dept. of ee, ndhu 1 chapter two formatting and baseband modulation
TRANSCRIPT
![Page 1: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/1.jpg)
1Dept. of EE, NDHU
Chapter Two
Formatting and Baseband Modulation
![Page 2: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/2.jpg)
2Dept. of EE, NDHU
Digital Communication Transformation
![Page 3: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/3.jpg)
3Dept. of EE, NDHU
Formatting and Transmission of Baseband Signals
![Page 4: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/4.jpg)
4Dept. of EE, NDHU
Message, Characters, and Symbols
![Page 5: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/5.jpg)
5Dept. of EE, NDHU
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
![Page 6: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/6.jpg)
6Dept. of EE, NDHU
Impulse Sampling (Ideal Case)
![Page 7: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/7.jpg)
7Dept. of EE, NDHU
Spectra for Various Sampling Rate
Sampled spectrum (fs > 2fm)
Sampled spectrum (fs < 2fm)
![Page 8: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/8.jpg)
8Dept. of EE, NDHU
Natural Sampling
)/(csin)/1( , ssn TnTTC
n
nsnp nffCfX )()(
![Page 9: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/9.jpg)
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
![Page 10: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/10.jpg)
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
![Page 11: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/11.jpg)
11Dept. of EE, NDHU
Aliasing for Sampling
![Page 12: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/12.jpg)
12Dept. of EE, NDHU
Eliminate Aliasing for Higher Sampling
![Page 13: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/13.jpg)
13Dept. of EE, NDHU
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
![Page 14: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/14.jpg)
14Dept. of EE, NDHU
Pre-filter Eliminates Alias
![Page 15: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/15.jpg)
15Dept. of EE, NDHU
Post-filter Eliminates Alias
![Page 16: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/16.jpg)
16Dept. of EE, NDHU
Alias Frequency by Sub-Nyquist Sampling Rate
![Page 17: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/17.jpg)
17Dept. of EE, NDHU
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
![Page 18: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/18.jpg)
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
![Page 19: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/19.jpg)
19Dept. of EE, NDHU
Analog Source Description
![Page 20: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/20.jpg)
20Dept. of EE, NDHU
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)
![Page 21: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/21.jpg)
21Dept. of EE, NDHU
Quantization Level
![Page 22: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/22.jpg)
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
![Page 23: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/23.jpg)
23Dept. of EE, NDHU
Quantization Samples
![Page 24: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/24.jpg)
24Dept. of EE, NDHU
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)
![Page 25: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/25.jpg)
25Dept. of EE, NDHU
Statistics of Speech Amplitudes
![Page 26: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/26.jpg)
26Dept. of EE, NDHU
Uniform and Non-uniform Quantization
![Page 27: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/27.jpg)
27Dept. of EE, NDHU
Quantizer Characteristics
![Page 28: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/28.jpg)
28Dept. of EE, NDHU
Compression Characteristics
Figure 2.20 Compression characteristics. (a) μ-law characteristic. (b) A-law characteristic.
![Page 29: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/29.jpg)
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
![Page 30: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/30.jpg)
30Dept. of EE, NDHU
Baseband Transmission
![Page 31: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/31.jpg)
31Dept. of EE, NDHU
Waveform Representation of Binary Digits
• Binary digits needs to be represented by physical waveform
![Page 32: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/32.jpg)
32Dept. of EE, NDHU
![Page 33: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/33.jpg)
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
![Page 34: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/34.jpg)
34Dept. of EE, NDHU
Spectral Densities of Various PCM Waveform
![Page 35: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/35.jpg)
35Dept. of EE, NDHU
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
![Page 36: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/36.jpg)
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
![Page 37: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/37.jpg)
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
![Page 38: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/38.jpg)
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
![Page 39: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/39.jpg)
39Dept. of EE, NDHU
Precoded Doubinary Signaling
![Page 40: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/40.jpg)
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
![Page 41: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/41.jpg)
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
![Page 42: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/42.jpg)
42Dept. of EE, NDHU
Duobinary Transfer Function
![Page 43: Dept. of EE, NDHU 1 Chapter Two Formatting and Baseband Modulation](https://reader035.vdocuments.us/reader035/viewer/2022081800/56649de55503460f94adda94/html5/thumbnails/43.jpg)
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)