dept. of ee, ndhu 1 chapter two formatting and baseband modulation
TRANSCRIPT
1Dept. of EE, NDHU
Chapter Two
Formatting and Baseband Modulation
2Dept. of EE, NDHU
Digital Communication Transformation
3Dept. of EE, NDHU
Formatting and Transmission of Baseband Signals
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Message, Characters, and Symbols
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Formatting Analog Information
• Formatting process
– Transform an analog waveform into a form that is compatible with a
digital communication system
• Sampling theorem
– A bandlimited signal having no spectral components above hertz
can be determined uniquely by values sampled at
, where is also called the
Nyquist rate
(2.1) sec 2
1
ms fT mf2
mf
6Dept. of EE, NDHU
Impulse Sampling (Ideal Case)
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Spectra for Various Sampling Rate
Sampled spectrum (fs > 2fm)
Sampled spectrum (fs < 2fm)
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Natural Sampling
)/(csin)/1( , ssn TnTTC
n
nsnp nffCfX )()(
9Dept. of EE, NDHU
Comparison of Impulse Sampling and Natural Sampling
• Impulse sampling (Ideal case)
• Natural sampling (A practical way)
n
ns
ss nffX
TX )(
11
sn
n
nss
s
n
nsns
TC
TnffXTnTcT
nffXCX
1
0 when ,)()/(sin1
)(1
10Dept. of EE, NDHU
Sample-and-Hold Operation
• Transfer function
where is the hold-operation and is the form of
• Two effects of hold-operation
– The significant attenuation of the higher frequency components
– The non-uniform spectral gain
• Post-filtering operation can compensate the effects of hold-
operation
(2.16) 1
)()(
ns
ss )X(f-nf
TfpfX
)( fp ss cfTT sin
)( fp
11Dept. of EE, NDHU
Aliasing for Sampling
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Eliminate Aliasing for Higher Sampling
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Aliasing Elimination
• Higher sampling rate
• Pre-filtering the original spectrum so that the new maximum frequency i
s reduced to fs/2 or less
• Post-filtering removes the aliased components
• Both the pre-filtering and the post-filtering will result a loss of signal inf
ormation
• Trade-off is required between the sampling rate and cutoff bandwidth
• Engineer’s version of the Nyquist sampling rate is ms ff 2.2
14Dept. of EE, NDHU
Pre-filter Eliminates Alias
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Post-filter Eliminates Alias
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Alias Frequency by Sub-Nyquist Sampling Rate
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Sampling Process (I)
• Without oversampling (sampling rate is the Nyquist rate)
– The analog signal passes through a high performance analog low-pas
s filter
– Sampling rate is the Nyquist rate for the band-limited signal
– The samples are mapped to a finite list of discrete output levels and p
rocessed by the following digital signal process
18Dept. of EE, NDHU
Sampling Process (II)
• With over-sampling (sampling rate is higher than the Nyquis
t rate)
– The analog signal passes through a low performance analog low-pass
filter
– The pre-filtered signal is sampled at the higher Nyquist rate for the b
and-limited signal
– The samples are mapped to a finite list of discrete output levels and p
rocessed by a high performance digital filter to reduce the bandwidth
of the digital samples
19Dept. of EE, NDHU
Analog Source Description
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Source of Corruption
• Sampling and quantizing effects
– Quantization noise due to round-off or truncation error
+ Increase the number of levels employed in the quantization process
– Quantizer saturation
+ AGC can be used to avoid the saturation
– Timing jitter
+ Stable clock
• Channel effects
– Channel noise (thermal noise, interference from other users)
– Intersymbol interference (ISI)
21Dept. of EE, NDHU
Quantization Level
22Dept. of EE, NDHU
Signal to Noise Ratio for Quantized Pulse
• Assume the quantization error ,e, is uniformly distributed over a single i
nterval q-wide, the quantizer error variance is
• The peak power is
• The ratio of signal peak power to average quantization error power
12
1)(
2
2/
2/
2/
2/
222
q
deq
edeepeq
q
q
q
222 )2
(]2
)1([
LqLqVp
22
22
312/
4/)( L
q
qL
N
Sq
23Dept. of EE, NDHU
Quantization Samples
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Pulse Code Modulation (PCM)
• Quantize PAM signal into a digital word
• Increase the number of levels
– Reduce the quantization noise
– Increase the number of bits per PCM sequence
– The data rate is thus increased, and the cost is a greater transmission
bandwidth
• Some communication systems can be tolerable to the time delay so that
the more quantization levels need not more bandwidth (ex: outer space
communication)
25Dept. of EE, NDHU
Statistics of Speech Amplitudes
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Uniform and Non-uniform Quantization
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Quantizer Characteristics
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Compression Characteristics
Figure 2.20 Compression characteristics. (a) μ-law characteristic. (b) A-law characteristic.
29Dept. of EE, NDHU
Compression Functions
• -law compression
• A-law
xxx
yy sgn)1log(
)]/(1log[ maxmax
11
sgnlog1
)]/(log[1
10 sgn
log1
)/(
max
maxmax
max
maxmax
x
x
Ax
A
xxAy
Ax
xx
A
xxAy
y
30Dept. of EE, NDHU
Baseband Transmission
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Waveform Representation of Binary Digits
• Binary digits needs to be represented by physical waveform
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33Dept. of EE, NDHU
PCM Waveform Considerations
• DC component
– Eliminate DC energy to enable the system to be ac coupled
• Self-clocking
– Some PCM coding schemes aid in the recovery of the clock signal
• Error detection
• Bandwidth compression
– Such as multi-level codes
• Differential encoding
• Noise immunity
– Some PCM schemes have better error performance
34Dept. of EE, NDHU
Spectral Densities of Various PCM Waveform
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Bits per PCM Word and Bits per Symbol
• PCM word size
– Required number of bits per analog sample for the allowable
quantization distortion
– For example, we specified the quantization error is specified not to
exceed a fraction of the peak-to-peak analog voltage ,
• Bits per symbol is decided by M-level signal transmission
p ppV
e
pppppppp pVL
V
L
V
L
Ve
2
2)1(2max
bits 2
1log levles
2
12 2 p
lp
Ll
36Dept. of EE, NDHU
Quantization Levels and Multi-level Signaling
• Example 2.3
– The information in an analog waveform, with the maximum frequency fm=3 kHz, is to
be transmitted over an M-ary PAM system, where the number of pulse levels is M=16.
The quantization distortion is specified not to exceed of the peak-to-peak analog
signal
(a) What is the minimum number of bits/sample, or bits/PCM word that should be used i
n digitizing the analog waveform?
(b) What is the minimum required sampling rate, and what is the resulting bit transmissio
n rate?
(c) What is the PAM pulse or symbol transmission rate?
(d) If the transmission bandwidth equals 12 KHz, determine the bandwidth efficiency for
this system
%1
37Dept. of EE, NDHU
Correlative Coding
• Transmit 2W symbols/s with zero ISI, using the theoretical minimum ba
ndwidth of W Hz, without infinitely sharp filters.
• Correlative coding (or duobinary signaling or partial response signaling)
introduces some controlled amount of ISI into the data stream rather than
trying to eliminate ISI completely
• Doubinary signaling
38Dept. of EE, NDHU
Duobinary Decoding
• Example
– Binary digit sequence xk: 0 0 1 0 1 1 0
– Bipolar amplitudes xk : -1 -1 +1 -1 +1 +1 -1
– Coding rule yk=xk+xk-1 -2 0 0 0 2 0
– Decoding decision rule
+ If , decide that
+ If , decide that
+ If , decide opposite of the previous decision
• Error propagation could cause further errors
1ˆ kx
0ˆ kx
2ˆ ky
2ˆ ky
0ˆ ky
39Dept. of EE, NDHU
Precoded Doubinary Signaling
40Dept. of EE, NDHU
Duobinary Precoding
• Example
– Binary digit sequence 0 0 1 0 1 1 0
– Precoded sequence 0 0 1 1 0 1 1
– Bipolar sequence -1 -1 +1 +1 -1 +1 +1
– Coding rule -2 0 +2 0 0 +2
– Decoding decision rule
+ If , decide that
+ If , decide that
+ Decoded binary sequence 0 1 0 1 1 0
1 kkk wxw
}{ kx
}{ kw
1 kkk wwy
2ˆ ky
0ˆ ky
0ˆ kx
1ˆ kx
}ˆ{ kx
41Dept. of EE, NDHU
Duobinary Equivalent Transfer Function
fTjefH 21 1)(
elsewhere 02
1for cos2)(
that so
)(
)1(
2
1for )()()(
2
21
TfTfH
eeeT
Te
TffHfHfH
e
fTjfTjfTj
fTj
e
elsewhere 02
1for )(2 T
fTfH
)(sin)(sin)( T
Ttc
T
tcthe
42Dept. of EE, NDHU
Duobinary Transfer Function
43Dept. of EE, NDHU
Comparison of Binary with Duobinary Signaling
• Binary signaling assumes the transmitted pulse amplitude are independe
nt of one another
• Duobinary signaling introduces correlation between pulse amplitudes
• Duobinary technique achieve zero ISI signal transmission using a smalle
r system bandwidth
• Duobinary coding requires three levels, compared with the usual two lev
els for binary coding
• Duobinary signaling requires more power than binary signaling (~2.5 dB
greater SNR than binary signaling)