1 4 장 신호 (Signals) 4.1 아날로그와 디지털 (Analog and Digital) 4.2 비주기와 주기 신호 (Aperiodic and periodic) 4.3 아날로그 신호 (Analog signal) 4.4 디지털 신호 (Digital signal) 4.5 요약

2 신호 (cont’d) zInformation can be voice, image, numeric data, characters, code, picture, and so on zTo be transmitted, information must be into electromagnetic signals.

3 신호 (cont’d) Transformation of Information to Signals

4 4.1 Analog and Digital zAnalog information: continuous( 연속 : 무게, 키 ) zDigital information: discrete( 불연속, 이산 : 학 생수 ) zAnalog and digital clocks

5 Analog and Digital(cont’d) zAnalog signals can have any value in a range. zDigital signals can have only a limited number of values. zComparison of analog and digital signals

6 4.2 Aperiodic and periodic signals zPeriodic signals( 주기신호 ) ~ consists of a continuously repeated pattern. zThe periodic of a signal(T) is expressed in seconds.

7 Aperiodic and periodic signals(cont’d) zExample of periodic signals

8 zAperiodic signals( 비주기 신호 ) ~ changes constantly without exhibiting a pattern or cycle that repeat over time. Aperiodic and periodic signals(cont’d)

9 zExample of aperiodic signals Aperiodic and periodic signals(cont’d)

Analog signals ~ can be classified as simple or complex. zSimple Analog signals ythe sine wave is the most fundamental form of a periodic analog signal.

11 Analog signals(cont’d) A sine wave

12 Analog signals(cont’d) zSine wave can be fully described by three characteristics yamplitude( 진폭 ) yperiod( 주기 ), frequency( 주파수 ) yphase( 위상 )

13 Analog signals(cont’d) zAmplitude( 진폭 ) ~ refer to the height of the signal. 특정 순간의 신호 값 ; voltage( 전압 ), amperes( 전 류 ), watts( 전력 ) zPeriod( 주기 ), Frequency( 주파수 ) yPeriod ~ refers to the amount of time, in seconds, a signal needs to complete one cycle. yFrequency ~ 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 yUnit of Frequency ~ is expressed in Hertz(Hz). yUnit of Period ~ is expressed in seconds.

15 Analog signals(cont’d) zUnits of frequency and period

16 Analog signals(cont’d) zExample 4.1 yA sine wave have a frequency of 8KHz. What is its period ? zSolution yLet T be the period and f be the frequency. Then, yT = 1/f = 1/8,000 = = 125  s

17 Analog signals(cont’d) zExample 4.2 yA sine wave completes one cycle in 25  s. what is its frequency? zSolution yLet T be the period and f be the frequency. Then, yf = 1/T = 1/(25*10 -6 ) = 40,000 = 40 KHz

18 Analog signals(cont’d) zPhase( 위상 ) ~ describes the position of the waveform relative to time zero( 단일 주기내에서 시간에 대한 상대적 인 위치 ).

19 Analog signals(cont’d) zRelationship between different phases

20 Analog signals(cont’d) zAmplitude change( 진폭 변조 )

21 Analog signals(cont’d) zFrequency change( 주파수 변조 )

22 Analog signals(cont’d) zPhase change( 위상 변조 )

23 Analog signals(cont’d) zMore about Frequency yFrequency is rate of change with respect to time yChange in a short span of time means high frequency. yChange in a long span of time means low frequency. zTwo Extremes yIf a signal does not change al all, its frequency is zero. yIf a signal changes instantaneously, its frequency is infinity.

24 Analog signals(cont’d) zTime versus Frequency Domain yTime Domain : instantaneous amplitude with respect to time. yFrequency Domain : maximum amplitude with respect to frequency.

25 Analog signals(cont’d) zTime and Frequency domains

26 Analog signals(cont’d) zTime and Frequency domains for different signals

27 Analog signals(cont’d) zComplex Signals yA periodic signal decomposed into two sine waves. xA signal with a DC component yA composite signal decomposed into four components. xComplex waveform

28 Analog signals(cont’d) zA signal with a DC component

29 Analog signals(cont’d) zComplex waveform

30 Analog signals(cont’d) zFrequency Spectrum and Bandwidth yThe frequency spectrum of a signal is the combination of all sine wave signals that make signal. yThe bandwidth of a signal is the width of the frequency spectrum.

31 Analog signals(cont’d) zBandwidth

32 Example 4.3 zIf a period signal is decomposed into five sine waves with frequencies of 100, 300, 500, 700, and 900 Hz, What is the bandwidth? zSolution yLet f h be the highest frequency, f l be the lowest frequency, and B be the bandwidth. Then, yB = f h - f l = = 800 Hz

33 Example 4.4 zA signal has a bandwidth of 20 KHz. The highest frequency is 60 KHz. What is the lowest frequency? zSolution yLet. f h : highest frequency f l : lowest frequency B : Bandwidth B = f h - f l  20 = 60 - f l = f l = = 40 KHz

Digital Signals zA digital signals

35 Digital Signals(cont’d) zAmplitude( 진폭 ), periodic( 주기 ), phase( 위상 )

36 Digital Signals(cont’d) zBit Interval and Bit Rate yBit Interval ~ is the time required to send one single bit. yBit Rate ~ is the number of bits sent in one second.

37 Digital Signals(cont’d) zBit rate and bit interval

38 Digital Signals(cont’d) zDecomposition of a Digital Signal yHarmonics( 조파 ) of a digital signal

39 Digital Signals(cont’d) zExact and significant spectrums

40 Digital Signals(cont’d) zThe bit rate has a relationship to the significant bandwidth such that when the bit rate increases, the significant bandwidth widens.

41 Digital Signals(cont’d) zBit rates and significant spectrums

42 zMedium Bandwidth and Significant Bandwidth ycorruption of a digital signal due to insufficient medium bandwidth Digital Signals(cont’d)

43 Digital Signals(cont’d) zMedium Bandwidth and Data Rate : Channel Capacity yMedium Bandwidth and Data Rate

44 Digital Signals(cont’d) zUse of Analog Signals to Transmit Digital Data yExample 4.5 xWhat bandwidth is required for data being sent at a rate of 10 bps using analog signals? Assume the each signal element is one bit. ySolution

45 Digital Signals(cont’d) zExample 4.6 ycompare the bandwidths required for analog data being sent at 1,000 and 10,000 bps zSolution y10 bps - 5 Hz y1,000 bps Hz y10,000 bps - 5,000 Hz RAs the data rate increases, the bandwidth also increases.

46 Digital Signals(cont’d) zExample 4.7 yWe want to transmit 10 pictures per second. Each picture is made 5-by-5 pixels. What is the required bandwidth using digital encoding. zSolution y1 page = 25 pixels y25 bit/picture * 10 = 250 bps R125 Hz

47 Digital Signals(cont’d) zExample 4.8 yA television screen is composed of a grid of 525 lines by 700 columns(total of 367,500 pixels). A pixel can be black or white(0 or 1). Thirty complete screens(frames) are scanned in one second. What is the theoretical bandwidth required? zSolution yBandwidth = (30 * 367,500)/2 = 11,025,000/2 = 5,512,500 = 6 MHz( 근사값 )

48 Digital Signals(cont’d) zExample 4.8