ppt of analog communication
DESCRIPTION
This ppt will cover the overall syllabus of analog communicationTRANSCRIPT
![Page 1: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/1.jpg)
Unit-1Signal Analysis
04/11/2023prepared 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.)
![Page 2: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/2.jpg)
Content• Periodic Function• Fourier Series• Complex Form of the Fourier Series• Impulse Train• Analysis of Periodic Waveforms• Half-Range Expansion
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 2
![Page 3: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/3.jpg)
Periodic Function
• Any function that satisfies
( ) ( )f t f t T
where T is a constant and is called the period of the function.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 3
![Page 4: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/4.jpg)
Example:
Find its period.4
cos3
cos)(tt
tf
)()( Ttftf )(4
1cos)(
3
1cos
4cos
3cos TtTt
tt
Fact: )2cos(cos m
mT
23
nT
24
mT 6
nT 8
24T smallest T
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 4
![Page 5: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/5.jpg)
Example:
Find its period.tttf 21 coscos)(
) ( ) (T t f t f )(cos)(coscoscos 2121 TtTttt
mT 21
nT 22n
m
2
1
2
1
must be a rational
number
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 5
![Page 6: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/6.jpg)
Example:
Is this function a periodic one?
tttf )10cos(10cos)(
10
10
2
1 not a rational number
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 6
![Page 7: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/7.jpg)
Fourier Series
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 7
![Page 8: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/8.jpg)
Introduction
• Decompose a periodic input signal into primitive periodic components.
A periodic sequenceA periodic sequence
T 2T 3T
t
f(t)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 8
![Page 9: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/9.jpg)
Synthesis
T
ntb
T
nta
atf
nn
nn
2sin
2cos
2)(
11
0
DC PartEven Part Odd Part
T is a period of all the above signals
)sin()cos(2
)( 01
01
0 tnbtnaa
tfn
nn
n
Let 0=2/T.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 9
![Page 10: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/10.jpg)
Orthogonal Functions
• Call a set of functions {k} orthogonal on an interval a < t < b if it satisfies
nmr
nmdttt
n
b
a nm
0)()(
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 10
![Page 11: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/11.jpg)
Orthogonal set of Sinusoidal Functions
Define 0=2/T.0 ,0)cos(
2/
2/ 0 mdttmT
T0 ,0)sin(
2/
2/ 0 mdttmT
T
nmT
nmdttntm
T
T 2/
0)cos()cos(
2/
2/ 00
nmT
nmdttntm
T
T 2/
0)sin()sin(
2/
2/ 00
nmdttntmT
T and allfor ,0)cos()sin(
2/
2/ 00
We now prove this one
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 11
![Page 12: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/12.jpg)
Proof
dttntmT
T 2/
2/ 00 )cos()cos(
0
)]cos()[cos(2
1coscos
dttnmdttnmT
T
T
T
2/
2/ 0
2/
2/ 0 ])cos[(2
1])cos[(
2
1
2/
2/00
2/
2/00
])sin[()(
1
2
1])sin[(
)(
1
2
1 T
T
T
Ttnm
nmtnm
nm
m n
])sin[(2)(
1
2
1])sin[(2
)(
1
2
1
00
nmnm
nmnm
00
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 12
![Page 13: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/13.jpg)
Proof
dttntmT
T 2/
2/ 00 )cos()cos(
0
)]cos()[cos(2
1coscos
dttmT
T 2/
2/ 02 )(cos
2/
2/
00
2/
2/
]2sin4
1
2
1T
T
T
T
tmm
t
m = n
2
T
]2cos1[2
1cos2
dttmT
T 2/
2/ 0 ]2cos1[2
1
nmT
nmdttntm
T
T 2/
0)cos()cos(
2/
2/ 00
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 13
![Page 14: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/14.jpg)
Proof
dttntmT
T 2/
2/ 00 )cos()cos(
0
)]cos()[cos(2
1coscos
dttmT
T 2/
2/ 02 )(cos
2/
2/
00
2/
2/
]2sin4
1
2
1T
T
T
T
tmm
t
m = n
2
T
]2cos1[2
1cos2
dttmT
T 2/
2/ 0 ]2cos1[2
1
nmT
nmdttntm
T
T 2/
0)cos()cos(
2/
2/ 00
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 14
![Page 15: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/15.jpg)
Orthogonal set of Sinusoidal Functions
Define 0=2/T.
0 ,0)cos(2/
2/ 0 mdttmT
T0 ,0)sin(
2/
2/ 0 mdttmT
T
nmT
nmdttntm
T
T 2/
0)cos()cos(
2/
2/ 00
nmT
nmdttntm
T
T 2/
0)sin()sin(
2/
2/ 00
nmdttntmT
T and allfor ,0)cos()sin(
2/
2/ 00 04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
15
![Page 16: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/16.jpg)
Decomposition
dttfT
aTt
t
0
0
)(2
0
,2,1 cos)(2
0
0
0
ntdtntfT
aTt
tn
,2,1 sin)(2
0
0
0
ntdtntfT
bTt
tn
)sin()cos(2
)( 01
01
0 tnbtnaa
tfn
nn
n
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 16
![Page 17: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/17.jpg)
ProofUse the following facts:
0 ,0)cos(2/
2/ 0 mdttmT
T0 ,0)sin(
2/
2/ 0 mdttmT
T
nmT
nmdttntm
T
T 2/
0)cos()cos(
2/
2/ 00
nmT
nmdttntm
T
T 2/
0)sin()sin(
2/
2/ 00
nmdttntmT
T and allfor ,0)cos()sin(
2/
2/ 00
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 17
![Page 18: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/18.jpg)
Example (Square Wave)
112
200
dta
,2,1 0sin1
cos2
200
nntn
ntdtan
,6,4,20
,5,3,1/2)1cos(
1 cos
1sin
2
200
n
nnn
nnt
nntdtbn
2 3 4 5--2-3-4-5-6
f(t)1
ttttf 5sin
5
13sin
3
1sin
2
2
1)(
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 18
![Page 19: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/19.jpg)
Harmonics
T
ntb
T
nta
atf
nn
nn
2sin
2cos
2)(
11
0
DC PartEven Part Odd Part
T is a period of all the above signals
)sin()cos(2
)( 01
01
0 tnbtnaa
tfn
nn
n
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 19
![Page 20: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/20.jpg)
Harmonics
tnbtnaa
tfn
nn
n 01
01
0 sincos2
)(
Tf
22 00Define , called the fundamental angular frequency.
0 nnDefine , called the n-th harmonic of the periodic function.
tbtaa
tf nn
nnn
n
sincos2
)(11
0
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 20
![Page 21: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/21.jpg)
Harmonics
tbtaa
tf nn
nnn
n
sincos2
)(11
0
)sincos(2 1
0 tbtaa
nnnn
n
12222
220 sincos2 n
n
nn
nn
nn
nnn t
ba
bt
ba
aba
a
1
220 sinsincoscos2 n
nnnnnn ttbaa
)cos(1
0 nn
nn tCC
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 21
![Page 22: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/22.jpg)
Amplitudes and Phase Angles
)cos()(1
0 nn
nn tCCtf
20
0
aC
22nnn baC
n
nn a
b1tan
harmonic amplitude phase angle
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 22
![Page 23: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/23.jpg)
Fourier SeriesComplex form of the Fourier Series
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 23
![Page 24: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/24.jpg)
Complex Exponentials
tnjtne tjn00 sincos0
tjntjn eetn 00
2
1cos 0
tnjtne tjn00 sincos0
tjntjntjntjn eej
eej
tn 0000
22
1sin 0
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 24
![Page 25: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/25.jpg)
Complex Form of the Fourier Series
tnbtnaa
tfn
nn
n 01
01
0 sincos2
)(
tjntjn
nn
tjntjn
nn eeb
jeea
a0000
11
0
22
1
2
1
0 00 )(2
1)(
2
1
2 n
tjnnn
tjnnn ejbaejba
a
1
000
n
tjnn
tjnn ececc
)(2
1
)(2
12
00
nnn
nnn
jbac
jbac
ac
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 25
![Page 26: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/26.jpg)
Complex Form of the Fourier Series
1
000)(
n
tjnn
tjnn ececctf
1
10
00
n
tjnn
n
tjnn ececc
n
tjnnec 0
)(2
1
)(2
12
00
nnn
nnn
jbac
jbac
ac
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 26
![Page 27: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/27.jpg)
Complex Form of the Fourier Series
2/
2/
00 )(
1
2
T
Tdttf
T
ac
)(2
1nnn jbac
2/
2/ 0
2/
2/ 0 sin)(cos)(1 T
T
T
Ttdtntfjtdtntf
T
2/
2/ 00 )sin)(cos(1 T
Tdttnjtntf
T
2/
2/
0)(1 T
T
tjn dtetfT
2/
2/
0)(1
)(2
1 T
T
tjnnnn dtetf
Tjbac )(
2
1
)(2
12
00
nnn
nnn
jbac
jbac
ac
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 27
![Page 28: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/28.jpg)
Complex Form of the Fourier Series
n
tjnnectf 0)(
dtetfT
cT
T
tjnn
2/
2/
0)(1 )(
2
1
)(2
12
00
nnn
nnn
jbac
jbac
ac
If f(t) is real, *
nn cc
nn jnnn
jnn ecccecc
|| ,|| *
22
2
1|||| nnnn bacc
n
nn a
b1tan
,3,2,1 n
00 2
1ac
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 28
![Page 29: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/29.jpg)
Complex Frequency Spectra
nn jnnn
jnn ecccecc
|| ,|| *
22
2
1|||| nnnn bacc
n
nn a
b1tan ,3,2,1 n
00 2
1ac |cn|
amplitudespectrum
n
phasespectrum
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 29
![Page 30: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/30.jpg)
Example
2
T
2
T TT
2
d
t
f(t)A
2
d
dteT
Ac
d
d
tjnn
2/
2/
0
2/
2/0
01
d
d
tjnejnT
A
2/
0
2/
0
0011 djndjn ejn
ejnT
A
)2/sin2(1
00
dnjjnT
A
2/sin1
002
1dn
nT
A
TdnT
dn
T
Adsin
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 30
![Page 31: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/31.jpg)
TdnT
dn
T
Adcn
sin
82
5
1
T ,
4
1 ,
20
1
0
T
dTd
Example
40 80 120-40 0-120 -80
A/5
50 100 150-50-100-150
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 31
![Page 32: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/32.jpg)
TdnT
dn
T
Adcn
sin
42
5
1
T ,
2
1 ,
20
1
0
T
dTd
Example
40 80 120-40 0-120 -80
A/10
100 200 300-100-200-300
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 32
![Page 33: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/33.jpg)
Example
dteT
Ac
d tjnn
0
0
d
tjnejnT
A
00
01
00
110
jne
jnT
A djn
)1(1
0
0
djnejnT
A
2/0
sindjne
TdnT
dn
T
Ad
TT d
t
f(t)
A
0
)(1 2/2/2/
0
000 djndjndjn eeejnT
A
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 33
![Page 34: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/34.jpg)
Fourier SeriesImpulse Train
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 34
![Page 35: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/35.jpg)
Dirac Delta Function
0
00)(
t
tt and 1)(
dtt
0 t Also called unit impulse function.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 35
![Page 36: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/36.jpg)
Property
)0()()(
dttt
)0()()0()0()()()(
dttdttdttt
(t): Test Function
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 36
![Page 37: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/37.jpg)
Impulse Train
0 tT 2T 3TT2T3T
n
T nTtt )()(
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 37
![Page 38: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/38.jpg)
Fourier Series of the Impulse Train
n
T nTtt )()(T
dttT
aT
T T
2)(
2 2/
2/0
Tdttnt
Ta
T
T Tn
2)cos()(
2 2/
2/ 0 0)sin()(
2 2/
2/ 0 dttntT
bT
T Tn
n
T tnTT
t 0cos21
)(
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 38
![Page 39: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/39.jpg)
Complex FormFourier Series of the Impulse Train
Tdtt
T
ac
T
T T
1)(
1
2
2/
2/
00
Tdtet
Tc
T
T
tjnTn
1)(
1 2/
2/
0
n
tjnT e
Tt 0
1)(
n
T nTtt )()(
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 39
![Page 40: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/40.jpg)
Fourier SeriesAnalysis of
Periodic Waveforms
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 40
![Page 41: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/41.jpg)
Waveform Symmetry
• Even Functions
• Odd Functions
)()( tftf
)()( tftf 04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
41
![Page 42: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/42.jpg)
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
)]()([)( 21 tftftfe
)]()([)( 21 tftftfo
Even Part
Odd Part
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 42
![Page 43: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/43.jpg)
Example
00
0)(
t
tetf
t
Even Part
Odd Part
0
0)(
21
21
te
tetf
t
t
e
0
0)(
21
21
te
tetf
t
t
o
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 43
![Page 44: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/44.jpg)
Half-Wave Symmetry
)()( Ttftf and 2/)( Ttftf
TT/2T/2
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 44
![Page 45: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/45.jpg)
Quarter-Wave Symmetry
Even Quarter-Wave Symmetry
TT/2T/2
Odd Quarter-Wave Symmetry
T
T/2T/2
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 45
![Page 46: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/46.jpg)
Hidden Symmetry
• The following is a asymmetry periodic function:
Adding a constant to get symmetry property.
A
TT
A/2
A/2
TT
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 46
![Page 47: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/47.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 47
![Page 48: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/48.jpg)
Fourier Coefficients of Even Functions
)()( tftf
tnaa
tfn
n 01
0 cos2
)(
2/
0 0 )cos()(4 T
n dttntfT
a
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 48
![Page 49: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/49.jpg)
Fourier Coefficients of Even Functions
)()( tftf
tnbtfn
n 01
sin)(
2/
0 0 )sin()(4 T
n dttntfT
b
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 49
![Page 50: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/50.jpg)
Fourier Coefficients for Half-Wave Symmetry
)()( Ttftf and 2/)( Ttftf
TT/2T/2
The Fourier series contains only odd harmonics.The Fourier series contains only odd harmonics.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 50
![Page 51: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/51.jpg)
Fourier Coefficients for Half-Wave Symmetry
)()( Ttftf and 2/)( Ttftf )sincos()(
100
n
nn tnbtnatf
odd for )cos()(4
even for 02/
0 0 ndttntfT
na T
n
odd for )sin()(4
even for 02/
0 0 ndttntfT
nb T
n
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 51
![Page 52: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/52.jpg)
Fourier Coefficients forEven Quarter-Wave Symmetry
TT/2T/2
])12cos[()( 01
12 tnatfn
n
4/
0 012 ])12cos[()(8 T
n dttntfT
a04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
52
![Page 53: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/53.jpg)
Fourier Transform and ApplicationsBy Njegos Nincic
Fourier04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
53
![Page 54: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/54.jpg)
Overview• Transforms
– Mathematical Introduction• Fourier Transform
– Time-Space Domain and Frequency Domain– Discret Fourier Transform
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 54
![Page 55: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/55.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 55
![Page 56: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/56.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 56
![Page 57: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/57.jpg)
Fourier Transform
• Property of transforms:– They convert a function from one domain to
another with no loss of information• Fourier Transform:
converts a function from the time (or spatial) domain to the frequency domain
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 57
![Page 58: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/58.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 58
![Page 59: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/59.jpg)
Time Domain and Frequency Domain
• Frequency domain:– Tells us how properties (amplitudes) change over
frequencies:
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 59
![Page 60: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/60.jpg)
Time Domain and Frequency Domain• Example:
– Human ears do not hear wave-like oscilations, but constant tone
• Often it is easier to work in the frequency domain
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 60
![Page 61: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/61.jpg)
Time Domain and Frequency Domain
• 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 one04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 61
![Page 62: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/62.jpg)
Time Domain and Frequency Domain
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 62
![Page 63: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/63.jpg)
Fourier Transform
• Because of the property:
• Fourier Transform takes us to the frequency domain:
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 63
![Page 64: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/64.jpg)
Fourier Series
Half-Range Expansions
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 64
![Page 65: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/65.jpg)
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, ).
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 65
![Page 66: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/66.jpg)
Without Considering Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 66
![Page 67: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/67.jpg)
Expansion Into Even Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T=2
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 67
![Page 68: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/68.jpg)
Expansion Into Odd Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T=2
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 68
![Page 69: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/69.jpg)
Expansion Into Half-Wave Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T=2
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 69
![Page 70: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/70.jpg)
Expansion Into Even Quarter-Wave Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T/2=2
T=4
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 70
![Page 71: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/71.jpg)
Expansion Into Odd Quarter-Wave Symmetry
• A non-periodic function f(t) defined over (0, ) can be expanded into a Fourier series which is defined only in the interval (0, ).
T/2=2 T=4
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 71
![Page 72: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/72.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 72
![Page 73: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/73.jpg)
Some Interesting Systems
• Communication system• Control systems• Remote sensing system• Biomedical system(biomedical signal
processing)• Auditory system
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 73
![Page 74: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/74.jpg)
Some Interesting Systems
• Communication system
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 74
![Page 75: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/75.jpg)
Some Interesting Systems
• Control systems
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 75
![Page 76: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/76.jpg)
Some Interesting Systems
Papero04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
76
![Page 77: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/77.jpg)
Some Interesting Systems
• 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.)04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
77
![Page 78: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/78.jpg)
Some Interesting Systems
• Biomedical system(biomedical signal processing)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 78
![Page 79: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/79.jpg)
Some Interesting Systems
• Auditory system
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 79
![Page 80: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/80.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 80
![Page 81: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/81.jpg)
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)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 81
![Page 82: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/82.jpg)
Continuous and Discrete valued singals
• CV corresponds to a continuous y-axis• DV corresponds to a discrete y-axis
Digital signal
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 82
![Page 83: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/83.jpg)
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))
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 83
![Page 84: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/84.jpg)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 84
![Page 85: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/85.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 85
![Page 86: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/86.jpg)
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.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 86
![Page 87: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/87.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 87
![Page 88: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/88.jpg)
Right-handed and left-handed Signals
• Right-handed and left handed-signal : zero between a given variable and positive or negative infinity
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 88
![Page 89: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/89.jpg)
Finite and infinite length
• Finite-length signal : nonzero over a finite interval tmin< t< tmax
• Infinite-length singal : nonzero over all real numbers
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 89
![Page 90: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/90.jpg)
Unit-2Modulation Techniques
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 90
![Page 91: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/91.jpg)
Amplitude Modulation
prepared by Arun Kumar & Shivendra Tiwari 04/11/2023 91
![Page 92: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/92.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Content
• What is Modulation• Amplitude Modulation (AM)• Demodulation of AM signals
04/11/2023 92
![Page 93: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/93.jpg)
prepared by Arun Kumar & Shivendra Tiwari
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
04/11/2023 93
![Page 94: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/94.jpg)
prepared by Arun Kumar & Shivendra Tiwari
About Modulation
• Application Examples– broadcasting of both audio and
video signals. – Mobile radio communications, such
as cell phone.
• Basic Modulation Types– Amplitude Modulation: changes the amplitude.– Frequency Modulation: changes the frequency.– Phase Modulation: changes the phase.
04/11/2023 94
![Page 95: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/95.jpg)
04/11/2023 prepared by Arun Kumar & Shivendra Tiwari
95
AM Modulation/Demodulation
Modulator Demodulator
Baseband Signalwith frequency
fm(Modulating Signal)
Bandpass Signalwith frequency
fc(Modulated Signal)
Channel
Original Signalwith frequency
fm
Source Sink
fc >> fm Voice: 300-3400Hz GSM Cell phone: 900/1800MHz
![Page 96: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/96.jpg)
04/11/2023 prepared by Arun Kumar & Shivendra Tiwari
96
Amplitude Modulation
• 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
![Page 97: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/97.jpg)
prepared by Arun Kumar & Shivendra Tiwari
* AM Signal Math Expression*• Mathematical expression for AM: time domain
• expanding this produces:
• In the frequency domain this gives:
( ) (1 cos )cosAM m cS t k t t
( ) cos cos cosc cAM mS t t k t t
)cos()cos(coscos :using 21 BABABA
2 2( ) cos cos( ) cos( )c c ck k
AM m mS t t t t
frequency
k/2k/2Carrier, A=1.
upper sideband
lower sideband
Amplitude
fcfc-fm fc+fm
04/11/2023 97
![Page 98: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/98.jpg)
prepared by Arun Kumar & Shivendra Tiwari
AM Power Frequency Spectrum
• AM Power frequency spectrum obtained by squaring the amplitude:
• Total power for AM:
.
2 22
2
4 4
12
k kA
k
freq
k2/4k2/4
Carrier, A2=12 = 1Power
fcfc-fm fc+fm
04/11/2023 98
![Page 99: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/99.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Amplitude Modulation
• 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).
04/11/2023 99
![Page 100: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/100.jpg)
prepared by Arun Kumar & Shivendra Tiwari
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.
frequency
1.4 MHz
1,385,000Hz to 1,399,980Hz
1,400,020Hz to 1,415,000Hz
fc
04/11/2023 100
![Page 101: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/101.jpg)
04/11/2023 prepared by Arun Kumar & Shivendra Tiwari
101
Modulation Index of AM Signal
m
c
Ak
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
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.
![Page 102: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/102.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Modulation Index of AM Signal
04/11/2023 102
![Page 103: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/103.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Modulation Index of AM Signal
04/11/2023 103
![Page 104: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/104.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Modulation Index of AM Signal
04/11/2023 104
![Page 105: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/105.jpg)
prepared by Arun Kumar & Shivendra Tiwari
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
04/11/2023 105
![Page 106: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/106.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Demodulation of AM Signals
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.
04/11/2023 106
![Page 107: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/107.jpg)
04/11/2023 prepared by Arun Kumar & Shivendra Tiwari
107
Envelope/Diode AM Detector
If the modulation depth is > 1, the distortion below occurs
K>1
![Page 108: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/108.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Synchronous or Coherent Demodulation
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.
04/11/2023 108
![Page 109: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/109.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Synchronous or Coherent Demodulation
If the AM input contains carrier frequency, the LO or synchronous carrier may be derived from the AM input.
04/11/2023 109
![Page 110: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/110.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Synchronous or Coherent Demodulation
If we assume zero path delay between the modulator and demodulator, then the ideal LO signal is cos(ct).
04/11/2023 110
![Page 111: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/111.jpg)
Unit-3Angle Modulation
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 111
![Page 112: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/112.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 112
![Page 113: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/113.jpg)
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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 113
![Page 114: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/114.jpg)
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.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 114
![Page 115: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/115.jpg)
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.04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
115
![Page 116: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/116.jpg)
Introduction to Angle Modulation
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 116
![Page 117: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/117.jpg)
FM and PM
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 117
![Page 118: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/118.jpg)
Types of FM
• Basically 2 types of FM:
– NBFM (Narrow Band Frequency Modulation)
– WBFM (Wide Band Frequency Modulation)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 118
![Page 119: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/119.jpg)
Generation of FM• Mainly there are 2 methods to generate FM Signal.
They are:
1. Direct Method1. Hartley Oscillator2. Basic Reactance Modulator
2. Indirect Method1. Amstrong Modulator (Using NB Phase Modulator)2. Frequency Multiplier
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 119
![Page 120: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/120.jpg)
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.04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
120
![Page 121: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/121.jpg)
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).
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 121
![Page 122: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/122.jpg)
Indirect Method – Amstrong Modulator
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 122
![Page 123: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/123.jpg)
Indirect Method
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 123
![Page 124: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/124.jpg)
Narrow Band Phase Modulator (NBPM)
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 124
![Page 125: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/125.jpg)
Detection of FM
• Types of FM Detectors:
1. RL Discriminator2. Tuned FM Discriminator3. Balanced Slope Detector4. Centre Tuned Discriminator / Phase Discriminator /
Foster – Seeley Discriminator5. Phase Locked Loop (PLL) Demodulator6. Ratio Detector
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 125
![Page 126: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/126.jpg)
Unit-4Radio Transmitters and Receiver
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 126
![Page 127: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/127.jpg)
Transmitters and Receivers• Generalized Transmitters
• AM PM Generation
• Inphase and Quadrature Generation
• Superheterodyne Receiver
• Frequency Division Multiplexing
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 127
![Page 128: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/128.jpg)
Generalized Transmitters
Re cos
cos sin
Where
cj tc
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)
TransmitterModulating
signalModulated
signal
Example:
( )
Type of Modulation g(m)
AM : [1 ( )]
PM : p
c
jD m t
c
A m t
A e
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 128
![Page 129: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/129.jpg)
Generalized Transmitters
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.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 129
![Page 130: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/130.jpg)
Generalized Transmitters
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.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 130
![Page 131: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/131.jpg)
IQ (In-phase and Quadrature-phase) Detector
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 131
![Page 132: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/132.jpg)
Generalized Receivers
Receivers
Tuned Radio Frequency (TRF) Receiver:Composed of RF amplifiers and detectors. No frequency conversionIt 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 frequencyMain amplifixcation takes place at IF
Two types of receivers:
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 132
![Page 133: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/133.jpg)
Tuned Radio Frequency (TRF) Receivers
ActiveTuningCircuit
DetectorCircuit
LocalOscillator
BandpassFilter
BasebandAudio 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
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 133
![Page 134: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/134.jpg)
Heterodyning(Upconversion/Downconversion)
SubsequentProcessing(common)
AllIncomingFrequencies
FixedIntermediateFrequency
Heterodyning
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 134
![Page 135: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/135.jpg)
Superheterodyne Receivers
Superheterodyne Receiver Diagram04/11/2023prepared by Arun Kumar & Shivendra
Tiwari
135
![Page 136: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/136.jpg)
Superheterodyne Receiver
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 136
![Page 137: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/137.jpg)
Superheterodyne Receivers The RF and IF frequency responses H1(f) and H2(f) are important in providing
the required reception characteristics.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 137
![Page 138: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/138.jpg)
Superheterodyne Receivers
fI
F
fIF
RF Response
IF Response
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 138
![Page 139: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/139.jpg)
Superheterodyne Receivers
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 139
![Page 140: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/140.jpg)
Superheterodyne Receiver Frequencies
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 140
![Page 141: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/141.jpg)
Superheterodyne Receiver Frequencies
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 141
![Page 142: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/142.jpg)
Frequency Conversion Process
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 142
![Page 143: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/143.jpg)
Image frequency not a problem.
Image Frequencies
Image frequency is also received
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 143
![Page 144: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/144.jpg)
AM Radio Receiver
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 144
![Page 145: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/145.jpg)
Superheterodyne Receiver Typical Signal Levels
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 145
![Page 146: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/146.jpg)
Double-conversion block diagram.
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 146
![Page 147: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/147.jpg)
Unit-5Noise
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 147
![Page 148: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/148.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Noise is the Undesirable portion of an electrical signal that interferes with the intelligence
04/11/2023 148
![Page 149: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/149.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Why is it important to study the effects of Noise?
a) Today’s telecom networks handle enormous volume of datab) The switching equipment needs to handle high traffic volumes as wellc) 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?
d) 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
04/11/2023 149
![Page 150: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/150.jpg)
prepared by Arun Kumar & Shivendra 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
04/11/2023 150
![Page 151: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/151.jpg)
prepared by Arun Kumar & Shivendra 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)
04/11/2023 151
![Page 152: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/152.jpg)
prepared by Arun Kumar & Shivendra 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
04/11/2023 152
![Page 153: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/153.jpg)
prepared by Arun Kumar & Shivendra Tiwari
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
04/11/2023 153
![Page 154: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/154.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Noise Types
• Atmospheric and Extraterrestrial noise
• Gaussian Noise• Crosstalk• Impulse Noise
04/11/2023 154
![Page 155: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/155.jpg)
prepared by Arun Kumar & Shivendra 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.
04/11/2023 155
![Page 156: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/156.jpg)
prepared by Arun Kumar & Shivendra 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 deviceBW = Circuit bandwidth
04/11/2023 156
![Page 157: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/157.jpg)
prepared by Arun Kumar & Shivendra 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 rmsq = charge of an electronI = DC current flowing through the devicef = system bandwidth (Hz)
04/11/2023 157
![Page 158: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/158.jpg)
prepared by Arun Kumar & Shivendra 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 eachother.
04/11/2023 158
![Page 159: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/159.jpg)
prepared by Arun Kumar & Shivendra 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
04/11/2023 159
![Page 160: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/160.jpg)
prepared by Arun Kumar & Shivendra Tiwari
Minimizing crosstalk in telecom systems
1) Using twisted pair of wires2) Use of shielding to prevent signals from radiating in to other conductors3) Transmitted and received signals over long distance are physically separated and shielded4) Differential amplifiers and receivers are used to reject common-mode signals5) Balanced transformers are used with twisted pair media to cancel crosstalk
signals coupled equally in both lines6) Maximum channels used within a cable are limited to a certain value
04/11/2023 160
![Page 161: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/161.jpg)
prepared by Arun Kumar & Shivendra 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 systemsc) Lightning
04/11/2023 161
![Page 162: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/162.jpg)
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
powernoiseoutputavailableF
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 162
![Page 163: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/163.jpg)
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
SNfGNF
)(1
))((
1o
i
SNR
SNRF
kT
NF
a1
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 163
![Page 164: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/164.jpg)
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
21
1...
11
n
n
GGG
F
GG
F
G
FFF
04/11/2023
prepared by Arun Kumar & Shivendra Tiwari
164
![Page 165: Ppt of analog communication](https://reader036.vdocument.in/reader036/viewer/2022081416/554a2fefb4c90520578b50eb/html5/thumbnails/165.jpg)
Thank you
04/11/2023prepared by Arun Kumar & Shivendra
Tiwari 165