View
223
Download
0
Category
Preview:
Citation preview
22Kyung Hee Universit
y
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
33Kyung Hee Universit
y
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.
44Kyung Hee Universit
y
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
55Kyung Hee Universit
y
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
66Kyung Hee Universit
y
Analog and Digital Signals (cont’d)Analog and Digital Signals (cont’d)
Comparison of analog and digital signals
77Kyung Hee Universit
y
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
88Kyung Hee Universit
y
Aperiodic and periodic signals (cont’d)Aperiodic and periodic signals (cont’d)
Example of periodic signals
99Kyung Hee Universit
y
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
1010Kyung Hee Universit
y
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.
1212Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
Sine wave can be fully described by three
characteristics
amplitude( 진폭 )
period( 주기 ), frequency( 주파수 )
phase( 위상 )
1313Kyung Hee Universit
y
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 )
1414Kyung Hee Universit
y
Analog signals(cont’d)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.
1616Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
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
1717Kyung Hee Universit
y
Analog signals(cont’d)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.
1818Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
Phase( 위상 )
~ describes the position of the waveform relative to time zero( 단일 주기내에서 시간에 대한 상대적인 위치 ).
1919Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)Relationship between different phases
2020Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
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
2727Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
Time versus Frequency Domain
Time Domain : instantaneous amplitude with respect
to time.
Frequency Domain : maximum amplitude with
respect to frequency.
2929Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
Time and Frequency domains for different signals
3030Kyung Hee Universit
y
Analog signals(cont’d)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-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.
3131Kyung Hee Universit
y
Analog signals(cont’d)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
3232Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d) Three harmonics
Adding first three harmonics
3333Kyung Hee Universit
y
Analog signals(cont’d)Analog signals(cont’d)
An demonstration on Fourier
http://www.earlevel.com/Digital%20Audio/harmonigraf.html
3636Kyung Hee Universit
y
Analog signals(cont’d)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.
3939Kyung Hee Universit
y
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.
4040Kyung Hee Universit
y
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
4141Kyung Hee Universit
y
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
4242Kyung Hee Universit
y
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.
4444Kyung Hee Universit
y
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
4747Kyung Hee Universit
y
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
1
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
4848Kyung Hee Universit
y
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
4949Kyung Hee Universit
y
3.4 Analog versus Digital3.4 Analog versus Digital
Low-pass versus Band-pass
5050Kyung Hee Universit
y
Analog versus DigitalAnalog versus Digital
• Digital transmission needs a low-pass channel.
• Analog transmission can use a band-pass channel.
5151Kyung Hee Universit
y
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
5252Kyung Hee Universit
y
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
5353Kyung Hee Universit
y
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
5454Kyung Hee Universit
y
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)
5555Kyung Hee Universit
y
Transmission ImpairmentTransmission Impairment p2 = (1/2) p1
Signal powers are increased 10 times by AMP
5757Kyung Hee Universit
y
Transmission ImpairmentTransmission Impairment
Distortion
Means that signal changes its form or shape
5858Kyung Hee Universit
y
Transmission ImpairmentTransmission 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.
6060Kyung Hee Universit
y
3. 7 More about Signals 3. 7 More about Signals
Throughput
is the measurement of how fast data can pass through a point
Recommended