) = B log2 (1) = B  0 = 0

53. 3.6 Transmission Impairment
Transmission media are not perfect because of impairment in the signal sent through the medium
Signal at the beginning and end of the medium are not same

54. Transmission Impairment
Attenuation
means loss of energy
When signal travels trough a medium, it losses some of it energy
So, to compensate for this loss, amplifiers are used to amplify the signal
Decibel (dB)
dB = 10 log10 (p2/p1)

55. Transmission Impairment
p2 = (1/2) p1
Signal powers are increased 10 times by AMP

56. Transmission Impairment
dB = = +1

57. Transmission Impairment
Distortion
Means that signal changes its form or shape

58. Transmission Impairment
Noise
- Noise types
thermal noise, induced noise, crosstalk and impulse noise
Thermal noise : random motion of electrons
Induced noise : from sources such as motors, appliances
Crosstalk : the effect of one wire on the other
Impulse noise : a spike that comes from power lines, lightning, and so on.

59. Transmission Impairment
noise

60. 3. 7 More about Signals Throughput
is the measurement of how fast data can pass through a point

61. More about Signals
Propagation Time

62. More about Signals
Wavelength = Lamda = c/f