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EE104: Lecture 16 Outline

EE104: Lecture 16 Outline. Announcements: Homework due Friday No lecture Monday 2/24 Lectures on 2/26 and 2/28 go from 12:50-2:05 Midterm Grade Distribution Autocorrelation of Energy Signals Power Spectral Density Autocorrelation of Power Signals Random Signals

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EE104: Lecture 16 Outline

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  1. EE104: Lecture 16 Outline • Announcements: • Homework due Friday • No lecture Monday 2/24 • Lectures on 2/26 and 2/28 go from 12:50-2:05 • Midterm Grade Distribution • Autocorrelation of Energy Signals • Power Spectral Density • Autocorrelation of Power Signals • Random Signals • PSD and Autocorrelation of Random Signals

  2. Midterm Grade Distribution 97+: A+ 85-95: A 75-84: B Average: 82.7 STD: 13

  3. x(f)=|X(f)|2 f Review of Last Lecture • Distortion • Distortionless transmission introduces scaling and delay • Equalizer removes channel distortion, can enhance noise • Ideal lowpass and bandpass filters introduce no distortion within the bandwidth of interest. • Energy Spectral Density: energy distribution over f. • Useful for filter analysis |H(f)|2x(f) x(f) H(f)

  4. Autocorrelation (Energy Signals) • Defined for real signals as Rx(t)=x(t)*x(-t) • Measures signal self-similarity at t • Useful for synchronization: |Rx(t)| Rx(0) • ESD and autocorrelation FT pairs: Rx(t) x(f) Rx(t) t 0

  5. Power Spectral Density • Similar to ESD but for power signals (P=E/t) • Distribution of signal power over frequency • Useful for filter and modulation analysis Sx(f) f cos(2pfct) |H(f)|2Sx(f) Sx(f) Sx(f) .25[Sx(f-fc)+ Sx(f+fc)] H(f) X For Sx(f) bandlimited [–B,B], B<<fc

  6. Autocorrelation(Power Signals) • Defined for real signals as • Useful for synchronization: |Rx(t)| Rx(0) • PSD and autocorrelation FT pairs: Rx(t) Sx(f) Rx(t) t 0

  7. Random Signals • Not deterministic (no Fourier transform) • Signal contained in some set of possible realizations • Characterize by average PSD Sn(f) • Autocorrelation Rn(t) Sn(f) is the correlation of the random signal after time t. • Measures how fast random signal changes Experiment

  8. Main Points • Autocorrelation of energy signals used for synchronization • Power signals often don’t have FTs: characterized with PSD and autocorrelation, which are FT pairs. • Can determine the impact of filtering and modulation on PSD • Random signals also characterized by PSD and autocorrelation

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