Ppt of analog communication

Unit-1
Signal Analysis
4/26/2014
prepared by Arun Kumar & Shivendra
Tiwari
1
Prepared by:
MR . Arun Kumar
(Asst.Prof. SISTec-E EC dept.)
MR . Shivendra Tiwari
(Asst.Prof. SISTec-E EC dept.)

Content
• Periodic Function
• Fourier Series
• Complex Form of the Fourier Series
• Impulse Train
• Analysis of Periodic Waveforms
• Half-Range Expansion
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Periodic Function
• Any function that satisfies
( ) ( )f t f t T
where T is a constant and is called the period
of the function.
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Example:
Find its period.
4
cos
3
cos)(
tt
tf
)()( Ttftf )(
4
1
cos)(
3
1
cos
4
cos
3
cos TtTt
tt
Fact: )2cos(cos m
m
T
2
3
n
T
2
4
mT 6
nT 8
24T smallest T
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Example:
Find its period.tttf 21 coscos)(
)()( Ttftf )(cos)(coscoscos 2121 TtTttt
mT 21
nT 22
n
m
2
1
2
1 must be a rational
number
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Example:
Is this function a periodic one?
tttf )10cos(10cos)(
10
10
2
1 not a rational
number
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Fourier Series
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Introduction
• Decompose a periodic input signal into
primitive periodic components.
A periodic sequence
T 2T 3T
t
f(t)
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Synthesis
T
nt
b
T
nt
a
a
tf
n
n
n
n
2
sin
2
cos
2
)(
11
0
DC Part Even Part Odd Part
T is a period of all the above signals
)sin()cos(
2
)( 0
1
0
1
0
tnbtna
a
tf
n
n
n
n
Let 0=2 /T.
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Orthogonal Functions
• Call a set of functions { k} orthogonal on
an interval a < t < b if it satisfies
nmr
nm
dttt
n
b
a
nm
0
)()(
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Orthogonal set of Sinusoidal
Functions
Define 0=2 /T.
0,0)cos(
2/
2/
0 mdttm
T
T
0,0)sin(
2/
2/
0 mdttm
T
T
nmT
nm
dttntm
T
T 2/
0
)cos()cos(
2/
2/
00
nmT
nm
dttntm
T
T 2/
0
)sin()sin(
2/
2/
00
nmdttntm
T
T
andallfor,0)cos()sin(
2/
2/
00
We now prove this one
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Proof
dttntm
T
T
2/
2/
00 )cos()cos(
0
)]cos()[cos(
2
1
coscos
dttnmdttnm
T
T
T
T
2/
2/
0
2/
2/
0 ])cos[(
2
1
])cos[(
2
1
2/
2/0
0
2/
2/0
0
])sin[(
)(
1
2
1
])sin[(
)(
1
2
1 T
T
T
T
tnm
nm
tnm
nm
m n
])sin[(2
)(
1
2
1
])sin[(2
)(
1
2
1
00
nm
nm
nm
nm
0
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Proof
dttntm
T
T
2/
2/
00 )cos()cos(
0
)]cos()[cos(
2
1
coscos
dttm
T
T
2/
2/
0
2
)(cos
2/
2/
0
0
2/
2/
]2sin
4
1
2
1
T
T
T
T
tm
m
t
m = n
2
T
]2cos1[
2
1
cos2
dttm
T
T
2/
2/
0 ]2cos1[
2
1
nmT
nm
dttntm
T
T 2/
0
)cos()cos(
2/
2/
00
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Proof
dttntm
T
T
2/
2/
00 )cos()cos(
0
)]cos()[cos(
2
1
coscos
dttm
T
T
2/
2/
0
2
)(cos
2/
2/
0
0
2/
2/
]2sin
4
1
2
1
T
T
T
T
tm
m
t
m = n
2
T
]2cos1[
2
1
cos2
dttm
T
T
2/
2/
0 ]2cos1[
2
1
nmT
nm
dttntm
T
T 2/
0
)cos()cos(
2/
2/
00
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Orthogonal set of Sinusoidal
Functions
Define 0=2 /T.
0,0)cos(
2/
2/
0 mdttm
T
T
0,0)sin(
2/
2/
0 mdttm
T
T
nmT
nm
dttntm
T
T 2/
0
)cos()cos(
2/
2/
00
nmT
nm
dttntm
T
T 2/
0
)sin()sin(
2/
2/
00
nmdttntm
T
T
2/
2/
00
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Decomposition
dttf
T
a
Tt
t
0
0
)(
2
0
,2,1cos)(
2
0
0
0
ntdtntf
T
a
Tt
t
n
,2,1sin)(
2
0
0
0
ntdtntf
T
b
Tt
t
n
)sin()cos(
2
)( 0
1
0
1
0
tnbtna
a
tf
n
n
n
n
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Proof
Use the following facts:
0,0)cos(
2/
2/
0 mdttm
T
T
0,0)sin(
2/
2/
0 mdttm
T
T
nmT
nm
dttntm
T
T 2/
0
)cos()cos(
2/
2/
00
nmT
nm
dttntm
T
T 2/
0
)sin()sin(
2/
2/
00
nmdttntm
T
T
2/
2/
00
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Example (Square Wave)
11
2
2
0
0 dta
,2,10sin
1
cos
2
2
00
nnt
n
ntdtan
,6,4,20
,5,3,1/2
)1cos(
1
cos
1
sin
2
2
00 

n
nn
n
n
nt
n
ntdtbn
2 3 4 5--2-3-4-5-6
f(t)
1
ttttf 5sin
5
1
3sin
3
1
sin
2
2
1
)(
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Harmonics
T
nt
b
T
nt
a
a
tf
n
n
n
n
2
sin
2
cos
2
)(
11
0
DC Part Even Part Odd Part
T is a period of all the above signals
)sin()cos(
2
)( 0
1
0
1
0
tnbtna
a
tf
n
n
n
n
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Harmonics
tnbtna
a
tf
n
n
n
n 0
1
0
1
0
sincos
2
)(
T
f
2
2 00
Define , called the fundamental angular frequency.
0nnDefine , called the n-th harmonic of the periodic function.
tbta
a
tf n
n
nn
n
n sincos
2
)(
11
0
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Harmonics
tbta
a
tf n
n
nn
n
n sincos
2
)(
11
0
)sincos(
2 1
0
tbta
a
nnn
n
n
1
2222
220
sincos
2 n
n
nn
n
n
nn
n
nn t
ba
b
t
ba
a
ba
a
1
220
sinsincoscos
2 n
nnnnnn ttba
a
)cos(
1
0 n
n
nn tCC
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Amplitudes and Phase Angles
)cos()(
1
0 n
n
nn tCCtf
2
0
0
a
C
22
nnn baC n
n
n
a
b1
tan
harmonic amplitude phase angle
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Fourier Series
Complex form of the Fourier Series
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Complex Exponentials
tnjtne tjn
00 sincos0
tjntjn
eetn 00
2
1
cos 0
tnjtne tjn
00 sincos0
tjntjntjntjn
ee
j
ee
j
tn 0000
22
1
sin 0
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Complex Form of the Fourier Series
tnbtna
a
tf
n
n
n
n 0
1
0
1
0
sincos
2
)(
tjntjn
n
n
tjntjn
n
n eeb
j
eea
a 0000
11
0
22
1
2
1
0 00
)(
2
1
)(
2
1
2 n
tjn
nn
tjn
nn ejbaejba
a
1
0
00
n
tjn
n
tjn
n ececc
)(
2
1
)(
2
1
2
0
0
nnn
nnn
jbac
jbac
a
c
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1
0
00
)(
n
tjn
n
tjn
n ececctf
1
1
0
00
n
tjn
n
n
tjn
n ececc
n
tjn
nec 0
)(
2
1
)(
2
1
2
0
0
nnn
nnn
jbac
jbac
a
c
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2/
2/
0
0 )(
1
2
T
T
dttf
T
a
c
)(
2
1
nnn jbac
2/
2/
0
2/
2/
0 sin)(cos)(
1 T
T
T
T
tdtntfjtdtntf
T
2/
2/
00 )sin)(cos(
1 T
T
dttnjtntf
T
2/
2/
0
)(
1 T
T
tjn
dtetf
T
2/
2/
0
)(
1
)(
2
1 T
T
tjn
nnn dtetf
T
jbac )(
2
1
)(
2
1
2
0
0
nnn
nnn
jbac
jbac
a
c
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n
tjn
nectf 0
)(
dtetf
T
c
T
T
tjn
n
2/
2/
0
)(
1 )(
2
1
)(
2
1
2
0
0
nnn
nnn
jbac
jbac
a
c
If f(t) is real,
*
nn cc
nn j
nnn
j
nn ecccecc ||,|| *
22
2
1
|||| nnnn bacc
n
n
n
a
b1
tan
,3,2,1n
00
2
1
ac
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Complex Frequency Spectra
nn j
nnn
j
nn ecccecc ||,|| *
22
2
1
|||| nnnn bacc
n
n
n
a
b1
tan ,3,2,1n
00
2
1
ac |cn| amplitude
spectrum
n
phase
spectrum
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Example
2
T
2
T TT
2
d
t
f(t)
A
2
d
dte
T
A
c
d
d
tjn
n
2/
2/
0
2/
2/0
0
1
d
d
tjn
e
jnT
A
2/
0
2/
0
00
11 djndjn
e
jn
e
jnT
A
)2/sin2(
1
0
0
dnj
jnT
A
2/sin
1
0
02
1
dn
nT
A
T
dn
T
dn
T
Ad
sin
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T
dn
T
dn
T
Ad
cn
sin
8
2
5
1
T
,
4
1
,
20
1
0
T
d
Td
Example
40 80 120-40 0-120 -80
A/5
5 0 10 0 15 0-5 0-10 0-15 0
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T
dn
T
dn
T
Ad
cn
sin
4
2
5
1
T
,
2
1
,
20
1
0
T
d
Td
Example
40 80 120-40
0
-120 -80
A/10
10 0 20 0 30 0-10 0-20 0-30 0
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Example
dte
T
A
c
d tjn
n
0
0
d
tjn
e
jnT
A
00
0
1
00
11 0
jn
e
jnT
A djn
)1(
1 0
0
djn
e
jnT
A
2/0
sin
djn
e
T
dn
T
dn
T
Ad
TT d
t
f(t)
A
0
)(
1 2/2/2/
0
000 djndjndjn
eee
jnT
A
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Fourier Series
Impulse Train
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Dirac Delta Function
0
00
)(
t
t
t and 1)( dtt
0 t Also called unit impulse function.
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Property
)0()()( dttt
)0()()0()0()()()( dttdttdttt
(t): Test Function
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Impulse Train
0
tT 2T 3TT2T3T
n
T nTtt )()(
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Fourier Series of the Impulse Train
n
T nTtt )()(
T
dtt
T
a
T
T
T
2
)(
2 2/
2/
0
T
dttnt
T
a
T
T
Tn
2
)cos()(
2 2/
2/
0
0)sin()(
2 2/
2/
0 dttnt
T
b
T
T
Tn
n
T tn
TT
t 0cos
21
)(
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Complex Form
Fourier Series of the Impulse Train
T
dtt
T
a
c
T
T
T
1
)(
1
2
2/
2/
0
0
T
dtet
T
c
T
T
tjn
Tn
1
)(
1 2/
2/
0
n
tjn
T e
T
t 0
1
)(
n
T nTtt )()(
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Fourier Series
Analysis of
Periodic Waveforms
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Waveform Symmetry
• Even Functions
• Odd Functions
)()( tftf
)()( tftf
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Decomposition
• Any function f(t) can be expressed as the sum
of an even function fe(t) and an odd function
fo(t).
)()()( tftftf oe
)]()([)( 2
1
tftftfe
)]()([)( 2
1
tftftfo
Even Part
Odd Part
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Example
00
0
)(
t
te
tf
t
Even Part
Odd Part
0
0
)(
2
1
2
1
te
te
tf t
t
e
0
0
)(
2
1
2
1
te
te
tf t
t
o
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Half-Wave Symmetry
)()( Ttftf and 2/)( Ttftf
TT/2T/2
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Quarter-Wave Symmetry
Even Quarter-Wave Symmetry
TT/2T/2
Odd Quarter-Wave Symmetry
T
T/2T/2
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Hidden Symmetry
• The following is a asymmetry periodic function:
 Adding a constant to get symmetry property.
A
TT
A/2
A/2
TT
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Fourier Coefficients of
Symmetrical Waveforms
• The use of symmetry properties simplifies the
calculation of Fourier coefficients.
– Even Functions
– Odd Functions
– Half-Wave
– Even Quarter-Wave
– Odd Quarter-Wave
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Fourier Coefficients of Even Functions
)()( tftf
tna
a
tf
n
n 0
1
0
cos
2
)(
2/
0
0 )cos()(
4 T
n dttntf
T
a
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Fourier Coefficients of Even Functions
)()( tftf
tnbtf
n
n 0
1
sin)(
2/
0
0 )sin()(
4 T
n dttntf
T
b
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FourierCoefficientsfor Half-Wave
Symmetry
TT/2T/2
The Fourier series contains only odd harmonics.
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FourierCoefficientsfor Half-Wave
Symmetry
)sincos()(
1
00
n
nn tnbtnatf
oddfor)cos()(
4
evenfor0
2/
0
0 ndttntf
T
n
a T
n
oddfor)sin()(
4
evenfor0
2/
0
0 ndttntf
T
n
b T
n
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Fourier Coefficients for
TT/2T/2
])12cos[()( 0
1
12 tnatf
n
n
4/
0
012 ])12cos[()(
8 T
n dttntf
T
a
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Fourier Transform and Applications
By Njegos Nincic
Fourier
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Overview
• Transforms
– Mathematical Introduction
• Fourier Transform
– Time-Space Domain and Frequency Domain
– Discret Fourier Transform
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Transforms
• Transform:
– In mathematics, a function that results when a
given function is multiplied by a so-called kernel
function, and the product is integrated between
suitable limits. (Britannica)
• Can be thought of as a substitution
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Transforms
• Example of a substitution:
• Original equation: x + 4x² – 8 = 0
• Familiar form: ax² + bx + c = 0
• Let: y = x²
• Solve for y
• x = √y
4
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Fourier Transform
• Property of transforms:
– They convert a function from one domain to
another with no loss of information
• Fourier Transform:
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Time Domain and Frequency Domain
• Time Domain:
– Tells us how properties (air pressure in a sound function,
for example) change over time:
• Amplitude = 100
• Frequency = number of cycles in one second = 200 Hz
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• Frequency domain:
– Tells us how properties (amplitudes) change over
frequencies:
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• Example:
– Human ears do not hear wave-like oscilations,
but constant tone
• Often it is easier to work in the frequency
domain
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• In 1807, Jean Baptiste Joseph Fourier showed
that any periodic signal could be represented
by a series of sinusoidal functions
In picture: the composition of the first two functions gives the bottom one4/26/2014
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Fourier Transform
• Because of the
property:
• Fourier Transform takes us to the frequency
domain:
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Fourier Series
Half-Range Expansions
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Non-Periodic Function Representation
• A non-periodic function f(t) defined over (0, )
can be expanded into a Fourier series which is
defined only in the interval (0, ).
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Without Considering Symmetry
T
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Expansion Into Even Symmetry
T=2
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Expansion Into Odd Symmetry
T=2
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Expansion Into Half-Wave Symmetry
T=2
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ExpansionInto
T/2=2
T=4
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Expansion Into
Odd Quarter-Wave Symmetry
T/2=2 T=4
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What is a System?
• (DEF) System : A system is formally defined as
an entity that manipulates one or more
signals to accomplish a function, thereby
yielding new signals.
system output
signal
input
signal
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Some Interesting Systems
• Communication system
• Control systems
• Remote sensing system
• Biomedical system(biomedical signal
processing)
• Auditory system
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• Communication system
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• Control systems
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Papero
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• Remote sensing system
Perspectival view of Mount Shasta (California), derived from a pair of
stereo radar images acquired from orbit with the shuttle Imaging Radar
(SIR-B). (Courtesy of Jet Propulsion Laboratory.)
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• Biomedical system(biomedical signal
processing)
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• Auditory system
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Classification of Signals
• Continuous and discrete-time signals
• Continuous and discrete-valued signals
• Even and odd signals
• Periodic signals, non-periodic signals
• Deterministic signals, random signals
• Causal and anticausal signals
• Right-handed and left-handed signals
• Finite and infinite length
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Continuous and discrete-time
signals
• Continuous signal
- It is defined for all time t : x(t)
• Discrete-time signal
- It is defined only at discrete instants of time :
x[n]=x(nT)
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Continuous and Discrete valued
singals
• CV corresponds to a continuous y-axis
• DV corresponds to a discrete y-axis
Digital signal
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Even and odd signals
• Even signals : x(-t)=x(t)
• Odd signals : x(-t)=-x(t)
• Even and odd signal decomposition
xe(t)= 1/2·(x(t)+x(-t)) xo(t)= 1/2·(x(t)-x(-t))
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Periodic signals, non-periodic
signals
• Periodic signals
- A function that satisfies the condition
x(t)=x(t+T) for all t
- Fundamental frequency : f=1/T
- Angular frequency : = 2 /T
• Non-periodic signals
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Deterministic signals, random
signals
 Deterministic signals
-There is no uncertainty with respect to its value at any
time. (ex) sin(3t)
 Random signals
- There is uncertainty before its actual occurrence.
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Causal and anticausal Signals
• Causal signals : zero for all negative time
• Anticausal signals : zero for all positive time
• Noncausal : nozero values in both positive
and negative time
causal
signal
anticausal
signal
noncausal
signal
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Right-handed and left-handed Signals
• Right-handed and left handed-signal : zero
between a given variable and positive or
negative infinity
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Finite and infinite length
• Finite-length signal : nonzero over a finite
interval tmin< t< tmax
• Infinite-length singal : nonzero over all real
numbers
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Unit-2
Modulation Techniques
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Amplitude Modulation
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Content
• What is Modulation
• Amplitude Modulation (AM)
• Demodulation of AM signals
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What is Modulation
• Modulation
– In the modulation process, some characteristic of a high-
frequency carrier signal (bandpass), is changed according to
the instantaneous amplitude of the information (baseband)
signal.
• Why Modulation
– Suitable for signal transmission (distance…etc)
– Multiple signals transmitted on the same channel
– Capacitive or inductive devices require high frequency AC
input (carrier) to operate.
– Stability and noise rejection
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About Modulation
• Application Examples
– broadcasting of both audio and
video signals.
– Mobile radio communications, such
as cell phone.
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• Basic Modulation Types
– Amplitude Modulation: changes the amplitude.
– Frequency Modulation: changes the frequency.
– Phase Modulation: changes the phase.
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AM Modulation/Demodulation
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Modulator Demodulator
Baseband Signal
with frequency
fm
(Modulating Signal)
Bandpass Signal
with frequency
fc
(Modulated Signal)
Channel
Original Signal
with frequency
fm
Source Sink
fc >> fm
Voice: 300-3400Hz GSM Cell phone: 900/1800MHz
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• The amplitude of high-carrier signal is varied
according to the instantaneous amplitude of the
modulating message signal m(t).
Carrier Signal: or
Modulating Message Signal: or
The AM Signal:
cos(2 ) cos( )
( ): cos(2 ) cos( )
( ) [ ( )]cos(2 )
c c
m m
AM c c
f t t
m t f t t
s t A m t f t
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* AM Signal Math Expression*
• Mathematical expression for AM: time domain
• expanding this produces:
• In the frequency domain this gives:
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( ) (1 cos ) cosAM m cS t k t t
( ) cos cos cosc cAM mS t t k t t
)cos()cos(coscos:using 2
1 BABABA
2 2( ) cos cos( ) cos( )c c c
k k
AM m mS t t t t
freque
ncy
k/2k/2
Carrier,
A=1.
upper
sideband
lower
sideband
Amplitud
e
fcfc-fm fc+fm
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AM Power Frequency Spectrum
• AM Power frequency spectrum obtained by squaring
the amplitude:
• Total power for AM:
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.
2 2
2
2
4 4
1
2
k k
A
k
freq
k2/4k2/4
Carrier, A2=12 = 1
Power
fcfc-fm fc+fm
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• The AM signal is generated using a multiplier.
• All info is carried in the amplitude of the
carrier, AM carrier signal has time-varying
envelope.
• In frequency domain the AM waveform are
the lower-side frequency/band (fc - fm), the
carrier frequency fc, the upper-side
frequency/band (fc + fm).
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AM Modulation – Example
• The information signal is usually not a single frequency but a
range of frequencies (band). For example, frequencies from
20Hz to 15KHz. If we use a carrier of 1.4MHz, what will be the
AM spectrum?
• In frequency domain the AM waveform are the lower-side
frequency/band (fc - fm), the carrier frequency fc, the upper-
side frequency/band (fc + fm). Bandwidth: 2x(25K-20)Hz.
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frequen
cy
1.4 MHz
1,385,000Hz to
1,399,980Hz
1,400,020Hz to
1,415,000Hz
fc
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Modulation Index of AM Signal
m
c
A
k
A
)2cos()( tfAtm mm
Carrier Signal: cos(2 ) DC:c Cf t A
Modulated Signal: ( ) [ cos(2 )]cos(2 )
[1 cos(2 )]cos(2 )
AM c m m c
c m c
S t A A f t f t
A k f t f t
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For a sinusoidal message signal
Modulation Index is defined as:
Modulation index k is a measure of the extent to
which a carrier voltage is varied by the modulating
signal. When k=0 no modulation, when k=1 100%
modulation, when k>1 over modulation.
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High Percentage Modulation
• It is important to use as high percentage of modulation as
possible (k=1) while ensuring that over modulation (k>1)
does not occur.
• The sidebands contain the information and have maximum
power at 100% modulation.
• Useful equation
Pt = Pc(1 + k2/2)
Pt =Total transmitted power (sidebands and carrier)
Pc = Carrier power
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Demodulation of AM Signals
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Demodulation extracting the baseband message from
the carrier.
•There are 2 main methods of AM Demodulation:
• Envelope or non-coherent detection or demodulation.
• Synchronised or coherent demodulation.
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Envelope/Diode AM Detector
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If the modulation depth is > 1, the distortion below occurs
K>1
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Synchronous or Coherent
Demodulation
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This is relatively more complex and more expensive. The Local
Oscillator (LO) must be synchronised or coherent, i.e. at the same
frequency and in phase with the carrier in the AM input signal.
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Demodulation
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If the AM input contains carrier frequency, the LO or synchronous
carrier may be derived from the AM input.
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Demodulation
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If we assume zero path delay between the modulator and
demodulator, then the ideal LO signal is cos( ct).
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Unit-3
Angle Modulation
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Angle Modulation
• Introduction
• Types of Angle Modulation – FM & PM
• Definition – FM & PM
• Signal Representation of FM & PM
• Generation of PM using FM
• Generation of FM using PM
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Angle Modulation
Consider again the general carrier cccc φ+tωV=tv cos
cc φ+tω represents the angle of the carrier.
There are two ways of varying the angle of the carrier.
a) By varying the frequency, c – Frequency Modulation.
b)By varying the phase, c – Phase Modulation
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Phase Modulation
• One of the properties of a sinusoidal wave is its phase, the
offset from a reference time at which the sine wave begins.
• We use the term phase shift to characterize such changes.
• If phase changes after cycle k, the next sinusoidal wave will
start slightly later than the time at which cycle k completes.
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Introduction to Angle Modulation
• High degree of noise immunity by bandwidth
expansion.
• They are widely used in high-fidelity music
broadcasting.
• They are of constant envelope, which is beneficial
when amplified by nonlinear amplifiers.
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Introduction to Angle Modulation
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FM and PM
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Types of FM
• Basically 2 types of FM:
– NBFM (Narrow Band Frequency Modulation)
– WBFM (Wide Band Frequency Modulation)
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Generation of FM
• Mainly there are 2 methods to generate FM Signal.
They are:
1. Direct Method
1. Hartley Oscillator
2. Basic Reactance Modulator
2. Indirect Method
1. Amstrong Modulator (Using NB Phase Modulator)
2. Frequency Multiplier
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Generation of FM
• Basically two methods:
1. Direct method
• Build a voltage controlled oscillator (VCO) where the
frequency is varied in response to an applied modulating
voltage by using a voltage-variable capacitor
• The main difficulty is that it is very difficult to maintain the
stability of the carrier frequency of the VCO when used to
generate wide-band FM.
2. Indirect method
• Use a narrow-band FM modulator followed by frequency
multiplier and mixer for up conversion.
• Allows to decouple the problem of carrier frequency stability
from the FM modulation.4/26/2014
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Edwin Howard Armstrong
(1890 - †1954)
Edwin Howard Armstrong received his engineering degree in
1913 at the Columbia University.
He was the inventor of the following basic electronic circuits
underlying all modern radio, radar, and television:
 Regenerative Circuit (1912)
 Superheterodyne Circuit (1918)
 Superregenerative Circuit (1922)
 FM System (1933).
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Indirect Method – Amstrong
Modulator
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Indirect Method
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Narrow Band Phase Modulator
(NBPM)
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Detection of FM
• Types of FM Detectors:
1. RL Discriminator
2. Tuned FM Discriminator
3. Balanced Slope Detector
4. Centre Tuned Discriminator / Phase Discriminator /
Foster – Seeley Discriminator
5. Phase Locked Loop (PLL) Demodulator
6. Ratio Detector
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Unit-4
Radio Transmitters and Receiver
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Transmitters and Receivers
• Generalized Transmitters
• AM PM Generation
• Inphase and Quadrature Generation
• Superheterodyne Receiver
• Frequency Division Multiplexing
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Generalized Transmitters
Re cos
cos sin
Where
cj t
c
c c
j t
v t g t e R t t t
v t x t t y t t
g t R t e x t jy t
Any type of modulated signal can be represented by
The complex envelope g(t) is a function of the
modulating signal m(t)
Transmitter
Modulating
signal
Modulated
signal
Example:
( )
Type of Modulation g(m)
AM : [1 ( )]
PM : p
c
jD m t
c
A m t
A e
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R(t) and θ(t) are functions of the modulating signal m(t) as
given in TABLE 4.1
• Two canonical forms for the generalized transmitter:
cos cv t R t t t
1. AM- PM Generation Technique: Envelope and phase functions are
generated to modulate the carrier as
Generalized transmitter using the AM–PM generation technique.
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x(t) and y(t) are functions of the modulating signal m(t) as
given in TABLE 4.1
ttyttxtv cc sincos
2. Quadrature Generation Technique: Inphase and quadrature signals are generated to
modulate the carrier as
Fig. 4–28 Generalized transmitter using the quadrature generation technique.
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IQ (In-phase and Quadrature-phase) Detector
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Generalized Receivers
Receivers
Tuned Radio Frequency (TRF) Receiver:
Composed of RF amplifiers and detectors.
No frequency conversion
It is not often used.
Difficult to design tunable RF stages.
Difficult to obtain high gain RF amplifiers
Superheterodyne Receiver:
Downconvert RF signal to lower IF frequency
Main amplifixcation takes place at IF
 Two types of receivers:
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Tuned Radio Frequency (TRF) Receivers
Active
Tuning
Circuit
Detector
Circuit
Local
Oscillator
Bandpass
Filter
Baseband
Audio Amp
 Composed of RF amplifiers and detectors.
 No frequency conversion. It is not often used.
 Difficult to design tunable RF stages.
 Difficult to obtain high gain RF amplifiers
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Heterodyning
(Upconversion/
Downconversion)
Subsequent
Processing
(common)
All
Incoming
Frequencies
Fixed
Intermediate
Frequency
Heterodyning
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Superheterodyne Receivers
Superheterodyne Receiver Diagram4/26/2014
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Superheterodyne Receiver
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 The RF and IF frequency responses H1(f) and H2(f) are important in providing
the required reception characteristics.
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fI
F
fI
F
RF
Response
IF
Response
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Frequencies
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Frequencies
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Frequency Conversion Process
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Image frequency not a problem.
Image Frequencies
Image frequency is also received
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AM Radio Receiver
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Superheterodyne Receiver Typical
Signal Levels
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Double-conversion block diagram.
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Unit-5
Noise
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Tiwari
Noise is the Undesirable portion of an
electrical signal that interferes
with the intelligence
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Why is it important to study the effects of Noise?
a) Today’s telecom networks handle enormous volume of data
b) The switching equipment needs to handle high traffic volumes as well
c) our ability to recover the required data without error is inversely
proportional to the magnitude of noise
What steps are taken to minimize the effects of noise?
a) Special encoding and decoding techniques used to optimize the recovery of
the signal
b) Transmission medium is chosen based on the bandwidth, end to end
reliability requirements, anticipated surrounding noise levels and the
distance to destination
c) Elaborate error detection and correction mechanisms utilized in the
communications systems
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Tiwari
The decibel (abbreviated dB) is the unit used to measure the
intensity of a sound.! The smallest audible sound (near total
silence) is 0 dB. A sound 10 times more powerful is 10 dB. A
sound 1,000 times more powerful than near total silence is 30
dB.
Here are some common sounds and their decibel ratings:
Normal conversation - 60 dB
A rock concert - 120 dB
It takes approximate 4 hours of exposure to a 120-dB sound to
cause damage to your ears, however 140-dB sound can result in
an immediate damage
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Tiwari
Signal to Noise ratio
It is a ratio of signal power to Noise power at some
point in a Telecom system expressed in decibels (dB)
It is typically measured at the receiving end of the
communications system BEFORE the detection of signal.
SNR = 10 Log (Signal power/ Noise power) dB
SNR = 10 Log (Vs/VN)2 = 20 Log (Vs/VN)
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Tiwari
1) The noise power at the output of receiver’s IF stage is measured at 45
µW. With receiver tuned to test signal, output power increases to 3.58
mW. Compute the SNR
SNR = 10 Log (Signal power/ Noise power) dB
= 10 Log (3.58 mW/ 45 µW) = 19 dB
2) A 1 kHZ test tone measured with an oscilloscope at the
input of receiver’s FM detector stage. Its peak to peak
voltage is 3V. With test tone at transmitter turned off, the
noise at same test point is measure with an rms voltmeter. Its
value is 640 mV. Compute SNR in dB.
SNR = 20 Log (Vs/Vn) = 20 Log ((.707 x Vp-p/2)/Vn)
= 20 Log (1.06V/640 mV)
= 4.39 dB
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Noise Factor (F)
It is a measure of How Noisy A Device Is
Noise figure (NF) = Noise factor expressed in dB
F = (Si/Ni) / (So/No)
NF = 10 Log F
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Tiwari
Noise Types
• Atmospheric and Extraterrestrial
noise
• Gaussian Noise
• Crosstalk
• Impulse Noise
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Tiwari
Atmospheric and Extraterrestrial Noise
• Lightning: The static discharge generates a
wide range of frequencies
• Solar Noise: Ionised gases of SUN produce a
wide range of frequencies as well.
• Cosmic Noise: Distant stars radiate intense
level of noise at frequencies that penetrate
the earth’s atmosphere.
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Tiwari
Gaussian Noise: The cumulative effect of all random
noise generated over a period of time (it includes all
frequencies).
Thermal Noise: generated by random motion of free
electrons and molecular vibrations in resistive
components. The power associated with thermal
noise is proportional to both temperature and
bandwidth
Pn = K x T x BW
K = Boltzmann’s constant 1.38x10 -23
T = Absolute temperature of device
BW = Circuit bandwidth
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Tiwari
Shot Noise
Results from the random arrival rate of discrete current carriers
at
the output electrodes of semiconductor and vaccum tube devices.
Noise current associated with shot noise can be computed as
In = √ 2qIf
In = Shot noise current in rms
q = charge of an electron
I = DC current flowing through the device
f = system bandwidth (Hz)
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Tiwari
Crosstalk:
electrical noise or interference caused by inductive and capacitive
coupling of signals from adjacent channels
In LANs, the crosstalk noise has greater effect on system
Performance than any other types of noise
Problem remedied by using UTP or STP. By twisting the cable
pairs together, the EMF surrounding the wires cancel out each
other.
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Tiwari
Near end crosstalk: Occurs at transmitting station when
strong signals radiating from transmitting pair of wires are coupled
in to adjacent weak signals traveling in opposite direction
Far end crosstalk: Occurs at the far end receiver as a result of
adjacent signals traveling in the same direction
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Tiwari
Minimizing crosstalk in telecom systems
1) Using twisted pair of wires
2) Use of shielding to prevent signals from radiating in to other conductors
3) Transmitted and received signals over long distance are physically separated
and shielded
4) Differential amplifiers and receivers are used to reject common-mode signals
5) Balanced transformers are used with twisted pair media to cancel crosstalk
signals coupled equally in both lines
6) Maximum channels used within a cable are limited to a certain value
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Tiwari
Impulse Noise:
Noise consisting of sudden bursts of irregularly shape
pulses and lasting for a few Microseconds to several
hundred milliseconds.
What causes Impulse noise?
a) Electromechanical switching relays at the C.O.
b) Electrical motors and appliances, ignition systems
c) Lightning
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Noise factor
• IEEE Standards: “The noise factor, at a specified
input frequency, is defined as the ratio of (1) the
total noise power per unit bandwidth available at
the output port when noise temperature of the
input termination is standard (290 K) to (2) that
portion of (1) engendered at the input frequency
by the input termination.”
sourcetoduenoiseoutputavailable
powernoiseoutputavailable
F
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Noise factor (cont.)
• It is a measure of the degradation of SNR due
to the noise added -
• Implies that SNR gets worse as we process the
signal
• Spot noise factor
• The answer is the bandwidth7/1/2013163
i
a
o
o
i
i
oi
iai
NfG
N
S
N
N
S
SN
SNfGN
F
)(
1
))((
1
o
i
SNR
SNR
F
kT
N
F
a
1
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Noise factor (cont.)
• Quantitative measure of receiver
performance wrt noise for a given
bandwidth
• Noise figure
– Typically 8-10 db for modern receivers
• Multistage (cascaded) system
)log(10 FNF
12121
3
1
2
1
1
...
11
n
n
GGG
F
GG
F
G
F
FF

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Thank you
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Ppt of analog communication

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