1 Kyung Hee University Signals

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 Kyung Hee University 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 Kyung Hee University 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 Kyung Hee University 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 Kyung Hee University Analog and Digital Signals (cont’d)  Comparison of analog and digital signals

7 Kyung Hee University 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 Kyung Hee University Aperiodic and periodic signals (cont’d)  Example of periodic signals

9 Kyung Hee University 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 Kyung Hee University 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 Kyung Hee University Analog signals(cont’d)  Sine Wave ( 정현파 )

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

13 Kyung Hee University 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 Kyung Hee University 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 Kyung Hee University Analog signals(cont’d)

16 Kyung Hee University Analog signals(cont’d)  Units of frequency and period

17 Kyung Hee University 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 Kyung Hee University Analog signals(cont’d)  Phase( 위상 ) ~ describes the position of the waveform relative to time zero( 단일 주기내에서 시간에 대한 상대적인 위치 ).

19 Kyung Hee University Analog signals(cont’d)  Relationship between different phases

20 Kyung Hee University 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 (2  / 360) rad = rad 2pi radians equal to 360 degrees, thus 1 radian = 180/pi

21 Kyung Hee University Analog signals(cont’d)  Sine wave examples

22 Kyung Hee University Analog signals(cont’d)  Sine wave examples

23 Kyung Hee University  Sine wave examples Analog Signals(cont’d)

24 Kyung Hee University Analog signals(cont’d)  Amplitude change

25 Kyung Hee University Analog signals(cont’d)  Frequency change

26 Kyung Hee University Analog signals(cont’d)  Phase change

27 Kyung Hee University 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 Kyung Hee University Analog signals(cont’d)  Time and Frequency domains

29 Kyung Hee University Analog signals(cont’d)  Time and Frequency domains for different signals

30 Kyung Hee University 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 Kyung Hee University 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 Kyung Hee University Analog signals(cont’d)  Three harmonics  Adding first three harmonics

33 Kyung Hee University Analog signals(cont’d)  An demonstration on Fourier

34 Kyung Hee University Analog signals(cont’d)  A signal with a DC component

35 Kyung Hee University Analog signals(cont’d)  Complex waveform

36 Kyung Hee University 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 Kyung Hee University  Frequency Spectrum Analog Signals (cont’d)

38 Kyung Hee University Analog Signals  Composite Signal and Transmission Media

39 Kyung Hee University 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 Kyung Hee University 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 f h be the highest frequency, f l be the lowest frequency, and B be the bandwidth. Then, B = f h - f l = = 800 Hz

41 Kyung Hee University Example 4  A signal has a bandwidth of 20 KHz. The highest frequency is 60 KHz. What is the lowest frequency?  Solution Let. f h : highest frequency f l : lowest frequency B : Bandwidth B = f h - f l  20 = 60 - f l = f l = = 40 KHz

42 Kyung Hee University 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 Kyung Hee University 3.3 Digital Signals  A digital signals

44 Kyung Hee University 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 Kyung Hee University Digital Signals(cont’d)  Bit rate and bit interval

46 Kyung Hee University Digital versus Analog

47 Kyung Hee University 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 Bit Rate Harmonic 1 Harmonics 1, 3 Harmonics 1, 3, 5 Harmonics 1, 3, 5, 7 1 Kbps500 Hz2 KHz4.5 KHz8 KHz 10 Kbps5 KHz20 KHz45 KHz80 KHz 100 Kbps50 KHz200 KHz450 KHz800 KHz

48 Kyung Hee University Digital versus Analog Bandwidth  The analog of a bandwidth of a medium is expressed in hertz; the digital bandwidth in bits per second

49 Kyung Hee University 3.4 Analog versus Digital  Low-pass versus Band-pass

50 Kyung Hee University Analog versus Digital Digital transmission needs a low-pass channel. Analog transmission can use a band-pass channel.

51 Kyung Hee University 3.5 Data Rate Limits  Data rate depends on three factors 1.The Bandwidth available 2. The levels of signals we can use 3. The quality of the channel (the level of the noise)  Noiseless channel : Nyquist Bit Rate -BitRate = 2 x Bandwidth x log 2 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  log 2 2 = 6000 bps Bit Rate = 2  3000  log 2 2 = 6000 bps

52 Kyung Hee University Data Rate Limits  Noisy channel: Shannon Capacity Capacity = Bandwidth x log 2 (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 log 2 (1 + SNR) = B log 2 (1 + 0) = B log 2 (1) = B  0 = 0

53 Kyung Hee University 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 Kyung Hee University 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 log 10 (p 2 /p 1 )

55 Kyung Hee University Transmission Impairment  p 2 = (1/2) p 1  Signal powers are increased 10 times by AMP

56 Kyung Hee University Transmission Impairment  dB = = +1

57 Kyung Hee University Transmission Impairment  Distortion Means that signal changes its form or shape

58 Kyung Hee University 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 Kyung Hee University Transmission Impairment  noise

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

61 Kyung Hee University More about Signals  Propagation Time

62 Kyung Hee University More about Signals  Wavelength = Lamda = c/f