Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Lecture 6: Signals Transmission Signals and Spectral Methods in Geoinformatics

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics modulation Modulation = placement of signal m(t) on a monochromatic signal x C (t) = a C cos(φ 0C +ω C t) with carrier frequency ω C Α. Amplitude modulation (general form) : Β. Angle modulation (general form) : Α. AM = Amplitude Modulation : Β. Angle modulation Β1. PM = Phase Modulation : Β2. FM = Frequency Modulation : m(t)m(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Example: Modulation of a sinusoidal signal m(t) = cosωt

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics signal to be modulated Example: Modulation of a sinusoidal signal m(t) = cosωt

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics signal to be modulated carrier frequency Example: Modulation of a sinusoidal signal m(t) = cosωt

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics signal to be modulated carrier frequency amplitude modulation Example: Modulation of a sinusoidal signal m(t) = cosωt AM

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics signal to be modulated carrier frequency amplitude modulation phase modulation Example: Modulation of a sinusoidal signal m(t) = cosωt AM PM

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 AM PM FM

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 AM PM FM

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics demodulation Demodulation = separation of main signal m(t) from the received modulated signal x(t)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 : Properties used :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 : Properties used : Modulation theorem

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals 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 : Properties used : Modulation theorem from which follows

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t ω  ω  ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t ω  ω+ω C ω  ω  ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t ω  ω+ω C ω  ω  ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t ω  ω+ω C ω  ω  ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation Demodulation = multiplication again with the carrier frequency cosω C t + low pass filter Modulation = multiplication of the signal m(t) with the carrier frequency cosω C t After the low pass filter remains : ω  ω+ω C ω  ω  ω C

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal | M(ω) | Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal modulated signal MODULATION | M(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal modulated signal TRANSMISSION - RECEPTION MODULATION | M(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal modulated signal TRANSMISSION - RECEPTION MODULATION DEMODULATION Multiplication with carrier frequency | M(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal modulated signal TRANSMISSION - RECEPTION MODULATION DEMODULATION Multiplication with carrier frequency Application of low pass filter | H(ω) | | M(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics original signal modulated signal TRANSMISSION - RECEPTION MODULATION DEMODULATION Multiplication with carrier frequency Application of low pass filter | H(ω) | ½ | M(ω) | | M(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | M(ω) | Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter | M(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter modulated signal | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC ωCωC ωCωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter Demodulation =multiplication with cosω C t + low pass filter modulated signal | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter Demodulation =multiplication with cosω C t + low pass filter modulated signal | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Modulation =multiplication with cosω C t + high pass filter Demodulation =multiplication with cosω C t + low pass filter modulated signal demodulated signal | M(ω) | ¼| M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC Double Band demodulation - preservation of outer parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Double Band demodulation - preservation of inner parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | M(ω) | Double Band demodulation - preservation of inner parts

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | M(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | H(ω) | | M(ω) | | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | H(ω) | | M(ω) | | Χ(ω) | ωCωC ωCωC ωCωC ωCωC Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter modulated signal

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | H(ω) | | M(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter Demodulation =multiplication with cosω C t + high pass filter modulated signal

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | H(ω) | | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC | Χ(ω) | ωCωC ωCωC Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter Demodulation =multiplication with cosω C t + high pass filter modulated signal

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics | H(ω) | | M(ω) | | H(ω) | | Χ(ω) | ωCωC ωCωC | D(ω) | 2ωC2ωC 2ωC2ωC | Χ(ω) | ωCωC ωCωC ¼| M(ω) | Double Band demodulation - preservation of inner parts Modulation =multiplication with cosω C t + low pass filter Demodulation =multiplication with cosω C t + high pass filter modulated signal demodulated signal

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) | M(ω) | ωmωm ωmωm

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) | M(ω) | ωmωm ωmωm

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) ωCωC ωCωC | Χ(ω) || M(ω) | ωmωm ωmωm

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) ωCωC ωCωC | Χ(ω) || M(ω) | ωmωm ωmωm ω C  ω m ωC ωmωC ωm ω C  ω m ωC ωmωC ωm

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) THEREFORE:Possibility of simultaneous moduletion of more signals as long as there spectra do not overlap ! Separation with band pass filters + (usual) demodulation

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) THEREFORE:Possibility of simultaneous moduletion of more signals as long as there spectra do not overlap ! Separation with band pass filters + (usual) demodulation Signals to be transmitted :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) THEREFORE:Possibility of simultaneous moduletion of more signals as long as there spectra do not overlap ! Separation with band pass filters + (usual) demodulation Signals to be transmitted : Corresponding carrier frequencyes :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) THEREFORE:Possibility of simultaneous moduletion of more signals as long as there spectra do not overlap ! Separation with band pass filters + (usual) demodulation Signals to be transmitted : Corresponding carrier frequencyes : Modulated signals :

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing band limited signals : (spectrum concentrated in a band 2ω m wide centered at zero) Modulation : για και (spectrum concentrated in two bands 2ω m wide centered at – ω C and ω C ) THEREFORE:Possibility of simultaneous moduletion of more signals as 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

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics ~ ~ ~ multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~  multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~   multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~   multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~   BPF = Band Pass Filter (inside band) multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~   BPF = Band Pass Filter (inside band) multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics   ~ ~ ~   multiplexing

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics BPF Application of band pass filter (BPF, inside band) = = preservation of a single term : multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics  ~ BPF  ~ ~  LPFBPF LPF Application of band pass filter (BPF, inside band) = = preservation of a single term : Usual demodulation = = [  cosω i ] + [ LPF ] = = retrieval of signal m k (t) multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics  ~ BPF  ~ ~  LPFBPF LPF BPF = Band Pass Filter, inside band LPF = Low Pass Filter Application of band pass filter (BPF, inside band) = = preservation of a single term : Usual demodulation = = [  cosω i ] + [ LPF ] = = retrieval of signal m k (t) multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics  ~ BPF  ~ ~  LPFBPF LPF BPF = Band Pass Filter, inside band LPF = Low Pass Filter Application of band pass filter (BPF, inside band) = = preservation of a single term : Usual demodulation = = [  cosω i ] + [ LPF ] = = retrieval of signal m k (t) multiplexing – mathematical description

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Με Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics signal of frequency f (angular ω ) with amplitude which varies periodicallywith frequency Δf angular Δω ) heterodyning Με Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Με Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f ) signal of frequency f (angular ω ) with amplitude which varies periodically with frequency Δf angular Δω )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Με Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f ) signal of frequency f (angular ω ) with amplitude which varies periodically with frequency Δf angular Δω )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Με Δf = f  f R (angular Δω = ω  ω R ) = beat frequency Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f ) signal of frequency f (angular ω ) with amplitude which varies periodically with frequency Δf angular Δω )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics heterodyning Με signal of frequency f (angular ω ) with amplitude which varies periodically with frequency Δf angular Δω ) Δf = f  f R (angular Δω = ω  ω R ) = beat frequency Application:observations in space geodesy utilizing the Doppler phaenomenon (variation of frequency caused by the variation of the receiver-transmitter relative position) Heterodyning =Mixing (sum) of received signal having frequency f, with a signal of slightly different frequency f R produced in the receiver ( f R  f )

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics Beat frequency : Δf = f – f R = 1 – 5/6 = 1/6 (T Δf = 6) T = 1f = 1 T R = 6/5f R = 5/6 Δf = f  f R = 1/6 T Δf = 6 Example : Received frequency : f = 1 (T = 1) Frequency at receiver : f R = 5/6 (T = 6/5)

Aristotle University of Thessaloniki – Department of Geodesy and Surveying A. DermanisSignals and Spectral Methods in Geoinformatics A. Dermanis Signals and Spectral Methods in Geoinformatics END