Lecture 3
Data Encoding and Signal Modulation
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Introduction
Data Encoding and Signal Modulation
Advantages of Signal Modulation
Amplitude Modulation
Amplitude Modulation of Digital Signals
Reducing Power and Bandwidth of AM Signals
Frequency Modulation
Power and Bandwidth of FM Signals
Conclusion
1
Introduction
A network and transport layers basic services
comprise the end-to-end transport of the bit streams
over a set of routers (switches). They are produced
using six basic mechanisms:
a. Multiplexing
b. Switching
c. Error control
d. flow control
e. congestion control
f. and resource allocation.
2
Multiplexing
Combines data streams of many such users into
one large bandwidth stream for long duration.
Users can share communication medium.
a. Switch
b. Multiplexer/Demultiplexer
a. Fully connected network
b. network with shared links.
3
Data Encoding
is
• the process of preparing data for efficient and accurate transmission.
• Because analog data is altered by noise in transmission, the process
of analog-to-digital conversion allows more accurate transmission of
data. The conversion process will not change the analog data, in
conversion the information contained in the analog data will not be
destroyed by the conversion process. Once the data is in digital
form, it can be encoded as a sequence of voltage levels.
Signal Modulation is
• the process of encoding a baseband source signal Sm (t) onto a carrier
signal.
• The carrier waveform is varied in a manner directly related to the
baseband signal. The carrier can be a sinusoidal signal or a pulse
signal. The result of modulating the carrier signal is called the
modulated signal.
4
Sampling using PAM.
S(t)
Original Signal
t
S(t)
s > 2B
Pulse
Amplitude
Modulated
t
Sampling Interval
5
Signal Modulation
Sc ( t ) = A · cos ( 2 f t+  )
A. Amplitude Modulation (AM), or Amplitude Shift
Keying (ASK): The amplitude A of the carrier signal
changes in direct proportion to the baseband signal.
B. Phase Modulation (PM), or Phase Shift Keying
(PSK): The phase  of the carrier signal changes in
direct proportion to the baseband signal.
C. Frequency Modulation (FM), or Frequency Shift
Keying (FSK): The frequency f of the carrier changes
6
in direct proportion to the baseband signal.
Amplitude, Phase, and Frequency
Modulation of a digital baseband signal
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
AM
PM
FM
7
Advantages of Signal Modulation
• Frequency Division Multiplexing
• Wavelength Division Multiplexing
Are the processes of transmitting several signals
over the same medium by using many carrier
waves, each with a different frequency
• Radio transmission of the signal.
To receive an electromagnetic signal using an
antenna, the dimensions of the antenna must be of
the same order of magnitude as the wavelength of
the signal being transmitted.
8
Frequency Division Multiplexing
allows several signals to share
the same transmission line.
Original Signals
Received Signals
Sc1 (t)
Sm1 (t)
M
Sc2 (t)
Sm2 (t)
M
Sc3 (t)
Sm3 (t)
Sc1 (t)
M
DM
Transmission
Line
?m1 (t)
Sc2 (t)
DM
?m2 (t)
Sc3 (t)
DM
?m3 (t)
9
Transmitting a 1 kHz sinusoidal waveform with radio waves
would require an antenna on the order of one signal
wavelength, or 300,000 meters.
m
3  10
1
c
s  3  10 5 m
f  1000 ;  

1
s
f
1000
s
8
Sc ( t ) = A · cos ( 2 fc )
fc =10 MHz
range (fc + f) and (fc - f) .
m
3  10
1
c
s  30 m
f  10  10 6 ;  

s
f
61
10  10
s
5GHz
8
6 cm
10
Amplitude Modulation
• AM is simply the multiplication of the baseband signal
with the carrier signal.
Sc ( t )  Ac  cos ( 2 f c t ) X

Sm ( t )
1
S ( t )    Ac   S m ( t )    cos ( 2 f c t )
k

S ( t )  k1  Ac   DC offset m  S m ( t )   cos ( 2 f c t )
 k1  Ac  DC offset m  cos ( 2 f c t )  k1  Ac  S m (t )  cos ( 2 f c t )
•Modulation coefficient k describes
how efficiently the modulator device multiplies the two signals.
11
DSBTC AM
• Double Side Band with Transmitted Carrier (DSBTC AM). In
this type of AM signal, the DC offset of the baseband signal is
equal to the amplitude of the carrier signal Ac .
• An important quality of a DSBTC AM signal is the modulation
index i. This value is the ratio of the maximum amplitude of the
baseband signal, max [ | | ], (without DC offset) to the amplitude
of the carrier signal Ac .
i
max
S
m (t )

Ac
• The simplest case of DSBTC AM, where the baseband signal is a
sinusoidal signal with DC offset equal to the carrier signal
amplitude:
Sm ( t ) = Ac + Am · cos ( 2 fm t)
12
S (t ) 
1
k



Am
 Ac   Ac   1 
cos ( 2 f m t )    cos ( 2 f c t )
Ac



Am
i
Ac
2
c
A
S (t ) 
  1  i  cos ( 2 f m t )   cos ( 2 f c t )
k
1
cos( x )  cos( y )  cos( x  y )  cos( x  y )
2
Ac2
S (t ) 
  1  i  cos ( 2 f m t )   cos ( 2 f c t )
k
Ac2
Ac2

 cos( 2 f c t ) 
 i  cos( 2 f m t )  cos( 2 f c t )
k
k
Ac2
Ac2
1

 cos( 2 f c t ) 
 i  cos( 2 ( f c  f m )t )  cos( 2 ( f c  f m )t )
k
k
2
 Carrier frequency component  Non  carrier frequency component
13
Power spectrum of DSBTC AM signal
with sinusoidal baseband signal,
i = 100%, k = 1.
Vrms
Ac2
2
Ac2
Ac2
2· 2
2· 2
fc - fm
fc
f c + fm
f
frequency
14
Sm (t)
Ac
t
Sc (t)
t
S(t)
t
15
S50% (t)
i = 50%
t
S100% (t)
i = 100%
t
S150% (t)
i = 150%
t
16
DSBSC AM
Sm ( t ) = Ac · cos ( 2 fm t)
S (t )  Ac   Ac  cos ( 2 f m t )   cos ( 2 f c t )
Vrms
S (t )  Ac2  cos ( 2 f m t )  cos ( 2 f c t )
2 1
 Ac  cos( 2 ( f c  f m )t )  cos( 2 ( f c  f m )t )
2
Ac2
Ac2
2· 2
2· 2
fc - fm
fc
f c + fm
f
frequency17
Sm (t)
t
Sc (t)
t
S(t)
t
18
Amplitude Modulation of Digital Signals
Baseband Signal
Sm ( t ) 
5V  4 
1
1







cos
2

f
t

cos
6

f
t

cos
10

f
t




m
m
m
 
3
5

Carrier Signal
S c ( t )  5V  cos  2 f c t 
Baseband Signal with DC shift
S m ( t )  5V 
5V  4 
1
1







cos
2

f
t

cos
6

f
t

cos
10

f
t




m
m
m
 
3
5

19
Transmitted Signal
25V 2
S (t ) 
cos( 2 f c t )
k
carrier frequency
15.92V 2

k
1
1














cos
2

f

f
t

cos
2

f

3
f
t

cos
2

f

5
f
t

...
c
m
c
m
c
m


3
5
lower sideband
15.92V 2

k
1
1














cos
2

f

f
t

cos
2

f

3
f
t

cos
2

f

5
f
t

...
c
m
c
m
c
m


3
5
upper sideband
20
DSBTC AM signal with
square wave baseband signal, i = 100%,
k = 10.
Vrms
2.50V
2
0.32V
1.59V
1.59V
2
2
0.53V
0.53V
2
2
2
fc - 5fm
0.32V
2
fc - 3fm
fc - f m fc f c + fm
fc + 3fm
fc + 5fm
f
frequency
21
Sm (t)
5V
t
Sc (t)
t
S(t)
t
22
DSBSC AM
S m (t ) 
5V  4 
1
1





cos
2

f
t

cos
6

f
t

cos  10 f m t    

m
m
 
3
5

15.92V 2
S (t ) 
k
15.92V 2

k
Vrms
1
1














cos
2

f

f
t

cos
2

f

3
f
t

cos
2

f

5
f
t

...
c
m
c
m
c
m


3
5
lower sideband
1
1














cos
2

f

f
t

cos
2

f

3
f
t

cos
2

f

5
f
t

...
c
m
c
m
c
m


3
5
upper sideband
0.32V
1.59V
1.59V
2
2
0.53V
0.53V
2
2
2
fc - 5fm
0.32V
2
fc - 3fm
fc - f m fc f c + fm
fc + 3fm
fc + 5fm
f
frequency
23
Sm (t)
t
Sc (t)
t
S(t)
180 degree phase shifts
t
24
Binary Phase Shift Keying and
Quadrature Phase Shift Keying
25V
S(t ) 
 cos  2 f c t   ( t ) 
k
 0 if S m ( t )   5V
 (t )  
 180  if S m ( t )   5V
Since the phase of the transmitted signal can take one of
two values (phase jumping), this type of modulation is
called binary phase-shift keying (BPSK). It is a constantamplitude method of modulation.
25
If we add together two BPSK signals that are offset by a 90
degree phase shift, there are four possible phase jumping during
every sampling period. Instead of one possible shift of 180º, there
are three possible transitions: +90º, 180º, and -90º (+270º). The
signal can be represented by the following formula:
25V
S(t ) 
 cos  2 f c t   ( t ) 
k
 45 

 135 
 (t )  
 225 

 315 
if S m1 ( t )   5V, S m 2 ( t )   5V
if S m1 ( t )   5V, S m 2 ( t )   5V
if S m1 ( t )   5V, S m 2 ( t )   5V
if S m1 ( t )   5V, S m 2 ( t )   5V
26
S1 (t)
1
0
1
0
0
t
Time domain
representation of
QPSK signal, created
by combining BPSK
signals S1 and S2 .
S2 (t)
1
0
1
0
0
t
phase shifts
S(t)
180º
00
90º
11
180º
01
-90º
10
00
t
27
Reducing Power and Bandwidth of AM Signals
• In DSBTC AM, the carrier frequency component carries no
information.
In all forms of amplitude modulation, the two sidebands contain
identical information.
• Eliminating one of the two sidebands.
• There are therefore four possibilities for transmitting an amplitude
modulated signal
• A. Dual sideband, transmitted carrier (DSBTC AM)
• B. Vestigial sideband
• C. Dual sideband, suppressed carrier (DSBSC AM)
• D. Single sideband
Selecting the type of transmission can depend on the following
factors:
• Power limitations
• Bandwidth limitations
• Simplicity of Demodulation Equipment
28
• The power required for transmitting a sinusoidal baseband
signal with DSBTC AM is:
1  Ac2
Pt 

2 
 2





i2
 P 
1  2

2
c
2
1
 Am Ac 
 2


2
2 2 
2




Pt : Total transmitted power, Ac :Carrier Signal Amplitude
• i : Modulation index
• For a modulation index of 100%, the transmitted power
will be 1.5 times the power squared of the carrier
frequency. Each sideband contributes 0.25 times the power
of the carrier frequency.
• Vestigial sideband uses only one of the two sidebands of
the signal, and also reduces the amplitude and power of the
29
carrier signal.
Four possible ways to transmit an AM signal.
Vrms
Vrms
fc
f
fc
(a) DSBTC AM
f
(c) DSBSC AM
Gain
Vrms
Bandpass Filter
fc
Bandpass Filter
f
Vrms
fc
f
Vrms
fc
(b) Vestigial sideband AM
f
fc
(d) Single sideband AM
f
30
Frequency Modulation
• Additive noise
• Frequency modulation is actually a special case of
phase modulation, where the phase of the
transmitted signal accumulates according to the
amplitude of the baseband signal:

S ( t )  Ac  cos  2 f c t 


  k  Sm (  ) d 

t
k : Constructional coefficient of the modulator
31
• To find the maximum possible frequency deviation of an FM signal,
we can assume the baseband signal is a constant voltage of +Am ,
then the integral will reduce to a linear function of t :
k  Am
 
S ( t )  Ac  cos  2 f c t  k  Am  t   Ac  cos 2  f c 
2
 
  f c max
( t ) 
t


k  Am

2
 
t 
 
Sm ( t ) = Am · sin (2 fm )
t
k  Sm (  )d   k  Am 
0
k  Am
sin ( 2 f m  )d 
cos ( 2 f m t )
2 f m
k  Am
kf 
2  f m

S ( t )  Ac  cos 2 f c t  k f cos( 2 f m t )

32
• Equation can be expanded using Bessel's trigonometric
identities into a series of phase-shifted sinusoidal terms.
• The amplitude of each term is determined by the Bessel function
of the first kind Jn ( kf ), where kf is the modulation index.


cos 2 f c t  k f cos( 2 f m t ) 


n 

J n ( k f )  cos  2 t  f c  n f m  

2 

n  
J  n ( x )  (  1) n  J n ( x )

S (t )  Ac 


J n ( k f )  cos  2 t  f c  n f m

n  
S (t )  Ac  J 0 ( k f )  cos 2 f c t

 Ac 

n 1
  n


2 

n 


J n ( k f )   cos  2   f c  n f m   t 

2 


n  

 cos  2   f c  n f m   t  33  
2  

Power and Bandwidth of FM Signals
• Calculating the power of an FM signal is much simpler in the
time domain.
PFM
1 2  2

 Ac   j0 ( k f )  2 
2
2

Ac2


1
jn2

(k f ) 

BT  2  B   k f  1 
In this equation B is effective bandwidth of baseband signal,
but BT is absolute bandwidth of FM signal
34
Ac · cos ( 2 fc + kf cos ( 2 fm ) ) at various values of kf .
Vrms
kf = 0.5
f
fc - 3fm
fc
fc + 3fm
Vrms
kf = 1
f
fc - 3fm
fc
fc + 3fm
Vrms
kf = 2
f
fc - 3fm
fc
fc + 3fm
Vrms
kf = 10
f
fc -9fm
fc -6fm
fc -3fm
fc
fc +3fm
fc +6fm
fc +9fm
35
S(t)
Original
Signal
t
S(t)
Quantizing of
sampled
amplitudes
t
S(t)
Recovery of
Original
Signal
t
36
• For instance, we want to use only 8 bits to store each
sample, and the maximum possible value of the analog
signal is 10, then we can quantize the signal into multiples
of 10/256 (0.03906). Each number will be represented as
an 8-bit binary number between 0 and 255. To
approximately reconstruct the original analog signal, each
8-bit sample must be multiplied by 0.03906.
• When sending a digital signal over a transmission line, the
sampling rate of the signal determines the bandwidth
required for successful transmission.
• Level detection and regeneration of a digital signal allows
the signal to be transmitted with a significantly smaller
bandwidth than the absolute bandwidth of the signal. 37
• The Nyquist criterion determines the
sampling rate necessary to capture all the
information of an analog signal with a
discrete sequence (taken by sampling the
signal at a certain rate).
• “The signal must be sampled at a rate of
twice the signal bandwidth
s > 2B
• (s is the sampling frequency, B is
bandwidth of analog signal’s.):
38
Digital Data Encoding Schemes
• When digital data is transmitted, it must be
mapped to a signal pattern. The signal pattern
should make transmission as reliable as possible.
• In the simplest encoding:
“1” is converted to signal voltage high, and
“0” is converted to signal voltage low.
This is called Non-Return to Zero-Level (NRZ-L)
encoding.
1
0
1
1
0
0
0
1
1
0
1
NRZ-L
Bit rate is twice the frequency
39
• Manchester Encoding, or Biphasic-Level:
0:Signal low (first half) / Signal high (second half)
1:Signal high (first half) / Signal low (second half)
1
0
1
1
0
0
0
1
1
1
0
Manchester
Bit rate = signal frequency
40