digital communication systems - t u 452 - 6 - digital... · digital communication systems ecs 452...
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Asst. Prof. Dr. Prapun [email protected]
6. Digital Modulation
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Digital Communication SystemsECS 452
Office Hours: BKD, 4th floor of Sirindhralai building
Monday 14:00-16:00Thursday 10:30-11:30Friday 12:00-13:00
Elements of digital commu. sys.
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Noise & In
terferen
ce
Information Source
Destination
Channel
ReceivedSignal
TransmittedSignal
Message
Recovered Message
Source Encoder
Channel Encoder
DigitalModulator
Source Decoder
Channel Decoder
DigitalDemodulator
Transmitter
Receiver
Remove redundancy(compression)
Add systematic redundancy to combat errors introduced by the channel
Map digital sequence to analog signal
Digital Modulation/Demodulation
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Noise & In
terferen
ce
Information Source
Destination
Channel
ReceivedSignal
TransmittedSignal
Message
Recovered Message
Source Encoder
Channel Encoder
DigitalModulator
Source Decoder
Channel Decoder
DigitalDemodulator
Transmitter
Receiver
Remove redundancy(compression)
Add systematic redundancy to combat errors introduced by the channel
Map digital sequence to analog signal
101001
101001
Energy and Power
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Consider a signal g(t).
Total (normalized) energy:
Average (normalized) power:
2 2 2( ) lim ( ) ( ) . T
g TTE g t dt g t dt G f df
/2
2 2 2
/2
1 1lim lim ( ) .2
T
T
g TT TT
P g t g t dt g t dtT T
Parseval’s Theorem
2( ) ( )g f G f ESD: Energy Spectral Density
Modulator and Waveform Channel
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Waveform Channel:
Transmission of the message is done by inputting the corresponding waveform into the channel.
Goal: Want to transmit the message (index) W {1, 2, 3, …, M}
Prior Probabilities: ip P W i
R t S t N t
Received waveformTransmitted waveform
Additive White Noise (Independent of S(t))
M-ary Scheme
M possible messages requiresM possibilities for S(t):
1 2, , , Ms t s t s t
Prior Probabilities: i ip P W i P S t s t
M =2: BinaryM = 3: TernaryM = 4: Quaternary
DigitalModulator
N t
R t S tW Digital
DeModulator W
Energy: ,i i is tE s t 21
logM
i ii
s bp EEE M
Gray Code
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Reflect-and-prefix method for 1-D Gray code construction
Gray code list for bits can be generated recursively from the list for bits by
[http://en.wikipedia.org/wiki/Gray_code#mediaviewer/File:Binary-reflected_Gray_code_construction.svg]
reflecting the list (i.e. listing the entries in reverse order),
concatenating the original list with the reversed list,
prefixing the entries in the original list with a binary 0, and then prefixing the entries in the reflected list with a binary 1.
Projection: Hand Shadow
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Projection: Shadow Art
8[http://thesuiteworld.com/wp-content/uploads/2011/07/Shadows-thesuiteworld.jpg]
Projection: Hand Shadow
9 [https://www.youtube.com/watch?v=VpC9HSYMwdY]
Projection: Engineering drawing
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