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1 DIGITAL-TO-ANALOG CONVERSION
Digital-to-analog conversion is the process of changing one of the characteristics (A, f and θ) of an analog signal based on the information in digital data.
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Digital Data, Analog Signal
Encoding Techniques
Amplitude shift keying (ASK)• used to
transmit digital data over optical fiber
Frequency shift keying (FSK)• most common
form is binary FSK (BFSK)
Phase shift keying (PSK)• phase of carrier
signal is shifted to represent data
main use is public telephone system has frequency range
of 300Hz to 3400Hz uses modem (modulator-demodulator)
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Aspects of Digital-to-Analogue Conversion
Bit rate (data rate N) and Baud rate (signal rate S)
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rNS
1
r is the number of data elements carried in one signal element. In analogue transmission, r=log2L, where L is the type of signal element , not the level (could be same level but different phase).
An analog signal carries 4 bits per signal element. If 1000 signal elements are sent per second, find the bit rate.
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Amplitude Shift Keying
encode 0/1 by different carrier amplitudesusually have one amplitude zero
susceptible to sudden gain changes inefficient used for:
up to 1200bps on voice grade linesvery high speeds over optical fiber
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0binary 0
1binary )2cos()(
tfAts c
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Figure Binary amplitude shift keying
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0<=d<=1, a factor depends on the modulation and filtering process.The bandwidth of ASK B between S(signal rate) and 2S, centred fc. Frequency moved from low to high..
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Example
In data communications, we normally use full-duplex links with communication in both directions. We need to divide the bandwidth into two with two carrier frequencies, as shown in Figure 5.5. The figure shows the positions of two carrier frequencies and the bandwidths. The available bandwidth for each direction is now 50 kHz, which leaves us with a data rate of 25 kbps in each direction (worst case, d=1, L=2).
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Binary Frequency Shift Keying
two binary values represented by two different frequencies (near carrier)
less susceptible to error than ASK used for:
up to 1200bps on voice grade lineshigh frequency radio ( 3 to 30 MHz)even higher frequency on LANs using coaxial
cable
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0binary )2cos(
1binary )2cos()(
2
1
tfA
tfAts
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Figure Binary frequency shift keying
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Carrier f1 for data “1”, f2 for data “0”Bandwidth of BFSK: B = (1+d) × S + 2 Δf0<=d<=1, a factor depends on the modulation and filtering process.
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Example 5.5
We have an available bandwidth of 100 kHz which spans from 200 to 300 kHz. What should be the carrier frequency and the bit rate if we modulated our data by using BFSK with d = 1?
SolutionThe midpoint of the band is at 250 kHz. We choose 2Δf to be 50 kHz; this means
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Multiple FSK
each signalling element represents more than one bit
more than two frequencies used more bandwidth efficient more prone to error
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e.g. 4 frequencies, f1, f2, f3 and f4 can be used to send 2 bits at a time;8 frequencies for 3 bits per signal. L frequencies for log2L bit per signal ( Bandwidth L×S )However, frequencies need to be 2Δf (minimum S) apart. If d = 0; the minimum bandwidth of MFSKB = (1+d)×S+(L-1)2Δf = L×SYa Bao
Phase Shift Keying
phase of carrier signal is shifted to represent data binary PSK
two phases represent two binary digits
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0binary )2cos(
1binary )2cos(
)2cos(
)2cos()(
tfA
tfA
tfA
tfAts
c
c
c
c
Bandwidth of BPSK is the same as that for BASK less than that for BFSK. No bandwidth wasted for separate two carrier signals.
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Quadrature PSK
more efficient use if each signal element represents more than one bit uses phase shifts separated by multiples of /2 (90o) each element represents two bits split input data stream in two and modulate onto
carrier and phase shifted carrier can use 8 phase angles and more than one
amplitude 9600bps modem uses 12 angles, four of which have
two amplitudes17
10binary )4
2cos(
00binary )4
32cos(
01binary )4
32cos(
11binary )4
2cos(
)(
tfA
tfA
tfA
tfA
ts
c
c
c
c
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Performance
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TB
RefficiencyBandwidth R: data rate, bit rate
BT: Transmission Bandwidth
RM
MdB
RM
dR
L
dB
RdB
T
T
T
)log
)1(( :MFSK
)log
1()
1( :MPSK
)1( :ASK
2
2
0<=d<=1, a factor depends on the modulation and filtering process.
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This parameter measures the efficiency with which bandwidth can be used to transmit data
Bandwidth Efficiency for Digital-to-Analog Encoding Schemes
d = 0 d = 0.5 d = 1
ASK 1.0 0.67 0.5
Multilevel FSK
M = 4, L = 2 0.5 0.33 0.25
M = 8, L = 3 0.375 0.25 0.1875
M = 16, L = 4 0.25 0.167 0.125
M = 32, L = 5 0.156 0.104 0.078
PSK 1.0 0.67 0.5
Multilevel PSK
M = 4, L = 2 2.00 1.33 1.00
M = 8, L = 3 3.00 2.00 1.50
M = 16, L = 4 4.00 2.67 2.00
M = 32, L = 5 5.00 3.33 2.50
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The advantage of multilevel signaling methods now becomes clear.
Performance of Digital to Analog Modulation Schemes
ASK/PSK bandwidth directly relates to bit rate
multilevel PSK gives significant improvements
bandwidth
bit error rate of PSK and QPSK are about 3dB superior to ASK and FSK
for MFSK and MPSK have tradeoff between bandwidth efficiency and error performance
in presence of noise:
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Theoretical Bit Error Rate for Various Encoding Schemes
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The ratio Eb/N0 increases, the bit error rate drops.
QPSK and BPSK are about 3 dB superior to ASK and BFSK
Bit Error Rates for Multilevel FSK and PSK
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For MFSK, the error probability for a given value Eb/N0 of decreases as M increases, while the opposite is true for MPSK. The bandwidth efficiency of MFSK decrease as M increases, while the opposite is true of MPSK. An increase in bandwidth efficiency results in an increase in error probability.
Quadrature Amplitude Modulation
QAM used on asymmetric digital subscriber line (ADSL) and some wireless
combination of ASK and PSK logical extension of QPSK send two different signals
simultaneously on same carrier frequencyuse two copies of carrier, one shifted 90°
each carrier is ASK modulatedtwo independent signals over same
mediumdemodulate and combine for original
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QAM Variants two level ASK
each of two streams in one of two states four state system essentially QPSK
four level ASK combined stream in one of 16 states
have 64 and 256 state systems improved data rate for given bandwidth
increased potential error rate
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Asymmetrical Digital Subscriber Line (ADSL)
link between subscriber and network uses currently installed twisted pair cable is Asymmetric - bigger downstream than
up uses Frequency Division Multiplexing
reserve lowest 25kHz for voice (POTS)uses echo cancellation or FDM to give two
bands has a range of up to 5.5km
ADSL Design
AsymmetricGreater capacity downstream than
upstream Frequency division multiplexing
Lowest 25kHz for voicePlain old telephone service (POTS)
Use echo cancellation or FDM to give two bands
Use FDM within bands Range 8km
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Discrete Multitone
DMT: Discrete Multitone Multiple carrier signals at different
frequencies Some bits on each channel 4kHz subchannels Send test signal and use subchannels
with better signal to noise ratio
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Broadband – Provider Side
a splitter separates telephone from Internet voice traffic is connected to public switched
telephone network (PSTN) data traffic connects to a DSL multiplexer (DSLAM)
which multiplexes multiple customer DSL connections to a single high-speed ATM line.
ATM line connects ATM switches to a router which provides entry to the Internet
xDSL
high data rate DSL (HDSL) 2B1Q coding on dual twisted pairs up to 2Mbps over 3.7km
single line DSL 2B1Q coding on single twisted pair (residential) with
echo cancelling up to 2Mbps over 3.7km
very high data rate DSL DMT/QAM for very high data rates separate bands for separate services