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Lecture 6: Signals Transmission

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 ).

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Lecture 6: Signals Transmission

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  1. SignalsandSpectral Methods in Geoinformatics Lecture 6: Signals Transmission

  2. Signaltransmission 1MODULATION :Placing the signal on a monochromatic signal (carrier frequency) 2TRANSMISSION 3RECEPTION 4DEMODULATION:Signal recovery (removal of carrier frequency)

  3. modulation

  4. modulation Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC

  5. modulation Modulation = placement of signalm(t) on a monochromatic signalxC(t) = aC cos(φ0C+ωCt) with carrier frequencyωC Α. Amplitude modulation (general form) :

  6. 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) :

  7. 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) :

  8. 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) :

  9. 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:

  10. 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:

  11. 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:

  12. 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

  13. 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:

  14. 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:

  15. 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:

  16. 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:

  17. 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:

  18. 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:

  19. Example: Modulation of a sinusoidal signalm(t) = cosωt

  20. Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated

  21. Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency

  22. AM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation

  23. AM PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation

  24. AM FM PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation frequency modulaion

  25. AM FM PM Example: Modulation of a sinusoidal signalm(t) = cosωt signal to be modulated carrier frequency amplitude modulation phase modulation frequency modulaion

  26. demodulation

  27. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t)

  28. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  29. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  30. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  31. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  32. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  33. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform :

  34. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform : Properties used:

  35. demodulation Demodulation = separation of main signalm(t)from the received modulated signalx(t) Spectrum of signalm(t) = Fourier transform : Properties used: Modulation theorem

  36. 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

  37. Double Band demodulation

  38. Double Band demodulation Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt

  39. Double Band demodulation Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter

  40. Double Band demodulation Modulation = multiplication of the signalm(t)with the carrier frequencycosωCt Demodulation= multiplication again with the carrier frequencycosωCt + low pass filter

  41. 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

  42. 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

  43. 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

  44. 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

  45. 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:

  46. Double Band demodulation

  47. |M(ω)| Double Band demodulation original signal

  48. |Χ(ω)| -ωC ωC |M(ω)| Double Band demodulation original signal MODULATION modulated signal

  49. |Χ(ω)| -ωC ωC |M(ω)| Double Band demodulation original signal MODULATION TRANSMISSION - RECEPTION modulated signal

  50. |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

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