1 physical layer: data and signals 01204325: data communication and computer networks asst. prof....
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Physical Layer: Physical Layer: Data and SignalsData and Signals
01204325: Data 01204325: Data Communication and Communication and Computer NetworksComputer Networks
Asst. Prof. Chaiporn Jaikaeo, Ph.D.Asst. Prof. Chaiporn Jaikaeo, [email protected]@ku.ac.th
http://www.cpe.ku.ac.th/~cpjhttp://www.cpe.ku.ac.th/~cpjComputer Engineering DepartmentComputer Engineering Department
Kasetsart University, Bangkok, ThailandKasetsart University, Bangkok, Thailand
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OutlineOutline Analog and digital data/signalsAnalog and digital data/signals Time and frequency domain views of Time and frequency domain views of
signalssignals Bandwidth and bit rateBandwidth and bit rate Transmitting digital signals as analogTransmitting digital signals as analog Theoretical data rateTheoretical data rate Signal impairmentSignal impairment
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Analog vs. Digital DataAnalog vs. Digital Data Analog dataAnalog data
Data take on continuous valuesData take on continuous values E.g., human voice, temperature readingE.g., human voice, temperature reading
Digital dataDigital data Data take on discrete valuesData take on discrete values E.g., text, integersE.g., text, integers
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Analog vs. Digital SignalsAnalog vs. Digital Signals
Analog signalsAnalog signals have an infinite number of have an infinite number of
values in a rangevalues in a range
Digital signalsDigital signals Have a limited number of Have a limited number of
valuesvalues
value
time
value
time
To be transmitted, data must be To be transmitted, data must be transformed to electromagnetic signalstransformed to electromagnetic signals
To be transmitted, data must be To be transmitted, data must be transformed to electromagnetic signalstransformed to electromagnetic signals
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Data and SignalsData and Signals
Telephone
Analog Data Analog Signal
Modem
Digital Data Analog Signal
Codec
Analog Data Digital Signal
Digitaltransmitter
Digital Data Digital Signal
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Periodic SignalsPeriodic Signals A A periodic signalperiodic signal completes a pattern completes a pattern
within a timeframe, called a within a timeframe, called a periodperiod A signal A signal xx((tt)) is periodic if and only if is periodic if and only if
x(t) = x(t+T) - < t <
value
time
period
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Simplest form of periodic signalSimplest form of periodic signal
General form: General form: xx((tt) =) = AA××sin(2sin(2ftft + + ))
periodT = 1/f
peakamplitude
time
signal strength
Sine WavesSine Waves
phase / phase shift
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-3
-2
-1
0
1
2
3
0 0.5 1 1.5 2 2.5 3
A = 1, f = 1, = 0 -3
-2
-1
0
1
2
3
0 0.5 1 1.5 2 2.5 3
A = 2, f = 1, = 0
-3
-2
-1
0
1
2
3
0 0.5 1 1.5 2 2.5 3
A = 1, f = 2, = 0 -3
-2
-1
0
1
2
3
0 0.5 1 1.5 2 2.5 3
A = 1, f = 1, = /4
Varying Sine WavesVarying Sine Waves
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Time vs. Frequency Time vs. Frequency DomainsDomains
Consider the signalConsider the signal
)32sin(3
1)2sin()( tttx
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.5 1 1.5 2 2.5 3+ =
Demo: sine.py
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Time vs. Frequency Time vs. Frequency DomainsDomains
0
1
-1
2 4 time
signal strength
0
1
-1
2 4
signal strength
frequency
Time Domain Representation plots amplitude as a function
of time
Frequency Domain Representation plots each sine wave’s peak
amplitude against its frequency
Demo: Equalizer
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Fourier AnalysisFourier Analysis Any periodic signal can be represented Any periodic signal can be represented
as a sum of sinusoidsas a sum of sinusoids known as a known as a Fourier SeriesFourier Series
E.g., a square wave:E.g., a square wave:
+ + + + …
=
Joseph Fourier(1768-1830)
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Fourier AnalysisFourier Analysis Every periodic signal consists ofEvery periodic signal consists of
DC componentDC component AC componentsAC components
Fundamental frequency (Fundamental frequency (ff00)) Harmonics (multiples of Harmonics (multiples of ff00))
DC component
AC components
fundamentalfrequency
3rd harmonic 5th harmonic
…
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Fourier Series: Fourier Series: RepresentationsRepresentations
Amplitude-phase formAmplitude-phase form
Sine-cosine formSine-cosine form
Complex exponential form (Euler Complex exponential form (Euler formula)formula)
1
000 )2sin()2cos()(n
nn ntfbntfaatx
1
00 )2cos()(n
nn ntfcctx
n
ntfjnectx 02)(
Note:Note:ccnn are complex are complex jj = = -1-1eeiixx = cos = cos xx + + jj sin sin xx
Demo: Falstad
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The time and frequency domains of a nonperiodic signal
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Frequency SpectrumFrequency Spectrum Frequency domain representation Frequency domain representation
shows the shows the frequency spectrumfrequency spectrum of a of a signalsignal
E.g., square waveE.g., square wave
0 0 f0 3f0 5f0 7f0 9f0 11f0
...
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BandwidthBandwidth A property of a mediumA property of a medium
Indicates the difference between the highest Indicates the difference between the highest and the lowest frequencies allowed to passand the lowest frequencies allowed to pass
<highest freq allowed><highest freq allowed> – – <lowest freq allowed><lowest freq allowed>
Also a property of a single spectrumAlso a property of a single spectrum
Cutoff frequency(half of power is lost)
Cutoff frequency(half of power is lost)
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Bandwidth of a MediumBandwidth of a Medium
Transmission medium
1
(low-pass channel)gain
freq
t t
0 f0 3f0 5f0 f0 f0 3f0 5f0 7f0
...
9f0 f
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ExampleExample What is the bandwidth of this signal?What is the bandwidth of this signal?
A medium can pass frequencies from A medium can pass frequencies from 4000 to 7000 Hz. Can the above 4000 to 7000 Hz. Can the above signal pass through?signal pass through?
)6000sin(3
1)2000sin(2)( tttx
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Digital SignalsDigital Signals Properties:Properties:
Bit rateBit rate – number of bits per second – number of bits per second Bit intervalBit interval – – duration of 1 bit duration of 1 bit
1 0 0 1 1 10 0
...
time
amplitude
bit interval
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Two digital signals: one with two signal levels and the other with four signal levels
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The time and frequency domains of periodic and nonperiodicdigital signals
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Baseband transmission
Baseband transmissionBaseband transmission Sending a digital signal over a channel Sending a digital signal over a channel
without changing it to an analog signalwithout changing it to an analog signal
Baseband transmission requires a Baseband transmission requires a low-passlow-pass channel channel
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A digital signal is a composite analog signal with an infinite bandwidth.
Note
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Baseband transmission using a dedicated medium
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Digital vs. AnalogDigital vs. Analog Using one harmonicUsing one harmonic
1 1 1 1 1 1
1 sec
Bit rate = 6
Digital
1 0 1 0 1 0
Bit rate = 6
Digital
1 0 1 0 1 0
f = 3
Analog
1 1 1 1 1 1
f = 0
Analog
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Digital vs. AnalogDigital vs. Analog Using more harmonicsUsing more harmonics
Adding 3Adding 3rdrd harmonic to improve quality harmonic to improve quality
1 0 1 0 1 0
f0 = 3, fmax = 9
Analog
1 0 1 0 1 0
Bit rate = 6
Digital
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Table 3.2 Bandwidth requirements
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Digital vs. Analog Digital vs. Analog BandwidthBandwidth
Digital bandwidthDigital bandwidth Expressed in Expressed in bits per second (bps)bits per second (bps)
Analog bandwidthAnalog bandwidth Expressed in Expressed in Hertz (Hz)Hertz (Hz)
Bit rate and bandwidth are proportional to each otherBit rate and bandwidth are proportional to each otherBit rate and bandwidth are proportional to each otherBit rate and bandwidth are proportional to each other
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Low-Pass and Band-Pass Low-Pass and Band-Pass ChannelsChannels
Low-pass channelLow-pass channel
Band-pass channelBand-pass channel
frequencyf1 f2
gain
frequencyf1
gain
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Modulation of a digital signal for transmission on a bandpass channel
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Transmission ImpairmentTransmission Impairment AttenuationAttenuation DistortionDistortion NoiseNoise
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Signal AttenuationSignal Attenuation Attenuation Attenuation Loss of energy Loss of energy
Signal strength falls off with distanceSignal strength falls off with distance
Attenuation dAttenuation depends on mediumepends on medium Attenuation is an increasing function Attenuation is an increasing function
of frequencyof frequency
Transmission medium
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Relative Signal StrengthRelative Signal Strength Measured in Measured in Decibel (dB)Decibel (dB)
PP11 and and PP22 are signal powers at points 1 and 2, are signal powers at points 1 and 2, respectivelyrespectively
Positive dB Positive dB signal is amplified (gains strength) signal is amplified (gains strength) Negative dB Negative dB signal is attenuated (loses signal is attenuated (loses
strength)strength)
dB = 10 log10 (P2/P1)dB = 10 log10 (P2/P1)
Point 1 Point 2
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Sometimes the decibel is used to measure signal power in milliwatts. In this case, it is referred to as dBm and is calculated as dBm = 10 log10 Pm , where Pm is the power in milliwatts. Calculate the power of a signal with dBm = −30.
SolutionWe can calculate the power in the signal as
Example
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The loss in a cable is usually defined in decibels per kilometer (dB/km). If the signal at the beginning of a cable with −0.3 dB/km has a power of 2 mW, what is the power of the signal at 5 km?SolutionThe loss in the cable in decibels is 5 × (−0.3) = −1.5 dB. We can calculate the power as
Example
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Signal DistortionSignal Distortion Distortion Distortion Change in signal shape Change in signal shape
Only happens in guided mediaOnly happens in guided media Propagation velocity varies with frequency Propagation velocity varies with frequency
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NoiseNoise Noise Noise Undesirable signals added Undesirable signals added
between the transmitter and the between the transmitter and the receiverreceiver
Types of noiseTypes of noise ThermalThermal
Due to random motion of electrons in a wireDue to random motion of electrons in a wire
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NoiseNoise Types of noise (cont’d)Types of noise (cont’d)
CrosstalkCrosstalk Signal from one line picked up by anotherSignal from one line picked up by another
ImpulseImpulse Irregular pulses or spikesIrregular pulses or spikes E.g., lightningE.g., lightning Short durationShort duration High amplitudeHigh amplitude
Wire 1
Wire 2
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Signal-to-Noise RatioSignal-to-Noise Ratio Signal-to-Noise Ratio (SNR)Signal-to-Noise Ratio (SNR)
noise
signal
Power
PowerSNR
noise
signal
Power
PowerSNR
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The power of a signal is 10 mW and the power of the noise is 1 μW; what are the values of SNR and SNRdB ?
SolutionThe values of SNR and SNRdB can be calculated as follows:
Example
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Data Rate: Noiseless Data Rate: Noiseless ChannelsChannels
Nyquist TheoremNyquist Theorem
Bit rateBit rate in bps in bps BandwidthBandwidth in Hz in Hz LL – number of signal levels – number of signal levels
Bit Rate = 2 × Bandwidth × log2LBit Rate = 2 × Bandwidth × log2L
Harry Nyquist(1889-1976)
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We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz. How many signal levels do we need?SolutionWe can use the Nyquist formula as shown:
Example
Since this result is not a power of 2, we need to either increase the number of levels or reduce the bit rate. If we have 128 levels, the bit rate is 280 kbps. If we have 64 levels, the bit rate is 240 kbps.
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Data Rate: Noisy ChannelsData Rate: Noisy Channels Shannon CapacityShannon Capacity
CapacityCapacity (maximum bit rate) in bps (maximum bit rate) in bps BandwidthBandwidth in Hz in Hz SNRSNR – – SSignal-to-ignal-to-NNoise oise RRatioatio
Capacity = Bandwidth × log2(1+SNR)Capacity = Bandwidth × log2(1+SNR)
Claude Elwood Shannon(1916-2001)
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A telephone line normally has a bandwidth of 3000. The signal-to-noise ratio is usually 3162. Calculate the theoretical highest bit rate of a regular telephone line.
Example
This means that the highest bit rate for a telephone line is 34.860 kbps. If we want to send data faster than this, we can either increase the bandwidth of the line or improve the signal-to-noise ratio.
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We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63. What are the appropriate bit rate and signal level?
SolutionFirst, use the Shannon capacity
followed by the Nyquist formula
Example
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The Shannon capacity gives us the upper limit; the Nyquist formula tells us
how many signal levels we need.
Note
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Network PerformanceNetwork Performance BandwidthBandwidth
HertzHertz Bits per second (bps)Bits per second (bps)
ThroughputThroughput Actual data rateActual data rate
Latency (delay)Latency (delay) Time it takes for an entire message to Time it takes for an entire message to
completely arrive at the destinationcompletely arrive at the destination
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LatencyLatency Composed ofComposed of
Propagation timePropagation time Transmission timeTransmission time Queuing timeQueuing time Processing timeProcessing time
Entiremessage
transmissiontime
propagationtime
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Data bits
LatencyLatency
Time Time
First bit leaves
Last bit leaves
First bit arrives
Last bit arrives
Sender Receiver
Propagation time
Transmission time
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Bandwidth-Delay ProductBandwidth-Delay Product The link is seen as a pipeThe link is seen as a pipe
Cross section = bandwidthCross section = bandwidth Length = delayLength = delay
Bandwidth-delay product defines the Bandwidth-delay product defines the number of bits that can fill the linknumber of bits that can fill the link
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Figure Filling the link with bits for case 1
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SummarySummary Data need to take form of signal to Data need to take form of signal to
be transmittedbe transmitted Frequency domain representation of Frequency domain representation of
signal allows easier analysissignal allows easier analysis Fourier analysisFourier analysis
Medium's bandwidth limits certain Medium's bandwidth limits certain frequencies to passfrequencies to pass
Bit rate is proportional to bandwidthBit rate is proportional to bandwidth Signals get impaired by attenuation, Signals get impaired by attenuation,
distortion, and noisedistortion, and noise