CHAPTER 2
Formatting &
Baseband
Modulation
School of Computer and Communication Engineering,
Amir Razif Arief b. Jamil Abdullah
EKT 431: Digital Communications
Last time, we talked about:


Important features of digital communication systems
Some basic concepts and definitions such as as signal
classification, spectral density, random process, linear
systems and signal bandwidth.
Today, we are going to talk
about:

The first important step in any DCS:

Transforming the information source to a form
compatible with a digital system
Formatting and Transmission
of Baseband Signal
Digital info.
Format
Textual
source info.
Analog
info.
Sample
Quantize
Pulse
modulate
Encode
Bit stream
Format
Analog
info.
sink
Low-pass
filter
Textual
info.
Decode
Pulse
waveforms
Demodulate/
Detect
Transmit
Channel
Receive
Digital info.
Digital data, textual information, analog information



Transmitted through baseband channel  pulses
Pulse modulate~ bit stream  pulse modulate
Demodulated~ pulse waveform demodulated to produce estimate
transmitted digit, recover estimate of source information.
Format Analog Signals

To transform an analog waveform into a form that is
compatible with a digital communication system, the
following steps are taken:
 Sampling
 Quantization and encoding
 Baseband transmission
formatting~ transfer information into digital message, in ‘1’ or ‘0’.
Sampling Theorem
Analog
signal
Sampling
process
Pulse amplitude
modulated (PAM) signal
Sample and hold  output is pulse amplitude modulation (PAM)
~ Can retrieve analog signal through LPF
~ Original waveform?

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.
- Allow analog signal to be reconstructed completely.

Sampling
Time domain
x
t)x
t)
x
(t)
s(
(
x(t )
x (t )
xs (t )
~ impulse sampling
 Time and frequency domain
Frequency domain
X
(f)
X
f)

X
(f)
s
(
| X(f )|
| X ( f ) |
| Xs ( f ) |
Aliasing Effect
- Aliasing ~undersampling
 (1) Higher sampling rate require.
 (2) Antialiasing filters fm reduced to fs/2 or less – LPF
 Transition bandwidth.. $
LP filter
Nyquist rate
aliasing
Quantization
Source of corruption~ (1) sampling & quantization (2) channel effect.
 Amplitude quantizing: Mapping samples of a continuous amplitude
waveform to a finite set of amplitudes.
- Quantile interval (q volt)
- linear quantizer, error q/2
-
Out
• Average quantization noise
power
Quantized
values
In
• Signal peak power
• Signal power to average
quantization noise power
Quantization Error

Quantizing error: The difference between the input and
output of a quantizer.
Quantization noise~ The distortion due to a round-off or truncation error.
~ Process of encoding PAM into a quantization PAM signal involve discarding
some of the original analog information.
ˆ(t)x(t)
e(t)x
~ Quantization noise is inversely proportional to the number of levels employed
in the quantization process.
Process of quantizing noise
Qauntizer
y  q(x)
Model of quantizing noise
AGC
xˆ (t )
x(t )
xˆ (t )
x(t )
x
e(t )
+
e(t) 
xˆ(t)  x(t) ACG~ employed to extend
the operating range of converter.
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:
s

E
{[
x

q
(
x
)]
}

e
(
x
)
p
(
x
)
dx

s

s

2
q
2

2


L
/2

12
l
q
s
2
p
(
x
q

l)
l Uniform q.
l
012
2
Lin
2 2
Lin
Sat
s2~ Average quantization noise power
s
2
Lin
q2

12
Encoding: Pulse Code Modulation
(PCM)

A uniform linear quantizer is called Pulse Code Modulation
(PCM).
~ PCM is class of baseband signals obtained from quantized PAM signals by
encoding each quantized sample into a digital word.

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 l = log2L.
The source information is quantized into one of L levels  each
quantized
sample is digitally encoded into l-bit (l = log2L) codeword.
For baseband transmission the codeword bits will then be
transformed to pulse waveform.
Increase the number of level reduce quantization noise. Should
increase the data rate however result in more transmission
bandwidth.
Quantization example

Analog signal from -4v to 4v, step size 1v, 8 quantize level (code#).
amplitude Example: to improve terrible music
x(t)  Increase quantization level  reduce noise cause greater transmission
bandwidth
111 3.1867
Quant. levels
110 2.2762
101 1.3657
100 0.4552
boundaries
011 -0.4552
010 -1.3657
001 -2.2762
xq(nTs): quantized values
x(nTs): sampled values
000 -3.1867
Ts: sampling time
PCM
codeword
t
110 110 111 110 100 010 011 100 100 011

Pg 80 text
PCM sequence
Statistics of Speech Amplitudes

In speech, weak signals (low amplitude) are more frequent than strong
ones (high amplitude).
Probability density
function
1.0
0.5
0.0

2.0
1.0
3.0
Normalized magnitude of speech signal
Using equal step sizes (uniform quantizer) gives low
signals and high  S  for strong signals.
 
 N q

S
  for
 N q
weak
Adjusting the step size of the quantizer by taking into account the
speech statistics improves the SNR for the input range.
~ non-uniform quantization provides fine quantization for weak
signal and coarse quantization for strong signal.
L2 q 2 / 4
S
 3L2
   2
q / 12
 N q

Uniform and Non-Uniform
Quantization
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
 Simple implementation


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
 Provide fine quantization for weak signal.

Application

of non-uniform quantizer:
Commonly used for speech
Non-uniform Quantization

It is achieved by uniformly quantizing the “compressed”
signal (1) distort signal through logarithmic compression
(2) uniform quantizer input to uniform quantizer  expansion
(3) companding:- process of compression & expansion

At the receiver, an inverse compression characteristic, called
“expansion” is employed to avoid signal distortion.
compression+expansion
y  C(x)
x(t )
companding
x̂
yˆ (t )
y (t )
xˆ (t )
x
Compress
ŷ
Qauntize
Transmitter
Expand
Channel
Receiver
Cont’d…
Companding Characteristics (1) u-law (2) A-Law
Companding Characteristics
• Today most PCM use a piecewise linear approximation to the logarithmic
compression characteristics.
Method of Companding
• For the compression, two laws are adopted: the μ-law in US and Japan
and the A-law in Europe.
μ-law
y  y max
log e [1   (| x | / x max )]
sgn x
log e (1   )
 1 for x  0
sgn x  
 1 for x  0
A-law
A(| x | / x max
|x| 1

y
sgn
x
0


max

1  log e A
x max
A
y
1  log e [ A(| x | / x max )]
1 |x|

sgn x

1

1  log e A
A x max
• The typical values used in practice are: μ=255 and A=87.6.
• After quantization the different quantized levels have to be represented
in a form suitable for transmission.
This is done via an encoding process.
Vmax= Max uncompressed analog input voltage
Vin= amplitude of the input signal at a particular of instant time
Vout= compressed output amplitude
A & μ= parameter define the amount of compression
Baseband Transmission



analog waveform transformed into binary digits via use of PCM.
binary digits representation with electrical pulse to transmit them
through baseband channel.
To transmit information through physical channels, PCM
sequences (codewords) are transformed to pulses
waveforms.
 Each waveform carries a symbol from a set of size M.
 Each transmit symbol represents k log
2 M bits of
the PCM words.
 PCM waveforms (line codes) are used for binary symbols
(M=2).
 M-ary pulse modulation are used for non-binary symbols
(M>2).
Cont’d…
Pg 86
Figure 2.21: Waveform representation of binary digits. (a) PCM sequence
(b) Pulse representation of PCM (3) Pulse Waveform.
PCM Waveforms Types
• PCM waveforms is when pulse modulation applied to a binary
symbol resulting binary waveform.
• PCM types;


telephony application called line code,
PCM applied to nonbinary symbol called M-ary pulse modulation
waveform.
• PCM waveform groups;




(1)
(2)
(3)
(4)
Nonreturn-to-zero (NRZ)
Return-to-zero (RZ)
Phase encoded
Multilevel binary
+V
NRZ-L
-V
Unipolar-RZ+V
0
+V
Bipolar-RZ 0
-V
0
1
0
T
1
1
0
+V
Manchester-V
Miller +V
-V
+V
Dicode NRZ 0
-V
2T 3T 4T 5T
0
1
0
T
1
1
0
2T 3T 4T 5T
Cont’d…
• NRZ types; very commonly used.
(i) NRZ-L (L for level)~ used extensively in digital logic.
(ii) NRZ-M (M for mark)~ mark or “1” represent change in level & “0” or
space no change. “differential encoding”. Used in magnetic tape
recording.
(iii) NRZ-S (s for space)~ compliment of NRZ-M.
• RZ types:
(i) Unipolar-RZ~ ‘1’ half-bit wide pulse, ‘0’ absence of pulse.
(ii) Bipolar-RZ~ ‘1’ and ‘0’ opposite pulse that is one-half bit wide.
(iii) RZ-AMI (alternate mark inversion)~ equal amplitude alternating
pulse. ‘0’ is represent by absence of pulse.
• Bi phase~ used in magnetic recording & optic comm.
(i) bi-f-L (bi phase level) or Manchester cooding~’1’ half bit wide pulse
1st half of interval & ‘0’ half bit wide pulse 2nd half of interval
(ii) bi-f-M (bi phase mark)~ transition occur at every bit interval.
(iii) bi-f-S (bi phase space)~ transition occur at every bit interval. ‘1’ no
transition & ‘0’ second transition second half bit later.
Cont’d…

Figure 2.22 pg 87
PCM Waveforms …
 In
•
•
•
•
•
•
choosing PCM, parameters to be considered;
DC components
Self-clocking
Error detection
Bandwidth Compression
Differential encoding
Noise immunity
Spectra of PCM Waveforms
M-ary Pulse Modulation

M-ary pulse modulations category:
 M-ary pulse-amplitude modulation (PAM)
 M-ary pulse-position modulation (PPM)
 M-ary pulse-duration modulation (PDM)
 M-ary PAM is a multi-level signaling where each symbol
takes one of the M allowable amplitude levels, each
representing k log
bits of PCM words.
2M
 For a given data rate, M-ary PAM (M>2) requires less
bandwidth than binary PCM.
 For a given average pulse power, binary PCM is easier to
detect than M-ary PAM (M>2).
M-ary PAM
 one of M allowable amplitude levels are assigned to each of the M possible
symbol values.
 M-ary PPM
 modulation is effected by delaying or advancing a pulse occurrence.
 M-ary PWM
 modulation is effected by varying the pulse width by an amount that
corresponds to the value of the symbols.

M-ary pulse modulation blockdiagram
Binary
PCM
sequence
k-bit
tuple
Symbol
Sequence
M-ary Pulse
Modulator
M-ary
Pulse-modulation
Waveform
Illustration of PCM signals
PAM example