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)

11Kyung Hee Universit

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SignalsSignals


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3. 3. 신호 신호 (Signals)(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


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Signals (cont’d)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.


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3.1 Analog and Digital3.1 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


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Analog and Digital SignalsAnalog 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


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Analog and Digital Signals (cont’d)Analog and Digital Signals (cont’d)

Comparison of analog and digital signals


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Aperiodic and periodic signalsAperiodic 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


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Aperiodic and periodic signals (cont’d)Aperiodic and periodic signals (cont’d)

Example of periodic signals


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Aperiodic and periodic signals (cont’d)Aperiodic and periodic signals (cont’d)

Aperiodic signals( 비주기 신호 )

~ changes constantly without exhibiting a patt

ern or cycle that repeat over time.

~ signal has no repetitive pattern.

In data communication, we commonly use periodic an

alog signals and aperiodic digital signals


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3.2 Analog signals3.2 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.


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Analog signals(cont’d)Analog signals(cont’d)

Sine Wave ( 정현파 )


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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)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 )


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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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Units of frequency and period

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


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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.


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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)Analog signals(cont’d)Relationship between different phases


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Example 2 : A sine wave is offset one-sixth of a cycle w

ith respect to time zero. What is its phase in degrees an

d 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 = 1.046 rad

2pi radians equal to 360 degrees, thus 1 radian = 180/pi


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Sine wave examples


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Sine wave examples


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Sine wave examples

Analog Signals(cont’d)Analog Signals(cont’d)


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Amplitude change


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Frequency change


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Phase change


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Time versus Frequency Domain

Time Domain : instantaneous amplitude with respect

to time.

Frequency Domain : maximum amplitude with

respect to frequency.


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Time and Frequency domains


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Time and Frequency domains for different signals


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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-When we change one or more characteristics of a single-

frequency signal, it becomes a composite signal made of many frequency signal, it becomes a composite signal made of many

frequencies.frequencies.


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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


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Analog signals(cont’d)Analog signals(cont’d) Three harmonics

Adding first three harmonics


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An demonstration on Fourier

http://www.earlevel.com/Digital%20Audio/harmonigraf.html


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


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Complex waveform


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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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Frequency Spectrum

Analog Signals (cont’d)Analog Signals (cont’d)


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Analog SignalsAnalog Signals

Composite Signal and Transmission Media


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Analog SignalsAnalog 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.


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Example 3Example 3 If a period signal is decomposed into five sine waves with frequen

cies 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 = 900 - 100 = 800 Hz


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Example 4Example 4 A signal has a bandwidth of 20 KHz. The highest frequency is 60 K

Hz. 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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Example 5Example 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.


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3.3 Digital Signals3.3 Digital Signals

A digital signals


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Digital Signals(cont’d)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 = 0.000500 s

= 0.000500 x 106 ms = 500 ms


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Digital Signals(cont’d)Digital Signals(cont’d)

Bit rate and bit interval


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Digital versus AnalogDigital versus Analog


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Digital versus AnalogDigital 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 <=2BBit

Rate

Harmonic

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Harmonics

1, 3

Harmonics

1, 3, 5

Harmonics

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


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Digital versus Analog BandwidthDigital versus Analog Bandwidth

The analog of a bandwidth of a medium is expressed in

hertz; the digital bandwidth in bits per second


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3.4 Analog versus Digital3.4 Analog versus Digital

Low-pass versus Band-pass


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Analog versus DigitalAnalog versus Digital

• Digital transmission needs a low-pass channel.

• Analog transmission can use a band-pass channel.


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3.5 Data Rate Limits3.5 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 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

BitBit Rate = 2 Rate = 2 3000 3000 log log22 2 = 6000 bps 2 = 6000 bps


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Data Rate LimitsData 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 logC = B log22 (1 + SNR) = B log (1 + SNR) = B log22 (1 + 0) (1 + 0)

= B log= B log22 (1) = B (1) = B 0 = 0 0 = 0


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3.6 Transmission Impairment3.6 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


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Transmission ImpairmentTransmission 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)


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Transmission ImpairmentTransmission Impairment p2 = (1/2) p1

Signal powers are increased 10 times by AMP


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dB = -3 + 7-3 = +1


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Distortion

Means that signal changes its form or shape


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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.


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noise


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3. 7 More about Signals 3. 7 More about Signals

Throughput

is the measurement of how fast data can pass through a point


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More about SignalsMore about Signals

Propagation Time


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More about SignalsMore about Signals

Wavelength = Lamda = c/f

Documents

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)