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EE354 : Communications System I

EE354 : Communications System I. Lecture 13,14: Modulation Bandpass signals Aliazam Abbasfar. Outline. Modulation Bandpass signals Bandpass processes. Modulation. Message signal m(t) modulates a carrier signal x c (t) Convert lowpass message to bandpass signal

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EE354 : Communications System I

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  1. EE354 : Communications System I Lecture 13,14: Modulation Bandpass signals Aliazam Abbasfar

  2. Outline • Modulation • Bandpass signals • Bandpass processes

  3. Modulation • Message signal m(t) modulates a carrier signal xc(t) • Convert lowpass message to bandpass signal • Sinusoid carrier : xc(t) = Accos( wct + fc) • Ac : carrier amplitude • fc /fc: carrier frequency/phase • AM/FM/PM • ASK/FSK/PSK • Pulse carrier : • PAM/PWM/PPM • Linear/Non-linear modulations

  4. Why modulation ? • Sending messages in passband channels • Allocated spectrum • Better channel characteristics • Design convenience • Transmission of several messages simultaneously • Frequency division multiplexing (FDM)

  5. Bandpass signals

  6. Bandpass signals (2) • Equivalent lowpass signal • vI(t) and vQ(t) are real, lowpass signals

  7. Hilbert transform • One-sided spectrum • Hilbert transform • H(f) = -j sgn(f)  h(t) = 1/pt • Quadrature filter: 90 phase shifter • Lowpass signal

  8. Bandpass transmission • Equivalent lowpass channel • If Xlp(f) is band limited • Narrowband/Wideband systems (B/fc)

  9. Modulation/Demodulation • Transmitter (modulator) • message signals are constructed as lowpass signals • Modulators generate bandpass signals • Receiver (demodulator) • bandpass received signals are demodulated to produce lowpass signals • Lowpass signals are processed to get messages • Lowpass to bandpass • Amplitude  Envelope • Constant phase  Carrier phase • Linear phase  Carrier frequency offset • Delay  Envelope(group) delay • Baseband transmission • fc = 0 (No modulation) • Lowpass signal = real

  10. Bandpass process • X(t) is bandpass if GX(f)= 0 for |f-fc|>W • The modulated signal • The filtered noise • Generalize bandpass signals • If X(t) is zero-mean stationary process, XI(t) and XQ(t) are zero-mean and jointly stationary • GXi(f)= GXq(f)= GX(f-fc) + GX(f+fc) |f|<fc • = 0 |f|>fc • XI(t0) and XQ(t0) are uncorrelated • Envelope and phase processes

  11. Bandpass WGN process • n(t) = nI(t) cos(wct) – nQ(t) sin(wct) • Bandwidth 2W • nI(t) and nQ(t) are independent and jointly Gaussian • A(t) : Rayleigh distributed • Q(t) : uniform distributed • If fc is in the middle of the band • Gni(f)= Gnq(f)= N0 |f|<W • nI and nQ are independent • If fc is on either end of the band • Gni(f)= Gnq(f)= N0/2 |f|<2W • Pni = Pnq = Pn = 2 N0 W • (nI +j nQ )= CN(0,4N0W)

  12. Reading • Carlson Ch. 4.1 and 3.6 • Proakis 2.5, 3.1, 3.2

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