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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

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신호 (cont’d)

Information can be voice, image, numeric data, characters, code, picture, and so on

To be transmitted, information must be into electromagnetic signals.

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신호 (cont’d)

Transformation of Information to Signals

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4.1 Analog and DigitalAnalog information: continuous( 연속 : 무게 ,

키 )Digital information: discrete( 불연속 , 이산 :

학생수 )Analog and digital clocks

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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

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4.2 Aperiodic and periodic signals

Periodic signals( 주기신호 )~ consists of a continuously repeated pattern.

The periodic of a signal(T) is expressed in seconds.

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Aperiodic and periodic signals(cont’d)

Example of periodic signals

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Aperiodic signals( 비주기 신호 )~ changes constantly without exhibiting a pattern or

cycle that repeat over time.

Aperiodic and periodic signals(cont’d)

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Example of aperiodic signals

Aperiodic and periodic signals(cont’d)

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4.3 Analog signals

~ can be classified as simple or complex.

Simple Analog signals the sine wave is the most fundamental form of a

periodic analog signal.

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Analog signals(cont’d)

A sine wave

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Analog signals(cont’d)

Sine wave can be fully described by three characteristics amplitude( 진폭 ) period( 주기 ), frequency( 주파수 ) phase( 위상 )

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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 secon

d.( 주기의 역수 (1/t), 초당 주기의 반복 횟수 )

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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.

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Analog signals(cont’d)

Frequency PeriodUnit Equivalent Unit Equivalent

Hertz(Hz) 1 Hz Second(s) 1 sKilohertz(KHz) 103 Hz Milisecond(ms) 10-3 sMegahertz(MHz) 106 Hz Microsecond(s) 10-6 sGigahertz(GHz) 109 Hz Nanosecond(ns) 10-9 sTerahertz(THz) 1012 Hz Picosecond(ps) 10-12 s

Units of frequency and period

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Analog signals(cont’d)

Example 4.1 A sine wave have 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

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Analog signals(cont’d)

Example 4.2 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

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Analog signals(cont’d)

Phase( 위상 )~ describes the position of the waveform relative to

time zero( 단일 주기내에서 시간에 대한 상대적인 위치 ).

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Analog signals(cont’d)

Relationship between different phases

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Analog signals(cont’d)

Amplitude change( 진폭 변조 )

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Analog signals(cont’d)

Frequency change( 주파수 변조 )

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Analog signals(cont’d)

Phase change( 위상 변조 )

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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 al all, its frequency is zero. If a signal changes instantaneously, its frequency is

infinity.

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Analog signals(cont’d)

Time versus Frequency Domain Time Domain : instantaneous amplitude with

respect to time. Frequency Domain : maximum amplitude with

respect to frequency.

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Analog signals(cont’d)

Time and Frequency domains

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Analog signals(cont’d)

Time and Frequency domains for different signals

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Analog signals(cont’d)

Complex Signals A periodic signal decomposed into two sine

waves.A signal with a DC component

A composite signal decomposed into four components.Complex waveform

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Analog signals(cont’d)

A signal with a DC component

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Analog signals(cont’d)Complex waveform

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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.

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Analog signals(cont’d)

Bandwidth

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Example 4.3

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 fre

quency, and B be the bandwidth. Then, B = fh - fl = 900 - 100 = 800 Hz

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Example 4.4

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

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4.4 Digital Signals

A digital signals

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Digital Signals(cont’d)

Amplitude( 진폭 ), periodic( 주기 ), phase(위상 )

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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.

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Digital Signals(cont’d)

Bit rate and bit interval

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Digital Signals(cont’d)Decomposition of a Digital Signal

Harmonics( 조파 ) of a digital signal

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Digital Signals(cont’d)Exact and significant spectrums

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Digital Signals(cont’d)

The bit rate has a relationship to the significant bandwidth such that when the bit rate increases, the significant bandwidth widens.

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Digital Signals(cont’d)

Bit rates and significant spectrums

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Medium Bandwidth and Significant

Bandwidth corruption of a digital signal due to insufficient

medium bandwidth

Digital Signals(cont’d)

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Digital Signals(cont’d)Medium Bandwidth and Data Rate : Channel

Capacity Medium Bandwidth and Data Rate

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Digital Signals(cont’d)Use of Analog Signals to Transmit Digital

Data Example 4.5

What bandwidth is required for data being sent at a rate of 10 bps using analog signals? Assume the each signal element is one bit.

Solution

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Digital Signals(cont’d)

Example 4.6 compare the bandwidths required for analog data being

sent at 1,000 and 10,000 bps

Solution 10 bps - 5 Hz 1,000 bps - 500 Hz 10,000 bps - 5,000 Hz

As the data rate increases, the bandwidth also increases.

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Digital Signals(cont’d)

Example 4.7 We want to transmit 10 pictures per second. Each

picture is made 5-by-5 pixels. What is the required bandwidth using digital encoding.

Solution 1 page = 25 pixels 25 bit/picture * 10 = 250 bps125 Hz

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Digital Signals(cont’d)

Example 4.8 A television screen is composed of a grid of 525 lines by 7

00 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?

Solution Bandwidth = (30 * 367,500)/2

= 11,025,000/2

= 5,512,500 = 6 MHz( 근사값 )

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Digital Signals(cont’d)

Example 4.8