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## Lecture 6: Signals Transmission

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**SignalsandSpectral Methods**in Geoinformatics Lecture 6: Signals Transmission**Signaltransmission**1MODULATION :Placing the signal on a monochromatic signal (carrier frequency) 2TRANSMISSION 3RECEPTION 4DEMODULATION:Signal recovery (removal of carrier frequency)**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC Α. Amplitude modulation (general form) :**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) :**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) :**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) :**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**modulation**Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC m(t) Α. Amplitude modulation (general form) : Β. Angle modulation (generalform) : Α. AM = Amplitude Modulation: Β. Angle modulation Β1. PM = Phase Modulation: Β2. FM = Frequency Modulation:**Example: Modulation of a sinusoidal signalm(t) = cosωt**signal to be modulated**Example: Modulation of a sinusoidal signalm(t) = cosωt**signal to be modulated carrier frequency**AM**Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation**AM**PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation**AM**FM PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation frequency modulaion**AM**FM PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation frequency modulaion**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t)**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform : Properties used:**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform : Properties used: Modulation theorem**demodulation**Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform : Properties used: Modulation theorem from which follows**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter ω ω-ωC**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter ω ω-ωC ω ω+ωC**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter ω ω-ωC ω ω+ωC**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter ω ω-ωC ω ω+ωC**Double Band demodulation**Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter ω ω-ωC ω ω+ωC After the low pass filter remains:**|M(ω)|**Double Band demodulation original signal**|Χ(ω)|**-ωC ωC |M(ω)| Double Band demodulation original signal MODULATION modulated signal**|Χ(ω)|**-ωC ωC |M(ω)| Double Band demodulation original signal MODULATION TRANSMISSION - RECEPTION modulated signal**|Χ(ω)|**-ωC ωC |D(ω)| -2ωC 2ωC |M(ω)| Double Band demodulation original signal MODULATION TRANSMISSION - RECEPTION modulated signal DEMODULATION Multiplication with carrier frequency