2. 1 Kyung Hee University Prof. Choong Seon HONG Signals

3. 2 Kyung Hee University 4. 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. 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.

5. 4 Kyung Hee University Signals (cont’d)  Transformation of Information to Signals

6. 5 Kyung Hee University 4.1 Analog and Digital  Analog information: continuous( 연속 : 무게, 키 )  Digital information: discrete( 불연속, 이산 : 학생수 )  Analog and digital clocks

7. 6 Kyung Hee University Analog and Digital (cont’d)  Analog signals can have any value in a range.  Digital signals can have only a limited number of values.  Comparison of analog and digital signals

8. 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.

9. 8 Kyung Hee University Aperiodic and periodic signals (cont’d)  Example of periodic signals

10. 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.

11. 10 Kyung Hee University Aperiodic and periodic signals (cont’d)  Example of aperiodic signals

12. 11 Kyung Hee University 4.3 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.

13. 12 Kyung Hee University Analog signals(cont’d)  Sine Wave ( 정현파 )

14. 13 Kyung Hee University Analog signals(cont’d)  Sine wave can be fully described by three characteristics amplitude( 진폭 ) period( 주기 ), frequency( 주파수 ) phase( 위상 )

15. 14 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 )

16. 15 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.

17. 16 Kyung Hee University Analog signals(cont’d)

18. 17 Kyung Hee University Analog signals(cont’d)  Units of frequency and period

19. 18 Kyung Hee University Analog signals(cont’d)  Example 4.4 A sine wave has a frequency of 8KHz. What is its period ?  Solution Let T be the period and f be the frequency. Then, T = 1/f = 1/8,000 = 0.000125 = 125  s

20. 19 Kyung Hee University Analog signals(cont’d)  Example 4.6 A sine wave completes one cycle in 25  s. what is its frequency?  Solution Let T be the period and f be the frequency. Then, f = 1/T = 1/(25*10 -6 ) = 40,000 = 40 KHz

21. 20 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 ).

22. 21 Kyung Hee University Analog signals(cont’d)  Relationship between different phases

23. 22 Kyung Hee University Analog signals(cont’d)  Amplitude change

24. 23 Kyung Hee University Analog signals(cont’d)  Frequency change

25. 24 Kyung Hee University Analog signals(cont’d)  Phase change

26. 25 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.

27. 26 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. 27 Kyung Hee University Analog signals(cont’d)  Time and Frequency domains

29. 28 Kyung Hee University Analog signals(cont’d)  Time and Frequency domains for different signals

30. 29 Kyung Hee University Analog signals(cont’d)  Complex Signals A periodic signal decomposed into two sine waves. l A signal with a DC component A composite signal decomposed into four components. l Complex waveform

31. 30 Kyung Hee University Analog signals(cont’d)  A signal with a DC component

32. 31 Kyung Hee University Analog signals(cont’d)  Complex waveform

33. 32 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.

34. 33 Kyung Hee University Analog signals(cont’d)  Bandwidth

35. 34 Kyung Hee University Example 4.8  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 = 900 - 100 = 800 Hz

36. 35 Kyung Hee University Example 4.9  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 = 60 - 20 = 40 KHz

37. 36 Kyung Hee University 4.4 Digital Signals  A digital signals

38. 37 Kyung Hee University Digital Signals(cont’d)  Amplitude( 진폭 ), periodic( 주기 ), phase( 위상 )

39. 38 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.

40. 39 Kyung Hee University Digital Signals(cont’d)  Bit rate and bit interval

41. 40 Kyung Hee University Digital Signals(cont’d)  Decomposition of a Digital Signal Harmonics of a digital signal

42. 41 Kyung Hee University Digital Signals(cont’d)  Exact and significant spectrums

43. 42 Kyung Hee University Digital Signals(cont’d)  Medium Bandwidth and Significant Bandwidth corruption of a digital signal due to insufficient medium bandwidth