1 / 8

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

zhen
Télécharger la présentation

EE104: Lecture 16 Outline

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related