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Fundamentals of Digital Communication. Digital communication system. Input Signal Analog/ Digital. Low Pass Filter. Sampler. Quantizer. Source Encoder. Channel Encoder. Multiplexer. Carrier. Modulator. Pulse Shaping Filters. Line Encoder. To Channel. De- Modulator. - PowerPoint PPT Presentation
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Fundamentals of Digital Communication
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Digital communication system
Low Pass Filter
Sampler Quantizer Channel Encoder
Line Encoder
Pulse Shaping
Filters
SourceEncoder
Modulator
MultiplexerInputSignalAnalog/Digital
To Channel
DetectorReceiverFilter
De-ModulatorFrom Channel
Channel Decoder
Digital-to-AnalogConverter
De-Multiplexer
Signalat the user end
Carrier
Carrier Ref.
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SamplingTime domain Frequency domain
)()()( txtxtxs )()()( fXfXfX s
|)(| fX)(tx
|)(| fX
|)(| fX s)(txs
)(tx
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Aliasing effect
LP filter
Nyquist rate
aliasing
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Sampling theorem
Sampling theorem: A bandlimited signal with no spectral components beyond , can be uniquely determined by values sampled at uniform intervals of
The sampling rate, is called Nyquist rate.
Sampling process
Analog signal
Pulse amplitudemodulated (PAM) signal
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Quantization Amplitude quantizing: Mapping samples of a continuous
amplitude waveform to a finite set of amplitudes.
In
Out
Qua
ntiz
edva
lues
Average quantization noise power
Signal peak power
Signal power to average quantization noise power
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Encoding (PCM)
Pulse code modulation (PCM): Encoding the quantized signals into a digital word (PCM word or codeword). Each quantized sample is digitally encoded into
an l bits codeword where L in the number of quantization levels and
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Quantization example
tTs: sampling time
x(nTs): sampled valuesxq(nTs): quantized values
boundaries
Quant. levels
111 3.1867
110 2.2762
101 1.3657
100 0.4552
011 -0.4552
010 -1.3657
001 -2.2762
000 -3.1867
PCMcodeword 110 110 111 110 100 010 011 100 100 011 PCM sequence
amplitudex(t)
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Quantization error Quantizing error: The difference between the input and
output of a quantizer )()(ˆ)( txtxte
+
)(tx )(ˆ tx
)()(ˆ)(
txtxte
AGC
x
)(xqy Qauntizer
Process of quantizing noise
)(tx )(ˆ tx
)(te
Model of quantizing noise
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Quantization error …
Quantizing error: Granular or linear errors happen for inputs within
the dynamic range of quantizer Saturation errors happen for inputs outside the
dynamic range of quantizer Saturation errors are larger than linear errors Saturation errors can be avoided by proper tuning of
AGC Quantization noise variance:
2Sat
2Lin
222 )()(})]({[
dxxpxexqxq E
ll
L
l
l qxpq )(12
212/
0
22Lin
Uniform q.12
22Lin
q
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Uniform and non-uniform quant.
Uniform (linear) quantizing: No assumption about amplitude statistics and correlation
properties of the input. Not using the user-related specifications Robust to small changes in input statistic by not finely tuned to a
specific set of input parameters Simply implemented
Application of linear quantizer: Signal processing, graphic and display applications, process
control applications Non-uniform quantizing:
Using the input statistics to tune quantizer parameters Larger SNR than uniform quantizing with same number of levels Non-uniform intervals in the dynamic range with same
quantization noise variance Application of non-uniform quantizer:
Commonly used for speech
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Non-uniform quantization It is done by uniformly quantizing the “compressed” signal. At the receiver, an inverse compression characteristic,
called “expansion” is employed to avoid signal distortion.
compression+expansion companding
)(ty)(tx )(ˆ ty )(ˆ tx
x
)(xCy x
yCompress Quantize
ChannelExpand
Transmitter Receiver
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Transmitting Analog Data with Digital Signals
•To convert analog data into a digital signal, there are two basic techniques:
•Pulse code modulation (used by telephone systems)
•Delta modulation
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Pulse Code Modulation
•Analog waveform is sampled at specific intervals•“Snapshots” are converted to binary values
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Pulse Code Modulation (continued)
•Binary values are later converted to an analog signal•Waveform similar to original results
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Pulse Code Modulation (continued)
•The more snapshots taken in the same amount of time, or the more quantization levels, the better the resolution
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Pulse Code Modulation (continued)
•Because the human voice has a fairly narrow bandwidth
•Telephone systems digitize voice into either 128 levels or 256 levels
•Called quantization levels
•If 128 levels, then each sample is 7 bits (2 ^ 7 = 128)
•If 256 levels, then each sample is 8 bits (2 ^ 8 = 256)
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Pulse Code Modulation (continued)
•How fast do you have to sample an input source to get a fairly accurate representation?
•Nyquist says 2 times the bandwidth
•Thus, if you want to digitize voice (4000 Hz), you need to sample at 8000 samples per second
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Delta Modulation
•An analog waveform is tracked using a binary 1 to represent a rise in voltage and a 0 to represent a drop
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Source Coding To eliminate redundancy
Huffman Coding Shannon-Fano Coding
To maximize information rate in a transmission
What is Information Rate ? Information per bit Entropy
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Channel Coding Error Control Coding
To reduce the impact of channel errors by controlled introduction of redundancy
Decrease in effective data rate Increased coding gain Forward Error Correcting Codes
Linear Block Codes Convolutional Codes
ARQ methods
