Post on 10-Jan-2016
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Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Lecture 6:Signals Transmission
Signals and Spectral Methodsin Geoinformatics
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Signal transmission
1 MODULATION : Placing the signal on a monochromatic signal (carrier frequency)
2 TRANSMISSION
3 RECEPTION
4 DEMODULATION : Signal recovery (removal of carrier frequency)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) : )cos()()( 0 ttatx CC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) : )cos()()( 0 ttatx CC
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
)()( tmkt p
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
)()( tmkt p )](cos[)( 0 tmktatx pCCCC
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
)()( tmkt p )](cos[)( 0 tmktatx pCCCC
)()()( tmktdt
dt f
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
)()( tmkt p )](cos[)( 0 tmktatx pCCCC
)()()( tmktdt
dt f
])()(cos[)(
0
0 t
tfC dttmktttx
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
modulation
Modulation = placement of signal m(t) on a monochromatic signal xC(t) = aC cos(φ0C+ωCt) with carrier frequency ωC
Α. Amplitude modulation (general form) :
Β. Angle modulation (general form) :
)cos()()( 0 ttatx CC
)](cos[)( 0 ttatx CCC
Α. AM = Amplitude Modulation :
)()( tmkAta a )cos()]([)( 0 ttmkAtx CCa
Β. Angle modulation
Β1. PM = Phase Modulation :
Β2. FM = Frequency Modulation :
)()( tmkt p )](cos[)( 0 tmktatx pCCCC
)()()( tmktdt
dt f
])()(cos[)(
0
0 t
tfC dttmktttx
)(t
m(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Example: Modulation of a sinusoidal signal m(t) = cosωt
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
Example: Modulation of a sinusoidal signal m(t) = cosωt
)(tm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
carrier frequency
Example: Modulation of a sinusoidal signal m(t) = cosωt
)(tm
)cos( tC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
carrier frequency
amplitude modulation
Example: Modulation of a sinusoidal signal m(t) = cosωt
)cos()]([)( ttmkAtx Ca
)(tm
)cos( tC
AM
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
carrier frequency
amplitude modulation
phase modulation
Example: Modulation of a sinusoidal signal m(t) = cosωt
)cos()]([)( ttmkAtx Ca
])(cos[)( tmkttx fC
)(tm
)cos( tC
AM
PM
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
carrier frequency
amplitude modulation
phase modulation
frequency modulaion
Example: Modulation of a sinusoidal signal m(t) = cosωt
)cos()]([)( ttmkAtx Ca
])(cos[)( tmkttx fC
])(cos[)(0
t
tpC dttmkttx
)(tm
)cos( tC
AM
PM
FM
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal to be modulated
carrier frequency
amplitude modulation
phase modulation
frequency modulaion
Example: Modulation of a sinusoidal signal m(t) = cosωt
)cos()]([)( ttmkAtx Ca
])(cos[)( tmkttx fC
dt
d
])(cos[)(0
t
tpC dttmkttx
dt
)(tm
)cos( tC
AM
PM
FM
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)(tm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)(tm
)(tmA A
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)(tm
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)cos()()cos()cos()]([)( ttmtAttmAtx CCC
)(tm
)(tmA
)(tx
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)cos()()cos()cos()]([)( ttmtAttmAtx CCC
)()()(2
1)(
2
1)( CCCC AAMMX
)(tm
)(tmA
)(tx
)(X
A02
1 M
CC 0
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)cos()()cos()cos()]([)( ttmtAttmAtx CCC
)()()(2
1)(
2
1)( CCCC AAMMX
Properties used :
)(2)(21 AA
)(tm
)(tmA
)(tx
)(X
A02
1 M
CC 0
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)cos()()cos()cos()]([)( ttmtAttmAtx CCC
)()()(2
1)(
2
1)( CCCC AAMMX
Properties used :
)(2)(21 AA
Modulation theorem
)]()([2
1cos)(
)()(
000
ZZtz
Ztz
)(tm
)(tmA
)(tx
)(X
A02
1 M
CC 0
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
demodulation
Demodulation = separation of main signal m(t) from the received modulated signal x(t)
Spectrum of signal m(t) = Fourier transform : dtetmM ti
)()(
)cos()()cos()cos()]([)( ttmtAttmAtx CCC
)()()(2
1)(
2
1)( CCCC AAMMX
Properties used :
)(2)(21 AA
Modulation theorem
)]()([2
1cos)(
)()(
000
ZZtz
Ztz
from which follows
)()()cos( CCC AAtA
)(2
1)(
2
1)cos()( CCC MMttm
)(tm
)(tmA
)(tx
)(X
A02
1 M
CC 0
)(tmA A)(M0M
A2
mm 0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
)(2
1)2(
2
1)(
2
1)(
2
1)( MMMMX CCCCCCω ωωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
)(2
1)2(
2
1)(
2
1)(
2
1)( MMMMX CCCCCC
)2(2
1)(
2
1)(
2
1)(
2
1)( CCCCCC MMMMX ω ω+ωC
ω ωωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
)(2
1)2(
2
1)(
2
1)(
2
1)( MMMMX CCCCCC
)2(2
1)(
2
1)(
2
1)(
2
1)( CCCCCC MMMMX
)2(
2
1)(
2
1
2
1)(
2
1)2(
2
1
2
1)( CC MMMMD
ω ω+ωC
ω ωωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
)(2
1)2(
2
1)(
2
1)(
2
1)( MMMMX CCCCCC
)2(2
1)(
2
1)(
2
1)(
2
1)( CCCCCC MMMMX
)2(
2
1)(
2
1
2
1)(
2
1)2(
2
1
2
1)( CC MMMMD
)2(4
1)(
2
1)2(
4
1)( CC MMMD
ω ω+ωC
ω ωωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
)(2
1)(
2
1)()cos()()( CCC MMXttmtx
Demodulation = multiplication again with the carrier frequency cosωC t + low pass filter
Modulation = multiplication of the signal m(t) with the carrier frequency cosωC t
)(cos)()()cos()()( 2 ttxtmttxtd CC )(2
1)(
2
1)( CC XXD
)(2
1)(
2
1)( CC MMX
)(2
1)2(
2
1)(
2
1)(
2
1)( MMMMX CCCCCC
)2(2
1)(
2
1)(
2
1)(
2
1)( CCCCCC MMMMX
)2(
2
1)(
2
1
2
1)(
2
1)2(
2
1
2
1)( CC MMMMD
)2(4
1)(
2
1)2(
4
1)( CC MMMD
After the low pass filter remains : )(2
1)(
2
1tmM
ω ω+ωC
ω ωωC
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
| M(ω) | Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
modulated signal
MODULATION
| M(ω) |
| Χ(ω) |
ωCωC
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
modulated signalTRANSMISSION - RECEPTION
MODULATION
| M(ω) |
| Χ(ω) |
ωCωC
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
modulated signalTRANSMISSION - RECEPTION
MODULATION
DEMODULATION
Multiplication with carrier frequency
| M(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
modulated signalTRANSMISSION - RECEPTION
MODULATION
DEMODULATION
Multiplication with carrier frequency
Application of low pass filter
| H(ω) |
| M(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
original signal
modulated signalTRANSMISSION - RECEPTION
MODULATION
DEMODULATION
Multiplication with carrier frequency
Application of low pass filter
| H(ω) |
½ | M(ω) |
| M(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| M(ω) | Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
| M(ω) |
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
| M(ω) |
| H(ω) || Χ(ω) |
ωCωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
modulated signal
| M(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
Demodulation = multiplication with cosωCt+ low pass filter
modulated signal
| M(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
Demodulation = multiplication with cosωCt+ low pass filter
modulated signal
| M(ω) |
| H(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Modulation = multiplication with cosωCt+ high pass filter
Demodulation = multiplication with cosωCt+ low pass filter
modulated signal
demodulated signal
| M(ω) |
¼| M(ω) |
| H(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
Double Band demodulation- preservation of outer parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Double Band demodulation- preservation of inner parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| M(ω) | Double Band demodulation- preservation of inner parts
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| M(ω) |
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| H(ω) |
| M(ω) |
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| H(ω) |
| M(ω) |
| Χ(ω) |
ωCωC
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
modulated signal
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| H(ω) |
| M(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
Demodulation = multiplication with cosωCt+ high pass filter
modulated signal
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| H(ω) |
| M(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
| Χ(ω) |
ωCωC
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
Demodulation = multiplication with cosωCt+ high pass filter
modulated signal
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
| H(ω) |
| M(ω) |
| H(ω) |
| Χ(ω) |
ωCωC
| D(ω) |
2ωC2ωC
| Χ(ω) |
ωCωC
¼| M(ω) |
Double Band demodulation- preservation of inner parts
Modulation = multiplication with cosωCt+ low pass filter
Demodulation = multiplication with cosωCt+ high pass filter
modulated signal
demodulated signal
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
| M(ω) |
ωmωm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
| M(ω) |
ωmωm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
ωCωC
| Χ(ω) || M(ω) |
ωmωm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
ωCωC
| Χ(ω) || M(ω) |
ωmωm
ωC ωmωC ωm ωC ωmωC ωm
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
THEREFORE: Possibility of simultaneous moduletion of more signalsas long as there spectra do not overlap !
Separation with band pass filters + (usual) demodulation
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
THEREFORE: Possibility of simultaneous moduletion of more signalsas long as there spectra do not overlap !
Separation with band pass filters + (usual) demodulation
Signals to be transmitted : )(,),(),( 21 tmtmtm n
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
THEREFORE: Possibility of simultaneous moduletion of more signalsas long as there spectra do not overlap !
Separation with band pass filters + (usual) demodulation
Signals to be transmitted :
Corresponding carrier frequencyes :
)(,),(),( 21 tmtmtm n
n ,,, 21
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
THEREFORE: Possibility of simultaneous moduletion of more signalsas long as there spectra do not overlap !
Separation with band pass filters + (usual) demodulation
Signals to be transmitted :
Corresponding carrier frequencyes :
Modulated signals :
)(,),(),( 21 tmtmtm n
n ,,, 21
)cos()(,),cos()(),cos()( 2211 ttmttmttm nn
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
band limited signals :
m
mmMtm||0
0)()(
(spectrum concentrated in a band 2ωm wide centered at zero)
Modulation : 0)()cos()()( Xttmtx C mCmC
mCmC
για
και
(spectrum concentrated in two bands 2ωm wide centered at –ωC and ωC )
THEREFORE: Possibility of simultaneous moduletion of more signalsas long as there spectra do not overlap !
Separation with band pass filters + (usual) demodulation
Signals to be transmitted :
Corresponding carrier frequencyes :
Modulated signals :
Multiplexing = sum of modulated signals with non overlapping spectra
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(,),(),( 21 tmtmtm n
n ,,, 21
)cos()(,),cos()(),cos()( 2211 ttmttmttm nn
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
)(tx
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
)(tx
)(X
1 1 22 33
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
)(tx
)(X
1 1 22 33
BPF = Band Pass Filter (inside band)
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
)(tx
)(X
1 1 22 33
BPF = Band Pass Filter (inside band)
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)(1 M
)(2 M
)(3 M
)(1 m
)(2 m
)(3 m
~1cos
~2cos
~3cos
)(tx
)(X
1 1 22 33
multiplexing
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(2
1)(
2
1)(
2
1)(
2
1)(
2
1)(
2
1)( 22221111 nnnn MMMMMMX
)(tx
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(2
1)(
2
1)(
2
1)(
2
1)(
2
1)(
2
1)( 22221111 nnnn MMMMMMX
BPF)(tx
BPF
BPF
Application of band pass filter (BPF, inside band) == preservation of a single term :
)cos()()()(2
1)(
2
1)( ttmtxMMX kkkkkkkk
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
~2cos
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(2
1)(
2
1)(
2
1)(
2
1)(
2
1)(
2
1)( 22221111 nnnn MMMMMMX
BPF
~3cos
~1cos
LPF
)(tx
BPF
BPF
LPF
LPF
Application of band pass filter (BPF, inside band) == preservation of a single term :
)cos()()()(2
1)(
2
1)( ttmtxMMX kkkkkkkk
Usual demodulation =
= [ cosωi ] + [ LPF ] =
= retrieval of signal mk(t)
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
~2cos
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(2
1)(
2
1)(
2
1)(
2
1)(
2
1)(
2
1)( 22221111 nnnn MMMMMMX
BPF
~3cos
~1cos
LPF
)(tx
BPF
BPF
LPF
LPF
BPF = Band Pass Filter, inside band
LPF = Low Pass Filter
Application of band pass filter (BPF, inside band) == preservation of a single term :
)cos()()()(2
1)(
2
1)( ttmtxMMX kkkkkkkk
Usual demodulation =
= [ cosωi ] + [ LPF ] =
= retrieval of signal mk(t)
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
~2cos
)cos()()cos()()cos()()( 2211 ttmttmttmtx nn
)(2
1)(
2
1)(
2
1)(
2
1)(
2
1)(
2
1)( 22221111 nnnn MMMMMMX
BPF
)(1 m
)(2 m
)(3 m
~3cos
~1cos
LPF
)(tx
BPF
BPF
LPF
LPF
BPF = Band Pass Filter, inside band
LPF = Low Pass Filter
Application of band pass filter (BPF, inside band) == preservation of a single term :
)cos()()()(2
1)(
2
1)( ttmtxMMX kkkkkkkk
Usual demodulation =
= [ cosωi ] + [ LPF ] =
= retrieval of signal mk(t)
multiplexing – mathematical description
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
2
sin2
sinsin2
sin)( 00 ttattaatx RR
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
signal of frequency f (angular ω) with amplitude which varies periodicallywith frequency Δf angular Δω)
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
2
sin2
sinsin2
sin)( 00 ttattaatx RR
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
2
sin2
sinsin2
sin)( 00 ttattaatx RR
signal of frequency f (angular ω) with amplitude which varies periodically with frequency Δf angular Δω)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
2
sin2
sinsin2
sin)( 00 ttattaatx RR
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
signal of frequency f (angular ω) with amplitude which varies periodically with frequency Δf angular Δω)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
Δf = f fR (angular Δω = ω ωR ) = beat frequency
2
sin2
sinsin2
sin)( 00 ttattaatx RR
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
signal of frequency f (angular ω) with amplitude which varies periodically with frequency Δf angular Δω)
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
heterodyning
Rfff RRfff 222
)sin()sin()2sin()2sin()( 0000 RRRRRR tatatfatfatx
:RΜε
signal of frequency f (angular ω) with amplitude which varies periodically with frequency Δf angular Δω)
Δf = f fR (angular Δω = ω ωR ) = beat frequency
Application: observations in space geodesy utilizing the Doppler phaenomenon (variation of frequency caused by the variation of the receiver-transmitter relative position)
2
sin2
sinsin2
sin)( 00 ttattaatx RR
Heterodyning = Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency fR produced in the receiver ( fR f )
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
Beat frequency :
Δf = f – fR = 1 – 5/6 = 1/6
(TΔf = 6)
T = 1 f = 1
TR = 6/5 fR = 5/6
Δf = f fR = 1/6
TΔf = 6
Example :
Received frequency : f = 1 (T = 1)
Frequency at receiver : fR = 5/6 (T = 6/5)
8
6
4
2
-2
-4
-6
-8
2 4 86 10 12 14 16
2 4 86 10 12 14 16
2 4 86 10 12 14 16
4
2
-2
-4
4
2
-2
-4
0
0
0
Aristotle University of ThessalonikiAristotle University of Thessaloniki – – Department of Geodesy and SurveyingDepartment of Geodesy and Surveying
A. DermanisA. Dermanis Signals and Spectral Methods in GeoinformaticsSignals and Spectral Methods in Geoinformatics
END