lecture 6: signals transmission
DESCRIPTION
Signals and Spectral Methods in Geoinformatics. Lecture 6: Signals Transmission. 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 ). - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/1.jpg)
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
![Page 2: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/2.jpg)
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)
![Page 3: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/3.jpg)
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
![Page 4: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/4.jpg)
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
![Page 5: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/5.jpg)
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
![Page 6: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/6.jpg)
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)
![Page 7: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/7.jpg)
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)
![Page 8: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/8.jpg)
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)
![Page 9: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/9.jpg)
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)
![Page 10: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/10.jpg)
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)
![Page 11: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/11.jpg)
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)
![Page 12: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/12.jpg)
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)
![Page 13: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/13.jpg)
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)
![Page 14: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/14.jpg)
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)
![Page 15: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/15.jpg)
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)
![Page 16: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/16.jpg)
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)
![Page 17: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/17.jpg)
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)
![Page 18: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/18.jpg)
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)
![Page 19: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/19.jpg)
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
![Page 20: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/20.jpg)
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
![Page 21: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/21.jpg)
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
![Page 22: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/22.jpg)
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
![Page 23: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/23.jpg)
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
![Page 24: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/24.jpg)
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
![Page 25: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/25.jpg)
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
![Page 26: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/26.jpg)
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
![Page 27: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/27.jpg)
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)
![Page 28: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/28.jpg)
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
)()(
![Page 29: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/29.jpg)
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
![Page 30: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/30.jpg)
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
![Page 31: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/31.jpg)
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
![Page 32: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/32.jpg)
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
![Page 33: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/33.jpg)
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
![Page 34: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/34.jpg)
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
![Page 35: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/35.jpg)
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
![Page 36: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/36.jpg)
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
![Page 37: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/37.jpg)
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
![Page 38: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/38.jpg)
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
![Page 39: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/39.jpg)
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
![Page 40: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/40.jpg)
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
![Page 41: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/41.jpg)
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
![Page 42: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/42.jpg)
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
![Page 43: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/43.jpg)
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
![Page 44: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/44.jpg)
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
![Page 45: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/45.jpg)
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
![Page 46: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/46.jpg)
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
![Page 47: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/47.jpg)
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
![Page 48: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/48.jpg)
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
![Page 49: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/49.jpg)
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
![Page 50: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/50.jpg)
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
![Page 51: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/51.jpg)
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
![Page 52: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/52.jpg)
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
![Page 53: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/53.jpg)
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
![Page 54: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/54.jpg)
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
![Page 55: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/55.jpg)
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
![Page 56: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/56.jpg)
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
![Page 57: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/57.jpg)
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
![Page 58: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/58.jpg)
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
![Page 59: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/59.jpg)
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
![Page 60: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/60.jpg)
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
![Page 61: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/61.jpg)
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
![Page 62: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/62.jpg)
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
![Page 63: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/63.jpg)
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
![Page 64: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/64.jpg)
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
![Page 65: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/65.jpg)
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
![Page 66: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/66.jpg)
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
![Page 67: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/67.jpg)
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
![Page 68: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/68.jpg)
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
![Page 69: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/69.jpg)
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
![Page 70: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/70.jpg)
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)()(
![Page 71: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/71.jpg)
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
![Page 72: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/72.jpg)
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
![Page 73: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/73.jpg)
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
![Page 74: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/74.jpg)
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
![Page 75: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/75.jpg)
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 )
![Page 76: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/76.jpg)
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
![Page 77: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/77.jpg)
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
![Page 78: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/78.jpg)
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
![Page 79: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/79.jpg)
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
![Page 80: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/80.jpg)
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
![Page 81: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/81.jpg)
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
![Page 82: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/82.jpg)
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
![Page 83: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/83.jpg)
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
![Page 84: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/84.jpg)
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
![Page 85: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/85.jpg)
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
![Page 86: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/86.jpg)
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
![Page 87: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/87.jpg)
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
![Page 88: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/88.jpg)
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
![Page 89: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/89.jpg)
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
![Page 90: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/90.jpg)
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
![Page 91: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/91.jpg)
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
![Page 92: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/92.jpg)
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
![Page 93: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/93.jpg)
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
![Page 94: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/94.jpg)
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
![Page 95: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/95.jpg)
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
![Page 96: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/96.jpg)
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
![Page 97: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/97.jpg)
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 )
![Page 98: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/98.jpg)
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 )
![Page 99: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/99.jpg)
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 )
![Page 100: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/100.jpg)
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
![Page 101: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/101.jpg)
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
![Page 102: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/102.jpg)
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)
![Page 103: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/103.jpg)
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)
![Page 104: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/104.jpg)
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)
![Page 105: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/105.jpg)
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 )
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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
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
![Page 107: Lecture 6: Signals Transmission](https://reader035.vdocuments.us/reader035/viewer/2022062314/568141e1550346895dadbdad/html5/thumbnails/107.jpg)
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