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EE104: Lecture 18 Outline

EE104: Lecture 18 Outline. Announcements: Lecture Friday goes from 12:50-2:05 Review of Last Lecture White Noise Introduction to Modulation AM Modulation Generation of AM Waves Detection of AM Waves. Review of Last Lecture. Autocorrelation of Power Signals

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EE104: Lecture 18 Outline

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  1. EE104: Lecture 18 Outline • Announcements: • Lecture Friday goes from 12:50-2:05 • Review of Last Lecture • White Noise • Introduction to Modulation • AM Modulation • Generation of AM Waves • Detection of AM Waves

  2. Review of Last Lecture • Autocorrelation of Power Signals • PSD and Autocorrelation of periodic signals • PSD is discrete • Autocorrelation is peroidic • Definition of Random Signals • A signal picked at random from deterministic signal set • PSD and Autocorrelation of Random Signals • Averages of PSD and autocorrelation over deterministic set • PSD and autorcorrelation typically measured in practice • Filtering and Modulating Random Signals

  3. Filtering and Modulation of Random Signals • Same PSD effect as for deterministic signals • Filtering: • Modulation: For q uniform [0,2p] • No bandwidth restriction on Sn(f) |H(f)|2Sn(f) Sn(f) H(f) cos(2pfct+q) Sn(f) .25[Sn(f-fc)+ Sn(f-fc)] X

  4. White Noise Sn(f) Rn(t) .5N0d(t) • Signal changes very fast • Uncorrelated after infinitesimally small delay • Good approximation in practice • Filtering white noise: introduces correlation .5N0 f t Sw(f)=.5N0 .5N0|H(f)|2 H(f)

  5. Introduction to Modulation • Basic concept is to vary carrier signal relative to information signal or bits • Analog modulation varies amplitude (AM), frequency (FM), or phase (PM) of carrier • Digital modulation varies amplitude (MAM), phase (PSK), pulse (PAM), or amplitude/phase (QAM)

  6. Amplitude Modulation cos(2pfct) • Constant added to signal m(t) • Simplifies demodulation if 1>|kam(t)| • Demodulate based on envelope Ac|1+kam(t)| • Constant is wasteful of power • Modulated signal has twice bandwidth of m(t) ka s(t)=Ac[1+kam(t)]cos2pfct 1 m(t) + X X

  7. Generation of AM Waves • Multipliers difficult to build in HW • AM waves generated using nonlinear device Accos(2pfct+f) m(t) s(t) Squarer or Switch + BPF

  8. Detection of AM Waves • Entails tradeoff between performance and complexity (cost) • Square law detector squares signal and then passes it through a LPF • Residual distortion proportional to m2(t) • Noncoherent (carrier phase not needed in receiver) • Envelope detector detects envelope of s(t) • Simple circuit (resistors, capacitor, diode) • Only works when |kam(t)|<1 (poor SNR), no distortion. • Noncoherent

  9. Main Points • White noise is a good approximation for random noise signals. • Modulation is the process of encoding a message signal or bits into a carrier signal • AM modulation modulates amplitude of carrier with m(t) • A constant term is added to message signal to simplify demodulation: wasteful of power and hurts SNR • AM waves typically generated using nonlinear devices • AM waves demodulated using nonlinear devices (some distortion) or envelope detectors (simple & good performance)

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